what mass of iron(iii) oxide is produced from excess iron metal and 6.8 l of oxygen gas at 102.5°c and 871 torr? 4 fe (s) 3 o2 (g) → 2 fe2o3 (s)

When granular polystyrene is placed in boiling water, it begins to soften and melt. As the temperature increases, the polystyrene molecules become more mobile and start to move around. If the melted polystyrene is then rapidly cooled, such as by pouring it into a mold or exposing it to cold air, the polystyrene solidifies in a cellular structure, forming a foam.

When granular polystyrene is heated, it softens and begins to melt. At high temperatures, it can decompose to form a mixture of styrene monomers and other byproducts. However, when the melted polystyrene is cooled rapidly, such as by pouring it into a mold or exposing it to cold air, it can solidify in a cellular structure, forming a foam.

Styrofoam is a brand name for a type of polystyrene foam that is made by suspending tiny beads of polystyrene in a liquid and then subjecting them to steam. The steam causes the beads to expand and fuse together, forming a foam with a low density and excellent thermal insulation properties.

In summary, the formation of Styrofoam from granular polystyrene when it is placed in boiling water is due to the melting of polystyrene followed by its rapid cooling, which results in the formation of a foam with a cellular structure.

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The final volume of the gas is 231 cm3.

To solve this problem, we can use the combined gas law, which relates the initial and final conditions of pressure, volume, and temperature. The combined gas law is given by the equation:

(P1 * V1) / (T1) = (P2 * V2) / (T2)

where P1 and P2 are the initial and final pressures, V1 and V2 are the initial and final volumes, and T1 and T2 are the initial and final temperatures.

Given:

P1 = 1.6 atm

V1 = 168 cm3

T1 = 255 K

P2 = 1.3 atm

T2 = 285 K

We need to find V2, the final volume of the gas.

Substituting the given values into the combined gas law equation, we get:

(1.6 atm * 168 cm3) / (255 K) = (1.3 atm * V2) / (285 K)

Simplifying the equation, we find:

V2 = (1.6 atm * 168 cm3 * 285 K) / (1.3 atm * 255 K)

V2 ≈ 231 cm3

Therefore, the final volume of the gas is approximately 231 cm3.

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The weight of child is 19.5 kg. The recommended low dose is 39 mg and high dose is 48.8 mg. The dose is safe which is 40 mg.

To calculate the weight of the child in kg

Weight in kg = 43 pounds / 2.205 pounds/kg = 19.5 kg (rounded to nearest tenth)

The recommended dose range for this child would be

Low dose: 2 mg/kg x 19.5 kg = 39 mg

High dose: 2.5 mg/kg x 19.5 kg = 48.8 mg

Round low dose to nearest tenth: 39 mg

Round high dose to nearest tenth: 48.8 mg

The ordered dose is 40 mg, which falls within the recommended range of 39-48.8 mg, so it is safe.

No further calculation is needed since the dosage ordered is safe.

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Faraday's constant is approximately equal to 96,485 coulombs/mol.
The reduction of one mole of Cr3+ to Cr requires the gain of three moles of electrons (Cr3+ + 3e- → Cr).

Therefore, the reduction of 0.20 mole of Cr3+ to Cr will require the gain of 0.60 moles of electrons (0.20 mol Cr3+ x 3 mol e-/mol Cr3+ = 0.60 mol e-).
Multiplying the number of moles of electrons by Faraday's constant gives us the total charge required:
0.60 mol e- x 96,485 C/mol = 57,891 C
Therefore, the answer is A) 0.60 C.So, the reduction of 0.20 mole of Cr3+ to Cr would require:0.20 moles of Cr3+ × 3 moles of e-/mol of Cr3+ = 0.60 moles of electrons One mole of electrons carries a charge of 96,485 Coulombs (C).

Therefore, 0.60 moles of electrons would carry a charge of: 0.60 moles of e- × 96,485 C/mol of e- = 58,091 C Therefore, the amount of charge required to cause the reduction of 0.20 mole of Cr3+ to Cr is approximately 58,091 Coulombs (C).

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To find the partial pressure of kr in the mixture, we need to use the mole fraction of kr in the mixture. The mole fraction of a gas component in a mixture is the number of moles of that gas divided by the total number of moles of all the gases in the mixture.

