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Chapter 6: Problem 17

The enthalpy of combustion of \(\mathrm{CH}_{4}(g)\) when \(\mathrm{H}_{2} \mathrm{O}(l)\) is formed is \(-891 \mathrm{~kJ} / \mathrm{mol}\) and the enthalpy of combustion of \(\mathrm{CH}_{4}(\mathrm{~g})\) when \(\mathrm{H}_{2} \mathrm{O}(g)\) is formed is \(-803 \mathrm{~kJ} / \mathrm{mol}\). Use these data and Hess's law to determine the enthalpy of vaporization for water.

Short Answer

Expert verified
The enthalpy of vaporization for water is \(88 \, kJ/mol\).

Step by step solution

01

Write the chemical equations for combustion of methane with different products

Equation 1: Combustion of methane with the formation of liquid water: \[CH_{4}(g) + 2O_{2}(g) \rightarrow CO_{2}(g) + 2H_{2}O(l)\] Enthalpy change for Equation 1: \(-891 \, kJ/mol\) Equation 2: Combustion of methane with the formation of gaseous water: \[CH_{4}(g) + 2O_{2}(g) \rightarrow CO_{2}(g) + 2H_{2}O(g)\] Enthalpy change for Equation 2: \(-803 \, kJ/mol\)
02

Get the chemical equation for enthalpy of vaporization

From the given data, we want to find the enthalpy of vaporization, which represents the conversion of liquid water to gaseous water: Equation 3: Enthalpy of vaporization of water: \[2H_{2}O(l) \rightarrow 2H_{2}O(g)\] By Hess's law, we can manipulate and add the given equations to find the enthalpy of vaporization:
03

Use Hess's law to solve for the enthalpy of vaporization

Our goal is to manipulate Equations 1 and 2 to isolate Equation 3. To do this, we can subtract Equation 1 from Equation 2: \[(-803 \, kJ/mol) - (-891 \, kJ/mol) = \Delta H\] where \(\Delta H\) is the enthalpy change for Equation 3. Calculate the enthalpy of vaporization: \[\Delta H = -803 \, kJ/mol + 891 \, kJ/mol\] \[\Delta H = 88 \, kJ/mol\] Our final result is:
04

Enthalpy of vaporization for water

The enthalpy of vaporization for water is \(88 \, kJ/mol\).

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Most popular questions from this chapter

Assume that \(4.19 \times 10^{6} \mathrm{~kJ}\) of energy is needed to heat a home. If this energy is derived from the combustion of methane \(\left(\mathrm{CH}_{4}\right)\), what volume of methane, measured at STP, must be burned? \(\left(\Delta H_{\text {combustion }}^{\circ}\right.\) for \(\mathrm{CH}_{4}=-891 \mathrm{~kJ} / \mathrm{mol}\) )

In a bomb calorimeter, the reaction vessel is surrounded by water that must be added for each experiment. Since the amount of water is not constant from experiment to experiment, the mass of water must be measured in each case. The heat capacity of the calorimeter is broken down into two parts: the water and the calorimeter components. If a calorimeter contains \(1.00 \mathrm{~kg}\) water and has a total heat capacity of \(10.84 \mathrm{~kJ} /{ }^{\circ} \mathrm{C}\), what is the heat capacity of the calorimeter components?

At \(298 \mathrm{~K}\), the standard enthalpies of formation for \(\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{~g})\) and \(\mathrm{C}_{6} \mathrm{H}_{6}(l)\) are \(227 \mathrm{~kJ} / \mathrm{mol}\) and \(49 \mathrm{~kJ} / \mathrm{mol}\), respectively. a. Calculate \(\Delta H^{\circ}\) for $$ \mathrm{C}_{6} \mathrm{H}_{6}(l) \longrightarrow 3 \mathrm{C}_{2} \mathrm{H}_{2}(g) $$ b. Both acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) and benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) can be used as fuels. Which compound would liberate more energy per gram when combusted in air?

The overall reaction in a commercial heat pack can be represented as $$ 4 \mathrm{Fe}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Fe}_{2} \mathrm{O}_{3}(s) \quad \Delta H=-1652 \mathrm{~kJ} $$ a. How much heat is released when \(4.00\) moles of iron are reacted with excess \(\mathrm{O}_{2}\) ? b. How much heat is released when \(1.00\) mole of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) is produced? c. How much heat is released when \(1.00 \mathrm{~g}\) iron is reacted with excess \(\mathrm{O}_{2}\) ? d. How much heat is released when \(10.0 \mathrm{~g} \mathrm{Fe}\) and \(2.00 \mathrm{~g} \mathrm{O}_{2}\) are reacted?

Give the definition of the standard enthalpy of formation for a substance. Write separate reactions for the formation of \(\mathrm{NaCl}\), \(\mathrm{H}_{2} \mathrm{O}, \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\), and \(\mathrm{PbSO}_{4}\) that have \(\Delta H^{\circ}\) values equal to \(\Delta H_{\mathrm{f}}^{\circ}\) for each compound.
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