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Chapter 17: Problem 60

The value of \(\Delta G^{\circ}\) for the reaction $$ 2 \mathrm{C}_{4} \mathrm{H}_{10}(g)+13 \mathrm{O}_{2}(g) \longrightarrow 8 \mathrm{CO}_{2}(g)+10 \mathrm{H}_{2} \mathrm{O}(l) $$ is \(-5490 . \mathrm{kJ} .\) Use this value and data from Appendix 4 to calculate the standard free energy of formation for \(\mathrm{C}_{4} \mathrm{H}_{10}(g)\).

Short Answer

Expert verified
The standard free energy of formation for butane gas (C4H10(g)) is -481.4 kJ/mol.

Step by step solution

01

Write down the reaction and known information

Write down the reaction: $$ 2 \mathrm{C}_{4} \mathrm{H}_{10}(g)+13 \mathrm{O}_{2}(g) \longrightarrow 8 \mathrm{CO}_{2}(g)+10 \mathrm{H}_{2} \mathrm{O}(l) $$ We are given: $$ \Delta G^{\circ}_{reaction}=-5490 \mathrm{kJ} $$ We need to find the \(\Delta G^{\circ}_{C_{4}H_{10}(g)}\).
02

Write down the standard free energy change formula and the known values

Write down the standard free energy change formula: $$\Delta G^{\circ}_{reaction} = \sum n \Delta G^{\circ}_{products} - \sum n \Delta G^{\circ}_{reactants}$$ Using the values from Appendix 4, we have: $$ \Delta G^{\circ}_{O_2(g)} = 0 \space \mathrm{kJ \space mol^{-1}} $$ $$ \Delta G^{\circ}_{CO_2(g)} = -394.4 \space \mathrm{kJ \space mol^{-1}} $$ $$ \Delta G^{\circ}_{H_2O(l)} = -237.2 \space \mathrm{kJ \space mol^{-1}} $$
03

Substitute the values into the formula and solve for \(\Delta G^{\circ}_{C_{4}H_{10}(g)}\)

Substitute the known values into the standard free energy change formula: $$ -5490 = \left[ 8 \times (-394.4) + 10 \times (-237.2) \right] - \left[ 2 \times \Delta G^{\circ}_{C_{4}H_{10}(g)} + 0 \right] $$ Solve for \(\Delta G^{\circ}_{C_{4}H_{10}(g)}\): $$ \Delta G^{\circ}_{C_{4}H_{10}(g)} = \frac{-5490 - 8 \times (-394.4) - 10 \times (-237.2)}{2} $$ $$ \Delta G^{\circ}_{C_{4}H_{10}(g)} = \frac{-5490 + 3155.2 + 2372}{2} $$ $$ \Delta G^{\circ}_{C_{4}H_{10}(g)} = -481.4 \mathrm{kJ \space mol^{-1}} $$
04

State the answer

The standard free energy of formation for butane gas (C4H10(g)) is -481.4 kJ/mol.

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Most popular questions from this chapter

Ethanethiol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{SH} ;\right.\) also called ethyl mercaptan \()\) is commonly added to natural gas to provide the "rotten egg" smell of a gas leak. The boiling point of ethanethiol is \(35^{\circ} \mathrm{C}\) and its heat of vaporization is \(27.5 \mathrm{~kJ} / \mathrm{mol}\). What is the entropy of vaporization for this substance?

What types of experiments can be carried out to determine whether a reaction is spontaneous? Does spontaneity have any relationship to the final equilibrium position of a reaction? Explain.

For ammonia \(\left(\mathrm{NH}_{3}\right)\), the enthalpy of fusion is \(5.65 \mathrm{~kJ} / \mathrm{mol}\) and the entropy of fusion is \(28.9 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol}\). a. Will \(\mathrm{NH}_{3}(s)\) spontaneously melt at \(200 . \mathrm{K}\) ? b. What is the approximate melting point of ammonia?

Predict the sign of \(\Delta S^{\circ}\) for each of the following changes. a. \(\mathrm{K}(s)+\frac{1}{2} \mathrm{Br}_{2}(g) \longrightarrow \mathrm{KBr}(s)\) b. \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\) c. \(\mathrm{KBr}(s) \longrightarrow \mathrm{K}^{+}(a q)+\mathrm{Br}^{-}(a q)\) d. \(\mathrm{KBr}(s) \longrightarrow \mathrm{KBr}(l)\)

For rubidium \(\Delta H_{\mathrm{vap}}^{\circ}=69.0 \mathrm{~kJ} / \mathrm{mol}\) at \(686^{\circ} \mathrm{C}\), its boiling point. Calculate \(\Delta S^{\circ}, q, w\), and \(\Delta E\) for the vaporization of \(1.00 \mathrm{~mole}\) of rubidium at \(686^{\circ} \mathrm{C}\) and \(1.00\) atm pressure.
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