So, the total number of moles in the mixture is:

0.220 moles kr + 0.350 moles Cl2 + 0.640 moles He = 1.21 moles

•The mole fraction of kr is:

0.220 moles kr / 1.21 moles total = 0.182

•The mole fraction of Cl2 is:

0.350 moles Cl2 / 1.21 moles total = 0.289

•The mole fraction of He is:

0.640 moles He / 1.21 moles total = 0.529

Now, to find the partial pressure of kr, we need to multiply the total pressure of the mixture by the mole fraction of kr:

Partial pressure of kr = 2.95 atm x 0.182 = 0.5369 atm

Therefore, the partial pressure of kr in the mixture is 0.5369 atm.

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The chemical equation for the reaction between (NH4)2CrO4(aq) and BaCl2(aq) can be written as follows (NH4)2CrO4(aq) + BaCl2(aq) → BaCrO4(s) + 2 NH4Cl(aq).

This equation represents a double displacement reaction, where the ammonium chromate (NH4)2CrO4 reacts with barium chloride (BaCl2) to form barium chromate (BaCrO4) as a precipitate, and ammonium chloride (NH4Cl) remains in the solution.

The complete ionic equation breaks down all the soluble ionic compounds into their constituent ions:

2 NH4+(aq) + CrO42-(aq) + Ba2+(aq) + 2 Cl-(aq) → BaCrO4(s) + 2 NH4+(aq) + 2 Cl-(aq)

In the net ionic equation, spectator ions are removed as they do not participate in the actual chemical reaction:

CrO42-(aq) + Ba2+(aq) → BaCrO4(s)

In this net ionic equation, the spectator ions are NH4+ and Cl-. They appear on both sides of the equation and do not undergo any change during the reaction. They are present in the solution but do not contribute to the formation of the precipitate. The formation of the yellow precipitate of barium chromate (BaCrO4) indicates the completion of the reaction.

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The element that has four completely filled s sublevels and three d electrons is D. Ti, which is Titanium.

Its electron configuration is [Ar] 4s² 3d², meaning it has two electrons in the 4s sublevel and two electrons in the 3d sublevel.

The electron configuration of Chromium is [Ar] 4s² 3d⁴. Chromium has 24 electrons in total, with two electrons occupying the 4s orbital and the remaining ten electrons distributed among the five 3d orbitals.

The electronic configuration can be represented as follows:

1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d⁵

However, in the case of Chromium, it exhibits an interesting electron configuration anomaly due to its stability. One electron from the 4s sublevel is actually "promoted" or excited to the 3d sublevel, resulting in the configuration:

1s² 2s² 2p⁶ 3s² 3p⁶ 4s⁰ 3d⁵

This arrangement allows for the 3d sublevel to have a half-filled configuration, which is more stable than a configuration with only four electrons in the d sublevel.

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We need 0.1126 g of NH3 to provide the same number of molecules as in 0.55 g of SF6.

To calculate the number of molecules of SF6 in 0.55 g, we need to first determine the number of moles of SF6 present in that amount.

We can use the molecular weight of SF6 to convert from grams to moles:

1 mole of SF6 = 32.06 g + (6 × 18.998 g) = 146.06 g/mol

Number of moles of SF6 = 0.55 g / 146.06 g/mol = 0.00377 mol

Next, we can use Avogadro's number to calculate the number of molecules of SF6 in 0.55 g:

Number of molecules of SF6 = 0.00377 mol × 6.022 × 10^23 molecules/mol = 2.27 × 10^21 molecules

Since SF6 has 7 atoms per molecule, we can say that there are 7 times as many atoms as there are molecules in 0.55 g of SF6:

Number of atoms in 0.55 g of SF6 = 7 × 2.27 × 10^21 atoms = 1.589 × 10^22 atoms

Now we can determine the number of molecules of NH3 that would contain the same number of atoms as 0.55 g of SF6:

1 molecule of NH3 contains 4 atoms (1 nitrogen atom and 3 hydrogen atoms), so the number of molecules of NH3 we need is:

Number of NH3 molecules = 1.589 × 10^22 atoms / 4 atoms per molecule = 3.9725 × 10^21 molecules

Finally, we can calculate the mass of NH3 that contains this number of molecules by using the molecular weight of NH3:

1 mole of NH3 = 14.01 g + 3 × 1.01 g = 17.04 g/mol

Number of moles of NH3 = 3.9725 × 10^21 molecules / 6.022 × 10^23 molecules/mol = 0.00661 mol

Mass of NH3 = 0.00661 mol × 17.04 g/mol = 0.1126 g

Therefore, we need 0.1126 g of NH3 to provide the same number of molecules as in 0.55 g of SF6.

