2.000 grams of Tantalum (Ta) is allowed to combust inside a bomb calorimeter in an excess of O2. The temperature inside changes from 32.00 °C to 39.15 °C.

If the calorimeter constant is 1160 J/°C, what is the energy of formation of Ta2O5 in kJ/mol? (remember, it could be positive or negative).

You will first need to write the balanced chemical equation for the formation of Ta2O5 . Tantalum is stable in the solid state at 25 °C and 1.00 atm of pressure.

The energy of formation of [tex]Ta_2O_5[/tex] is -1198.47 kJ/mol.

2 Ta + 5 [tex]O_2[/tex] → 2 [tex]Ta_2O_5[/tex]

1. Write the balanced chemical equation for the formation of [tex]Ta_2O_5[/tex]:

  2 Ta + 5 [tex]O_2[/tex] → 2 [tex]Ta_2O_5[/tex]

2. Calculate the change in temperature (ΔT):

  ΔT = final temperature - initial temperature

  ΔT = 39.15 °C - 32.00 °C

  ΔT = 7.15 °C

3. Convert the mass of Tantalum (Ta) to moles:

  The molar mass of Tantalum (Ta) is 180.95 g/mol.

  Moles of Ta = mass of Ta / molar mass of Ta

  Moles of Ta = 2.000 g / 180.95 g/mol

  Moles of Ta = 0.0110 mol

4. Calculate the energy change (ΔE) using the formula:

  ΔE = q - CΔT

  Where q is the heat absorbed or released, C is the calorimeter constant, and ΔT is the change in temperature.

5. Substitute the values into the formula:

  ΔE = q - CΔT

  ΔE = q - (1160 J/°C)(7.15 °C)

  ΔE = q - 8294 J

6. The heat absorbed or released (q) can be calculated using the equation:

  q = n × ΔH

  Where n is the number of moles and ΔH is the molar enthalpy of the reaction.

7. Rearrange the equation to solve for ΔH:

  ΔH = q / n

8. Convert the energy change (ΔE) to kilojoules:

  1 kJ = 1000 J

  ΔE = ΔE / 1000

9. Substitute the values into the equation:

  ΔH = ΔE / n

  ΔH = (-8294 J) / 0.0110 mol

  ΔH = -753,090 J/mol

10. Convert the enthalpy change (ΔH) to kilojoules per mole:

   ΔH = ΔH / 1000

   ΔH = -753.09 kJ/mol

11. Since the stoichiometry of the balanced equation is 2:1, divide the enthalpy change by 2:

   ΔH = -753.09 kJ/mol / 2

   ΔH = -376.55 kJ/mol

12. The energy of formation of [tex]Ta_2O_5[/tex] is the negative of the enthalpy change:

   Energy of formation = -ΔH

   Energy of formation = -(-376.55 kJ/mol)

   Energy of formation = 376.55 kJ/mol

13. Finally, round the answer to the appropriate number of significant figures:

   Energy of formation of [tex]Ta_2O_5[/tex] = -1198.47 kJ/mol

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