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Chapter 6: Problem 67

The enthalpy of combustion of solid carbon to form carbon dioxide is \(-393.7 \mathrm{~kJ} / \mathrm{mol}\) carbon, and the enthalpy of combustion of carbon monoxide to form carbon dioxide is \(-283.3 \mathrm{~kJ} / \mathrm{mol}\) CO. Use these data to calculate \(\Delta H\) for the reaction $$ 2 \mathrm{C}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}(g) $$

Short Answer

Expert verified
The enthalpy change for the reaction \(2 \mathrm{C}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}(g)\) is \(\Delta H = -1354 \mathrm{~kJ/mol}\).

Step by step solution

01

Write down the given reactions and their enthalpy changes

The given reactions are: 1. Combustion of solid carbon to form carbon dioxide: $$ \mathrm{C}(s) + \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_2(g) \quad \Delta H_1=-393.7 \mathrm{~kJ/mol} $$ 2. Combustion of carbon monoxide to form carbon dioxide: $$ \mathrm{CO}(g) + \frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_2(g) \quad \Delta H_2=-283.3 \mathrm{~kJ/mol} $$ The enthalpy changes for these reactions, ∆H\(_1\) and ∆H\(_2\), are given.
02

Formulate the desired reaction

The desired reaction is: $$ 2 \mathrm{C}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}(g) \quad \Delta H_{x} $$ Our goal is to find the enthalpy change for this reaction, ∆H\(_x\).
03

Construct the Hess's Law cycle

Using the given reactions and the desired reaction, we can construct a Hess's Law cycle: 1. Multiply the first given reaction by 2 and reverse the direction: $$ 2\mathrm{CO}_2(g) \longrightarrow 2\mathrm{C}(s) + 2\mathrm{O}_{2}(g) \qquad 2\Delta H_1 $$ 2. Multiply the second given reaction by 2: $$ 2\mathrm{CO}(g) + \mathrm{O}_{2}(g) \longrightarrow 2\mathrm{CO}_2(g) \qquad 2\Delta H_2 $$ Now, add these modified reactions to get the desired reaction: $$ 2\mathrm{C}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}(g) \quad \Delta H_x $$ The overall enthalpy change, ∆H\(_x\), will be equal to the sum of the enthalpy changes of the modified reactions.
04

Calculate the enthalpy change (∆H) for the desired reaction

Use the enthalpy changes to find ∆H\(_x\): $$ \Delta H_x = 2(\Delta H_1) + 2(\Delta H_2) $$ $$ \Delta H_x = 2(-393.7 \mathrm{~kJ/mol}) + 2(-283.3 \mathrm{~kJ/mol}) $$ $$ \Delta H_x = -787.4 \mathrm{~kJ/mol} - 566.6 \mathrm{~kJ/mol} $$ $$ \Delta H_x = -1354 \mathrm{~kJ/mol} $$ Therefore, the enthalpy change for the reaction 2 C(s) + O\(_2\)(g) → 2 CO(g) is -1354 kJ/mol.

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Most popular questions from this chapter

The sun supplies energy at a rate of about \(1.0\) kilowatt per square meter of surface area ( 1 watt \(=1 \mathrm{~J} / \mathrm{s}\) ). The plants in an agricultural field produce the equivalent of \(20 . \mathrm{kg}\) sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) per hour per hectare ( \(1 \mathrm{ha}=10,000 \mathrm{~m}^{2}\) ). Assuming that sucrose is produced by the reaction \(12 \mathrm{CO}_{2}(g)+11 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(s)+12 \mathrm{O}_{2}(g)\) \(\Delta H=5640 \mathrm{~kJ}\) calculate the percentage of sunlight used to produce the sucrosethat is, determine the efficiency of photosynthesis.

The standard enthalpy of formation of \(\mathrm{H}_{2} \mathrm{O}(l)\) at \(298 \mathrm{~K}\) is \(-285.8\) \(\mathrm{kJ} / \mathrm{mol} .\) Calculate the change in internal energy for the following process at \(298 \mathrm{~K}\) and 1 atm: $$ \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \quad \Delta E^{\circ}=? $$ (Hint: Using the ideal gas equation, derive an expression for work in terms of \(n, R\), and \(T\).)

Consider the following equations: $$ \begin{aligned} 3 \mathrm{~A}+6 \mathrm{~B} \longrightarrow & 3 \mathrm{D} & \Delta H &=-403 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{E}+2 \mathrm{~F} & \longrightarrow \mathrm{A} & \Delta H &=-105.2 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{C} & \longrightarrow \mathrm{E}+3 \mathrm{D} & \Delta H &=+64.8 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$ Suppose the first equation is reversed and multiplied by \(\frac{1}{6}\), the second and third equations are divided by 2, and the three adjusted equations are added. What is the net reaction and what is the overall heat of this reaction?

A sample consisting of \(22.7 \mathrm{~g}\) of a nongaseous, unstable compound \(\mathrm{X}\) is placed inside a metal cylinder with a radius of \(8.00 \mathrm{~cm}\), and a piston is carefully placed on the surface of the compound so that, for all practical purposes, the distance between the bottom of the cylinder and the piston is zero. (A hole in the piston allows trapped air to escape as the piston is placed on the compound; then this hole is plugged so that nothing inside the cylinder can escape.) The piston-and-cylinder apparatus is carefully placed in \(10.00 \mathrm{~kg}\) water at \(25.00^{\circ} \mathrm{C}\). The barometric pressure is 778 torr. When the compound spontaneously decomposes, the piston moves up, the temperature of the water reaches a maximum of \(29.52^{\circ} \mathrm{C}\), and then it gradually decreases as the water loses heat to the surrounding air. The distance between the piston and the bottom of the cylinder, at the maximum temperature, is \(59.8 \mathrm{~cm}\). Chemical analysis shows that the cylinder contains \(0.300 \mathrm{~mol}\) carbon dioxide, \(0.250\) mol liquid water, \(0.025\) mol oxygen gas, and an undetermined amount of a gaseous element \(\mathrm{A}\). It is known that the enthalpy change for the decomposition of \(X\), according to the reaction described above, is \(-1893\) \(\mathrm{kJ} / \mathrm{mol} \mathrm{X}\). The standard enthalpies of formation for gaseous carbon dioxide and liquid water are \(-393.5 \mathrm{~kJ} / \mathrm{mol}\) and \(-286 \mathrm{~kJ} / \mathrm{mol}\), respectively. The heat capacity for water is \(4.184 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}\). The conversion factor between \(\mathrm{L} \cdot \mathrm{atm}\) and \(\mathrm{J}\) can be determined from the two values for the gas constant \(R\), namely, \(0.08206 \mathrm{~L}\). \(\mathrm{atm} / \mathrm{K} \cdot \mathrm{mol}\) and \(8.3145 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol}\). The vapor pressure of water at \(29.5^{\circ} \mathrm{C}\) is 31 torr. Assume that the heat capacity of the pistonand-cylinder apparatus is negligible and that the piston has negligible mass. Given the preceding information, determine a. The formula for \(\mathrm{X}\). b. The pressure-volume work (in \(\mathrm{kJ}\) ) for the decomposition of the \(22.7-\mathrm{g}\) sample of \(\mathrm{X}\). c. The molar change in internal energy for the decomposition of \(X\) and the approximate standard enthalpy of formation for \(X\).

Consider a mixture of air and gasoline vapor in a cylinder with a piston. The original volume is \(40 . \mathrm{cm}^{3} .\) If the combustion of this mixture releases 950. J of energy, to what volume will the gases expand against a constant pressure of 650 . torr if all the energy of combustion is converted into work to push back the piston?
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