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Substance increases in temperature by 255°c when a 983g sampleof it absorbs 8300j of heat. the specific heat capacity of the substance is approximately 32.28 J/(kg·°C).

To determine the specific heat capacity of a substance, we can use the equation:

Q = mcΔT

Where Q is the heat absorbed, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.

In this case, the substance increases in temperature by 255°C when a 983g sample of it absorbs 8300J of heat. We can plug these values into the equation:

8300J = (983g) * c * 255°C

First, we need to convert the mass from grams to kilograms:

983g = 0.983kg

Now, we rearrange the equation to solve for the specific heat capacity, c:

C = (8300J) / (0.983kg * 255°C)

C ≈ 32.28 J/(kg·°C)

Therefore, the specific heat capacity of the substance is approximately 32.28 J/(kg·°C). This value represents the amount of heat energy required to raise the temperature of one kilogram of the substance by one degree Celsius.

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The density of the borosilicate glass is different from the weighted average of the densities of its components because the addition of different elements can change the packing efficiency of the atoms in the material.

In this case, the borosilicate glass contains a mixture of SiO₂, Al₂O₃, Na₂O, and B₂O₃. The different atomic sizes of these elements result in a non-uniform packing density, which leads to a higher overall density than would be expected from a simple weighted average. Additionally, the boron in B₂O₃ forms strong covalent bonds with the silicon atoms, which can also contribute to the higher density of the borosilicate glass compared to fused silica glass.

Borosilicate glass is a type of glass with silica and boron trioxide as the main glass-forming constituents. Borosilicate glasses are known for having very low coefficients of thermal expansion, making them more resistant to thermal shock than any other common glass. Fused quartz, fused silica or quartz glass is a glass consisting of almost pure silica in amorphous form. This differs from all other commercial glasses in which other ingredients are added which change the glasses optical and physical properties, such as lowering the melt temperature.

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Primary source documents that can confirm the use of buttonhooks in the medical inspection of immigrants include medical reports and journals, photographs, and immigration records.

To confirm the use of buttonhooks in the medical inspection of immigrants, one can refer to primary sources such as medical reports and journals from the early 20th century.

These documents may contain descriptions of the medical examinations performed on immigrants and the tools used during the process. Photographs taken during this time may also provide evidence of the use of buttonhooks or other medical instruments.

Additionally, immigration records from the time may contain information on the medical inspections conducted on immigrants, including details on the tools used.

By consulting a variety of primary source materials, researchers can gather evidence that supports the historical use of buttonhooks in the medical inspection of immigrants.

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Li F and NaCl have comparable electron configurations to [He] and [Ne] because they both have full valence electron shells with the same number of electrons as those noble gases.

a. Li F and NaCl b. MgO and CaCl2 c. He Ne+ and A r F- d. NeO2+ and ArF3

b. MgO and CaCl2 have comparable electron configurations to [Ne] and [Ne] because they both have full valence electron shells with the same number of electrons as that noble gas.

c. He Ne+ and A r F- have comparable electron configurations to [He] and [A r] because they both have full valence electron shells with one less or one more electron, respectively, than those noble gases.

d. NeO2+ and ArF3 have comparable electron configurations to [Ne] and [A r] because they both have full valence electron shells with one less or one more electron, respectively, than those noble gases.

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The given reaction can be represented as:2SO2(g) + O2(g) ⇌ 2SO3(g). The balanced chemical equation for the reaction can be represented as,2SO2(g) + O2(g) ⇌ 2SO3(g)It is an exothermic reaction because the enthalpy change (ΔH) is negative.

The formation of SO3(g) from SO2(g) and O2(g) releases heat.

The equilibrium constant (Kc) expression for the reaction is, Kc = [SO3]2 / [SO2]2 [O2]Let the initial moles of SO2, O2 and SO3 be ‘x’, ‘y’ and ‘0’ respectively.

