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Chapter 17: Problem 29

Consider the decomposition of calcium carbonate: $$ \mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{CaO}(s)+\mathrm{CO}_{2}(g) $$ Calculate the pressure in atm of \(\mathrm{CO}_{2}\) in an equilibrium process (a) at \(25^{\circ} \mathrm{C}\) and \((\mathrm{b})\) at \(800^{\circ} \mathrm{C}\). Assume that \(\Delta H^{\circ}=177.8 \mathrm{~kJ} / \mathrm{mol}\) and \(\Delta S^{\circ}=160.5 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol}\) for the temperature range.

Short Answer

Expert verified
The pressure of \(\mathrm{CO}_{2}\) at \(25^{\circ} \mathrm{C}\) and \(800^{\circ} \mathrm{C}\) can be obtained by utilizing the Van't Hoff equation and the ideal gas law based on the given \( \Delta H^{\circ} \) and \( \Delta S^{\circ} \) values. Solve for K then substitute it into \( P = K \) for each temperature to obtain the respective pressures.

Step by step solution

01

Calculation at \(25^{\circ} \mathrm{C}\)

First, convert the temperature from Celcius to Kelvin. Thus, \(T = 25 + 273.15 = 298.15 \, K\). Then, use the Van't Hoff equation \( \ln K = -\frac{\Delta H}{R} \times \frac{1}{T} + \frac{\Delta S}{R}\) to solve for K, where R is the gas constant with a value of \(0.008314 \, \mathrm{kJ} \cdot \mathrm{K}^{-1} \cdot \mathrm{mol}^{-1}\). This will yield \( K = e^{-\frac{177.8}{0.008314 \times 298.15} + \frac{160.5}{0.008314}} \).
02

Calculation of Pressure at \(25^{\circ} \mathrm{C}\)

Solving for the equilibrium constant K from Step 1, substitute this value into the expression for pressure in an ideal gas, \( P = K \). Thus, the pressure at \(25^{\circ} \mathrm{C}\) can be obtained.
03

Calculation at \(800^{\circ} \mathrm{C}\)

Repeat Steps 1 and 2 at \(800^{\circ} \mathrm{C}\). Thus, \(T = 800 + 273.15 = 1073.15 \, K\). Then, compute for the equilibrium constant K, and subsequently the pressure in the similar manner as Steps 1 and 2.

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Most popular questions from this chapter

State which of the following processes are spontaneous and which are nonspontaneous:(a) dissolving table salt (NaCl) in hot soup;(b) climbing Mt. Everest; (c) spreading fragrance in a room by removing the cap from a perfume bottle; (d) separating helium and neon from a mixture of the gases.

A certain reaction is spontaneous at \(72^{\circ} \mathrm{C}\). If the enthalpy change for the reaction is \(19 \mathrm{~kJ} / \mathrm{mol}\), what is the minimum value of \(\Delta S\) (in \(\mathrm{J} / \mathrm{K} \cdot \mathrm{mol}\) ) for the reaction?

Explain the difference between \(\Delta G\) and \(\Delta G^{\circ} .\)

The molar heat of vaporization of ethanol is 39.3 kJ/mol and the boiling point of ethanol is \(78.3^{\circ} \mathrm{C}\). Calculate \(\Delta S\) for the vaporization of 0.50 mol ethanol.

For a reaction with a negative \(\Delta G^{\circ}\) value, which of the following statements is false? (a) The equilibrium constant \(K\) is greater than one. (b) The reaction is spontaneous when all the reactants and products are in their standard states. (c) The reaction is always exothermic.
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