B. Answer the question.
How is living in space different from living on Earth?

The temperature of the oxygen gas sample is 609 K, which is approximately 336°C or 637°F. The answer is A.

We can use the ideal gas law equation, PV = nRT, to solve for the temperature of the oxygen gas sample.

First, we need to calculate the number of moles of oxygen gas present in the sample using its mass and molar mass:

n = m/M

where:

n = number of moles

m = mass (in grams)

M = molar mass (in g/mol)

The molar mass of oxygen gas (O2) is 32.00 g/mol.

n = 48 g / 32.00 g/mol = 1.50 mol

Next, we can rearrange the ideal gas law equation to solve for temperature (T):

T = (PV) / (nR)

where:

T = temperature (in Kelvin)

P = pressure (in atm)

V = volume (in liters)

n = number of moles

R = gas constant (0.0821 L atm/mol K)

Plugging in the given values, we get:

T = (3.0 atm x 25 L) / (1.50 mol x 0.0821 L atm/mol K)

T = 609 K

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The number that is the same as the exponentiation given as follows: 2.5 × 10-³ is 0.0025.

Exponentiation is the process of calculating a power by multiplying together a number of equal factors, where the exponent specifies the number of factors to multiply.

For example, if 10 is multiplied three times, then it can be written as "10 raised to 3" which means 10³. In this case, 10 is the base, and 3 is the exponent.

Therefore, a number 0.0025 can be written in exponentiation as 2.5 × 10-³ by counting the number of zeros forward.

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Considering the definition of pH, the pH is 6.35 and the solution is acidic.

pH is the Hydrogen Potential and it is a measure of acidity or alkalinity. pH indicates the amount of hydrogen ions present in a solution or substance.

Mathematically, pH is calculated as the negative base 10 logarithm of the activity of hydrogen ions:

pH= - log [H⁺]

The numerical scale that measures the pH of substances includes the numbers from 0 to 14. The pH value 7 corresponds to neutral substances. Acidic substances are those with a pH lower than 7, while basic substances have a pH higher than 7.

In this case, being [H⁺]=4.5×10⁻⁷ M, you can replace this value in the definition of pH:

pH= -log (4.5×10⁻⁷ M)

Solving:

pH= 6.35

Finally, the pH is lower than 7, the solution is acidic.

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The energy associated with the formation of 2.55 g of 4He by the fusion of 3H and 1H is -2.982 x 10⁻¹⁰ J.

The given masses of the isotopes can be converted to kilograms using the conversion factor: 1 u = 1.661 x 10⁻²⁷ kg.

Mass of 4He = 2.55 g = 2.55 x 10⁻³ kg

Mass of 3H = 3.01605 u = 3.01605 x 1.661 x 10⁻²⁷ kg/u

= 5.0099 x 10⁻²⁷ kg

Mass of 1H = 1.00783 u = 1.00783 x 1.661 x 10⁻²⁷ kg/u

= 1.6737 x 10⁻²⁷ kg

The balanced equation for the fusion reaction is;

3H + 1H → 4He

The molar mass of 4He is 4.0026 g/mol, which can be converted to kg/mol using the conversion factor: 1 g/mol = 1 x 10⁻³ kg/mol.

Molar mass of 4He = 4.0026 g/mol = 4.0026 x 10⁻³ kg/mol

The number of moles of 4He formed can be calculated from its mass;

n(4He) = m(4He) / M(4He)

= 2.55 x 10⁻³ kg / 4.0026 x 10⁻³ kg/mol

= 0.638 mol

From the balanced equation, 3 moles of H atoms react with 1 mole of He atoms to form 1 mole of He atoms. Therefore, the number of moles of H atoms required for the reaction is;

n(H) = 3/4 x n(4He)

= 3/4 x 0.638 mol

= 0.479 mol

The energy released in the reaction can be calculated using the mass-energy equivalence equation;

E = Δm c²

where Δm is change in mass, c is the speed of light.

The change in mass is;

Δm = [3H + 1H - 4He] = [5.0099 x 10⁻²⁷ kg + 1.6737 x 10⁻²⁷kg - 4.0026 x 10⁻³ kg]

= -3.315 x 10⁻²⁷ kg (negative because mass is lost in the reaction)

The energy released is;

E = (-3.315 x 10⁻²⁷ kg) c²

= (-3.315 x 10⁻²⁷ kg) (2.998 x 10⁸ m/s)²

= -2.982 x 10⁻¹⁰ J

The negative sign indicates that energy is released in the reaction (exothermic reaction).

Therefore, the energy associated is -2.982 x 10⁻¹⁰ J.

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