At equilibrium, the moles of SO2 and O2 consumed will be ‘a’ and ‘b’ respectively.

So, the moles of SO3 formed will be 2a.

Let’s prepare the ICE table below,Reaction2SO2(g) + O2(g) ⇌ 2SO3(g)Initial (I)x y 0Change (C)- a - b + 2a.

Equilibrium (E)x - a y - b 2a.

On substituting the equilibrium values in the equilibrium constant expression, we get, Kc = (2a)2 / (x - a)2(y - b).

Thus, the value of Kc depends on the moles of SO2, O2 and SO3 present at equilibrium.

As given, PO2 = 0.21 atm, Ptotal = 1 atm.

Thus, PN2 = PO2=0.21 atm.

At equilibrium, for the given reaction to proceed in the forward direction, the value of Kc should be greater than the calculated value.

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There are approximately 0.97 moles of Neon gas.

To calculate the number of moles of Neon gas, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.

Given:

Pressure (P) = 89.9 KPa

Volume (V) = 25.0 Liters

Temperature (T) = 278K

Gas constant (R) = 8.314 J/(mol·K)

Rearranging the ideal gas law equation to solve for n, we have:

n = PV / RT

Substituting the given values into the equation, we get:

n = (89.9 KPa * 25.0 L) / (8.314 J/(mol·K) * 278K)

Performing the calculations, we find that the number of moles (n) is approximately 0.97 mol.

Therefore, the correct answer is option c) 0.97 mol.

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To prepare the following alcohols using Grignard reactions, you would perform the following steps:

1. 2-Methyl-2-propanol: React methylmagnesium bromide (Grignard reagent) with acetone.
2. 1-Methylcyclohexanol: React methylmagnesium bromide with cyclohexanone.
3. 3-Methyl-3-pentanol: React 2-bromo-3-methylpentane with magnesium, then add ethanal.
4. 2-Phenyl-2-butanol: React phenylmagnesium bromide with 2-butanone.
5. Benzyl alcohol: React phenylmagnesium bromide with formaldehyde.
6. 4-Methyl-1-pentanol: React 1-bromo-4-methylpentane with magnesium, then add methanal.

In each case, the Grignard reagent (alkyl or aryl magnesium halide) reacts with a carbonyl compound (aldehyde or ketone) to produce the desired alcohol.

The reaction proceeds through nucleophilic addition of the Grignard reagent to the carbonyl carbon, followed by protonation with a weak acid, like water or a saturated ammonium chloride solution, to yield the alcohol product.

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Answer: 0.75 L

Explanation:

First, calculate the number of moles of AgNO3 in 1.0 L of 0.20 M solution:

[tex]0.20 mol/L x 1.0 L = 0.20 mol[/tex]

Since the stoichiometric ratio of AgNO3 to CaCl2 is 2:1, we need 0.10 mol of CaCl2 to completely precipitate the Ag+ in the solution.

Next, we can use the molarity and the number of moles of CaCl2 to calculate the volume of 1.5 M CaCl2 needed:

[tex]0.10 mol / 1.5 mol/L = 0.067 L or 67 mL[/tex]

However, we are asked to round to two significant figures, so the final answer is 0.75 L.

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The preferred Lewis structure for the thiocyanate ion (NCS-) is [tex][C≡N-S]⁻[/tex].

The Lewis structures and formal charges for the thiocyanate ion[tex](NCS-)[/tex]. Here are the steps:

a) Adding lone pair electrons to each structure:

1. [tex][C≡N-S]⁻: C[/tex] has 2 lone pairs, N has 1 lone pair, and S has 2 lone pairs.
2. [tex][N=C=S]⁻: N[/tex] has 2 lone pairs, C has 3 lone pairs, and S has 2 lone pairs.
3. [tex][N-C≡S]⁻: N[/tex]has 3 lone pairs, C has 2 lone pairs, and S has 1 lone pair.

b) Determining the formal charges:

1. [tex][C≡N-S]⁻: C: 0, N: 0, S: -1[/tex]
2.[tex][N=C=S]⁻: N: -1, C: 0, S: 0[/tex]
3.[tex][N-C≡S]⁻: N: -1, C: 0, S: 0[/tex]

c) Deciding the preferred Lewis structure:

Considering the rules, Structure 1 is preferred because:
i) The sum of all formal charges equals -1, which is the charge on the ion.
ii) It has smaller or zero formal charges on individual atoms.
iii) The negative charge is on the more electronegative atom (Sulfur).

