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Chapter 5: Problem 75

Complete combustion of 1 mol of acetone $\left(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}\right)\( liberates \)1790 \mathrm{~kJ}:$ $$ \begin{aligned} \mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}(l)+4 \mathrm{O}_{2}(g) \longrightarrow 3 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(l) & \\ \Delta H^{\circ}=&-1790 \mathrm{~kJ} \end{aligned} $$ Using this information together with the standard enthalpies of formation of \(\mathrm{O}_{2}(g), \mathrm{CO}_{2}(g),\) and \(\mathrm{H}_{2} \mathrm{O}(l)\) from Appendix C, calculate the standard enthalpy of formation of acetone.

Short Answer

Expert verified
The standard enthalpy of formation of acetone is 247.9 kJ/mol.

Step by step solution

01

Write the combustion equation with standard enthalpy changes

Write the given balanced combustion equation and the standard enthalpy change: \[C_3H_6O(l) + 4O_2(g) \rightarrow 3CO_2(g) + 3H_2O(l)\] \[\Delta H_1^\circ = -1790 kJ\]
02

Write the formation equations for each substance involved in the combustion

Write the formation equations for acetone, oxygen, carbon dioxide, and water: 1. Acetone (C3H6O) formation: \[3C(s) + 3H_2(g) + \frac{1}{2}O_2(g) \longrightarrow C_3H_6O(l)\] \[\Delta H_2^\circ= ?\] 2. Oxygen (O2) formation: \[\frac{1}{2}O_2(g) \longrightarrow O_2(g)\] \[\Delta H_3^\circ= 0kJ\] (standard enthalpy of formation of an element in its standard state is zero) 3. Carbon dioxide (CO2) formation: \[C(s) + O_2(g) \longrightarrow CO_2(g)\] \[\Delta H_4^\circ= -393.5 kJ/mol\] (use value from Appendix C) 4. Water (H2O) formation: \[H_2(g) + \frac{1}{2}O_2(g) \longrightarrow H_2O(l)\] \[\Delta H_5^\circ= -285.8 kJ/mol\] (use value from Appendix C)
03

Multiply each formation equation with an appropriate factor

Multiply the formation equations to match the coefficients of the substances in the combustion equation, keeping the enthalpy changes in mind: 1. Acetone formation: \[3C(s) + 3H_2(g) + \frac{1}{2}O_2(g) \longrightarrow C_3H_6O(l)\] \[\Delta H_2^\circ= ?\] 2. Oxygen formation: (multiplied by 4) \[2O_2(g) \longrightarrow 4O_2(g)\] \[\Delta H_3^\circ= 4 \times 0kJ = 0kJ\] 3. Carbon dioxide formation: (multiplied by 3) \[3C(s) + 3O_2(g) \longrightarrow 3CO_2(g)\] \[\Delta H_4^\circ= 3 \times -393.5 kJ/mol = -1180.5 kJ/mol\] 4. Water formation: (multiplied by 3) \[3H_2(g) + \frac{3}{2}O_2(g) \longrightarrow 3H_2O(l)\] \[\Delta H_5^\circ= 3 \times -285.8 kJ/mol = -857.4 kJ/mol\]
04

Use Hess's Law to find the enthalpy of formation of acetone

Hess's Law states that the sum of the series of reactions is equal to the sum of the reaction enthalpies. So, \(\Delta H_1^\circ = \Delta H_2^\circ + \Delta H_3^\circ + \Delta H_4^\circ + \Delta H_5^\circ\). Plug in the known values and solve for the standard enthalpy of formation of acetone, \(\Delta H_2^\circ\): \[-1790 kJ = \Delta H_2^\circ + 0 kJ - 1180.5 kJ - 857.4 kJ\] Solve for \(\Delta H_2^\circ\): \[\Delta H_2^\circ = -1790kJ + 1180.5kJ + 857.4kJ\] \[\Delta H_2^\circ = -1790 + 2037.9\] \[\Delta H_2^\circ = 247.9 kJ/mol\] The standard enthalpy of formation of acetone is 247.9 kJ/mol.

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Most popular questions from this chapter

(a) According to the first law of thermodynamics, what quantity is conserved? (b) What is meant by the internal energy of a system? (c) By what means can the internal energy of a closed system increase?

A coffee-cup calorimeter of the type shown in Figure 5.18 contains $150.0 \mathrm{~g}\( of water at \)25.2^{\circ} \mathrm{C}\(. A \)200-\mathrm{g}$ block of silver metal is heated to \(100.5^{\circ} \mathrm{C}\) by putting it in a beaker of boiling water. The specific heat of \(\mathrm{Ag}(s)\) is $0.233 \mathrm{~J} /(\mathrm{g} \cdot \mathrm{K})\(. The \)\mathrm{Ag}$ is added to the calorimeter, and after some time the contents of the cup reach a constant temperature of \(30.2^{\circ} \mathrm{C} .(\mathbf{a})\) Determine the amount of heat, in J, lost by the silver block. (b) Determine the amount of heat gained by the water. The specific heat of water is $4.184 \mathrm{~J} /(\mathrm{g} \cdot \mathrm{K}) .(\mathbf{c})$ The difference between your answers for (a) and (b) is due to heat loss through the Styrofoam \(^{\circ}\) cups and the heat necessary to raise the temperature of the inner wall of the apparatus. The heat capacity of the calorimeter is the amount of heat necessary to raise the temperature of the apparatus (the cups and the stopper) by \(1 \mathrm{~K} .\) Calculate the heat capacity of the calorimeter in \(\mathrm{J} / \mathrm{K}\). (d) What would be the final temperature of the system if all the heat lost by the silver block were absorbed by the water in the calorimeter?

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In a thermodynamic study, a scientist focuses on the properties of a solution in an apparatus as illustrated. A solution is continuously flowing into the apparatus at the top and out at the bottom, such that the amount of solution in the apparatus is constant with time. (a) Is the solution in the apparatus a closed system, open system, or isolated system? (b) If the inlet and outlet were closed, what type of system would it be?

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