So, the preferred Lewis structure for the thiocyanate ion[tex](NCS-) is [C≡N-S]⁻.[/tex]

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12 hydrogens in the molecule[tex]C_9H_1_2NO[/tex] with 1 ring and 3 double bonds.

To determine how many hydrogens are in the molecule C9H?NO with 1 ring and 3 double bonds, follow these steps:

1. Calculate the number of hydrogen atoms required for a fully saturated molecule using the formula H = 2C + 2, where C is the number of carbon atoms. In this case, C = 9.
  H = 2(9) + 2 = 18 + 2 = 20

2. Subtract the hydrogen atoms corresponding to the presence of the ring and double bonds. Each double bond and ring removes 2 hydrogen atoms from the fully saturated molecule.
  Total removed hydrogens = 2(double bonds) + 2(rings) = 2(3) + 2(1) = 6 + 2 = 8

3. Calculate the actual number of hydrogen atoms in the molecule by subtracting the removed hydrogens from the fully saturated molecule.
  Actual hydrogens = H - Total removed hydrogens = 20 - 8 = 12

So, there are 12 hydrogens in the molecule[tex]C_9H_1_2NO[/tex] with 1 ring and 3 double bonds.

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The VSEPR theory geometry for XeF5- would be square pyramidal, with a bond angle of 90 degrees. The molecule is polar due to the asymmetrical distribution of the XeF5- molecule.

To draw the Lewis structure for each molecule, we need to first count the total number of valence electrons in each atom. Chlorine (Cl) has 7 valence electrons and Fluorine (F) has 7 valence electrons, and Xenon (Xe) has 8 valence electrons.
For the molecule ClF3, we have a total of 28 valence electrons. The Lewis structure would look like:

                   Cl
                  /  \
                F    F
                 \   /
                   Cl

The VSEPR theory geometry for ClF3 would be trigonal bipyramidal, with a bond angle of 120 degrees. The molecule is polar due to the asymmetrical distribution of the ClF3 molecule, which results in a dipole moment.
For the ClF4- molecule, we would add an extra electron to the total valence electrons to account for the negative charge, giving us a total of 32 valence electrons. The Lewis structure would look like:

                    Cl
                   / \
                 F   F
                |     |
                 F   F
                   \ /
                    Cl-

The VSEPR theory geometry for ClF4- would be square planar, with a bond angle of 90 degrees. The molecule is nonpolar due to the symmetrical distribution of the ClF4- molecule.
For the ClF2 molecule, we have a total of 20 valence electrons. The Lewis structure would look like:

                   Cl
                   |
                 F    F

The VSEPR theory geometry for ClF2 would be linear, with a bond angle of 180 degrees. The molecule is polar due to the asymmetrical distribution of the ClF2 molecule.
For the XeF5- molecule, we would add an extra electron to the total valence electrons to account for the negative charge, giving us a total of 42 valence electrons. The Lewis structure would look like:

                     F
                    / \
               F - Xe - F
                    \ /
                     F
                      -

The VSEPR theory geometry for XeF5- would be square pyramidal, with a bond angle of 90 degrees. The molecule is polar due to the asymmetrical distribution of the XeF5- molecule.

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Answer:If a substance is impure, the presence of impurities will lower the melting point of the substance and broaden its melting range. This occurs because the impurities disrupt the crystal lattice structure of the substance, making it more difficult for the molecules to pack together neatly and requiring less energy to break the intermolecular forces between them. As a result, the substance will melt at a lower temperature and over a broader range of temperatures. Therefore, a lower and broader melting point would indicate the presence of impurities in the sample.

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The products of base hydrolysis of an (b) ester depend on the strength of the base used. When a strong base, such as sodium hydroxide (NaOH), is used to hydrolyze an ester, the products are a carboxylate ion (from the ester) and an alcohol.

For example, the base hydrolysis of methyl acetate (CH₃COOCH₃) with NaOH produces sodium acetate (CH₃COO⁻Na⁺) and methanol (CH₃OH). However, if a weaker base such as water is used, the products are a carboxylic acid (from the ester) and an alcohol.

For instance, the base hydrolysis of methyl acetate with water produces acetic acid (CH₃COOH) and methanol. The hydrolysis of an ester by base is also called saponification, which is a process used in the production of soaps.

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To compute the number of moles of each compound in a closed container with 0.5 moles and a total pressure of 1.5 bar, given the equilibrium constant (K) of 800 for the gas phase reaction, we'll follow these steps:

1. Identify the balanced chemical equation for the reaction.

2. Write the equilibrium expression based on the balanced equation.

3. Set up the equilibrium table (ICE: Initial, Change, Equilibrium).

4. Solve for the unknown equilibrium concentrations.

Unfortunately, the chemical equation for the reaction is missing in your question.

Please provide the balanced chemical equation so that I can help you calculate the number of moles of each compound at equilibrium.

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Phenyl acetate hydrolyzes more rapidly than benzyl acetate, while methyl acetate hydrolyzes faster than phenyl acetate.

The rate at which esters hydrolyze depends on the stability of the intermediate formed during the reaction.

In the case of phenyl acetate and benzyl acetate, phenyl acetate hydrolyzes more rapidly because it forms a more stable intermediate. The phenoxide ion produced is stabilized through resonance with the phenyl ring.

Comparing methyl acetate and phenyl acetate, methyl acetate hydrolyzes faster because the methyl group is less bulky, resulting in a more accessible carbonyl carbon for nucleophilic attack, which leads to a faster hydrolysis reaction.

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Benzyl acetate hydrolyzes more rapidly than phenyl acetate, and methyl acetate hydrolyzes more rapidly than phenylacetate. the correct answer is (a) benzyl acetate and (b) methyl acetate.

The rate of hydrolysis of an ester depends on several factors, including the size of the alkyl group attached to the carbonyl carbon and the electron density around the carbonyl group. In general, esters with larger alkyl groups attached to the carbonyl carbon undergo hydrolysis more slowly than those with smaller alkyl groups. This is because larger alkyl groups hinder the approach of water molecules to the carbonyl carbon, thus reducing the rate of hydrolysis.  Comparing the given options, benzyl acetate has a larger alkyl group than phenyl acetate, so it undergoes hydrolysis more rapidly. Similarly, methyl acetate has a smaller alkyl group than phenyl acetate, so it undergoes hydrolysis more rapidly. Therefore, the correct answer is (a) benzyl acetate and (b) methyl acetate.

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Main answer:

The length of the steel rail segment on a hot Utah day at 104 °F would be 25.047 m.

Supporting answer:

The coefficient of linear thermal expansion of steel is approximately 1.2 x 10^-5 /°C. To convert from Fahrenheit to Celsius, we can use the formula:

C = (F - 32) * 5/9

Using this formula, we can convert the initial temperature of 68.0 °F to Celsius:

C1 = (68.0 - 32) * 5/9 = 20.0 °C

Likewise, we can convert the final temperature of 104 °F to Celsius:

C2 = (104 - 32) * 5/9 = 40.0 °C

The change in temperature is therefore:

ΔT = C2 - C1 = 20.0 °C

The change in length of the steel rail segment is given by:

ΔL = αLΔT

where α is the coefficient of linear thermal expansion, L is the original length of the rail segment, and ΔT is the change in temperature.

Plugging in the given values, we get:

ΔL = (1.2 x 10^-5 /°C) * (25.000 m) * (20.0 °C) = 0.006 m

Therefore, the final length of the steel rail segment on a hot Utah day at 104 °F would be:

L2 = L1 + ΔL = 25.000 m + 0.006 m = 25.047 m

It's important to note that thermal expansion is an important phenomenon in many fields of engineering, including civil, mechanical, and aerospace engineering.

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Lowering the[tex]Cu_2^+[/tex]concentration causes the cell voltage to decrease from 0.78 V to 0.75 V.

The cell notation represents a redox reaction where copper metal (Cu) is oxidized to [tex]Cu_2^+[/tex] ions, and iron(III) ions ([tex]Fe_3^+[/tex]) are reduced to iron(II) ions ([tex]Fe_2^+[/tex]):

Cu | [tex]Cu_2^+[/tex] (aq, 1.6 M) || [tex]Fe_3^+[/tex](aq, 2.5 mM), [tex]Fe_2^+[/tex](aq, 1.5 M) | Pt

The double vertical line (||) represents a phase boundary between the two half-cells, and the comma separates the species in the same solution.

To determine the effect of lowering the [tex]Cu_2^+[/tex] concentration on the cell voltage, we need to consider the Nernst equation:

E = E° - (RT/nF) * ln(Q)

where E is the cell potential, E° is the standard cell potential, R is the gas constant, T is the temperature, n is the number of electrons transferred in the reaction, F is the Faraday constant, and Q is the reaction quotient.

At standard conditions (25°C, 1 atm, 1 M concentration), the standard cell potential can be found in a table of standard reduction potentials. Using the values for [tex]Cu_2^+[/tex]/Cu and [tex]Fe_3^+[/tex]/[tex]Fe_2^+[/tex], we have:

E°cell = E°cathode - E°anode = 0.34 V - (-0.44 V) = 0.78 V

Now, let's consider what happens when the [tex]Cu_2^+[/tex] concentration is lowered. This means that the reaction quotient Q will change, and the cell potential will change accordingly.

Specifically, decreasing the[tex]Cu_2^+[/tex]concentration will cause Q to decrease, which will result in a more negative value for ln(Q) and a corresponding increase in the cell potential.

The reaction quotient Q can be written as:

Q = [[tex]Fe_2^+[/tex]]/[[tex]Cu_2^+[/tex]] = (1.5 M)/(1.6 M) = 0.94

Substituting the given values and the new value of Q into the Nernst equation, we get:

E = 0.78 V - (0.0257 V) * ln(0.94) = 0.75 V

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The rate constant (k) for the reaction at 66.0 °C, with an activation energy (Ea) of 89.4 kJ/mol and a frequency factor (A) of 9.49 × [tex]10^1^1[/tex] [tex]s^−^1[/tex], can be calculated using the Arrhenius equation.

1: Recall the Arrhenius equation, which relates the rate constant (k), activation energy (Ea), temperature (T), and the frequency factor (A):

   k = A * exp(-Ea / (R * T))

2: Convert the activation energy from kilojoules per mole (kJ/mol) to joules per mole (J/mol):

   Ea = 89.4 kJ/mol * 1000 J/kJ = 89400 J/mol

3: Convert the temperature from degrees Celsius (°C) to Kelvin (K):

   T = 66.0 °C + 273.15 = 339.15 K

4: Plug in the values into the Arrhenius equation and calculate the rate constant:

   k = (9.49 × [tex]10^1^1 s^-^1[/tex]) * exp(-89400 J/mol / (8.314 J/(mol·K) * 339.15 K))

5: Perform the exponent calculation:

   k = (9.49 ×) * exp(-89400 J/mol / (8.314 J/(mol·K) * 339.15 K))

     ≈ (9.49 ×[tex]10^1^1 s^-^1[/tex]) * exp(-89400 J/mol / (8.314 J/(mol·K) * 339.15 K))

6: Calculate the rate constant (k) using the exponential function:

   k ≈ (9.49 × [tex]10^1^1 s^-^1[/tex]) * exp(-89400 J/mol / (8.314 J/(mol·K) * 339.15 K))

7: Perform the final calculation to obtain the rate constant (k).

Note: The final answer will depend on the specific values of the exponential function in Step 6.[tex]10^1^1 s^-^1[/tex]

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The Arrhenius equation can be used to determine the rate constant (k) for the reaction at 66.0 °C with an activation energy (Ea) of 89.4 kJ/mol and a frequency factor (A) of 9.49.

1: Recall the relationship between the temperature (T), the frequency factor (A), the activation energy (Ea), and the rate constant (k) in the Arrhenius equation:

  A = * exp (-Ea / (R * T))

2. Convert kilojoules per mole (kJ/mol) activation energy to joules per mole (J/mol):

  Ea = 1000 J/kJ x 89.4 kJ/mol, or 89400 J/mol.

3: Calculate the temperature in Kelvin (K) rather than degrees Celsius (°C):

  T = 66.0 °C + 273.15 = 339.15 K

4: Calculate the rate constant by plugging the numbers into the Arrhenius equation:

  k is equal to (9.49 ) * exp(-89400 J/mol / (8.314 J/(molK) * 339.15 K))

Five: Calculate the exponent:

k is equal to (9.49 ) * exp(-89400 J/mol / (8.314 J/(molK) * 339.15 K))

    (9.49 * exp (-89400 J/mol / 8.314 J/mol (mol K) * 339.15 K))

6. Use the exponential function to determine the rate constant (k):

  9.49 * exp (-89400 J/mol / 8.314 J/(molK) * 339.15 K) = k

To get the rate constant (k), perform the last computation.

Note: The precise values of the exponential function used in Step 6 will determine the final result.

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The time taken for the decay rate to fall to 2.5×10³, given that the sample has a half-life of 1.83 hours is

We'll begin by obtaining the number of half lives that has passed during the decay. Details below

2ⁿ = A₀ / A

2ⁿ = 1.5×10⁵ / 2.5×10³

2ⁿ = 60

Take the log of both sides

Log 2ⁿ = log 60

nLog2 = log 60

Divide both sides by log 2

n = log 60 / log 2

n = 5.907

Finally, we shall determine the time taken. Details below

n = t / t½

5.907 = t / 1.83

Cross multiply

t = 5.907 × 1.83

t = 10.81 hours

Thus, the time taken is 10.81 hours

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The change in heat for the given reaction is approximately is -946 kJ/mol.

The change in heat for the reaction of methane (CH4) with fluorine (F2) to form tetrafluoromethane (CF4) and hydrogen gas (H2) can be calculated using the given average bond dissociation energies (D).

ΔH = [(bonds broken) - (bonds formed)] x D

For this reaction, the bonds broken are:
1 C-H bond in CH4, 2 F-F bonds in F2, with respective D values of 410 kJ/mol, and 158 kJ/mol.

The bonds formed are:
4 C-F bonds in CF4, 2 H-H bonds in H2, with respective D values of 450 kJ/mol, and 436 kJ/mol.

Now, let's calculate the ΔH:
ΔH = [(1 x 410) + (2 x 158) - (4 x 450) - (2 x 436)] kJ/mol
ΔH = [410 + 316 - 1800 - 872] kJ/mol
ΔH = -946 kJ/mol

Thus, the change in heat for the given reaction is approximately -946 kJ/mol.

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For a chemical reaction to be considered for use in a fuel cell, it is absolutely essential for the free-energy change to be negative.

This is because a negative free-energy change indicates that the reaction is exothermic and releases energy, which is necessary to generate electricity in a fuel cell. The physical state of the reactants (whether they are solids, liquids, or gases) is not as important as the free-energy change.

For a chemical reaction to be considered for use in a fuel cell, it is absolutely essential for the free-energy change to be negative. A negative free-energy change indicates that the reaction is spontaneous and can release energy, which is required for fuel cells to generate electricity. The reactants in a fuel cell can be in different states, such as solids, liquids, or gases, but the key factor is the negative free-energy change.

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The specific heat of the turpentine is 0.254 cal/g·C.

The specific heat of a substance is the amount of heat required to raise the temperature of one gram of the substance by one degree Celsius. In this problem, we are given the mass and specific heat of a copper cylinder and the initial and final temperatures of a mixture of the copper cylinder and turpentine. We are asked to find the specific heat of the turpentine.

To solve the problem, we can use the formula for heat transfer:

Q = mcΔT

where Q is the heat transferred, m is the mass of the substance, c is the specific heat, and ΔT is the change in temperature.

We can use this formula to calculate the heat transferred from the copper cylinder to the turpentine:

Q(copper) = mc(copper)ΔT(copper) = (76.8 g)(0.092 cal/g·C)(86.5 C - 31.9 C) = 329.9 cal

Assuming no heat is lost to the surroundings, the heat transferred from the copper cylinder is equal to the heat transferred to the turpentine:

Q(turpentine) = mx(turpentine)ΔT(turpentine)

Solving for cturpentine, we get:

c(turpentine) = Q(turpentine) / (mx(turpentine)ΔT(turpentine))

Substituting in the known values and solving, we get:

c(turpentine) = 329.9 cal / (68.7 g)(31.9 C - 19.5 C) = 0.254 cal/g·C

Therefore, the specific heat of turpentine is 0.254 cal/g·C.

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