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Chapter 6: Problem 48

For the following reactions at constant pressure, predict if \(\Delta H>\) \(\Delta E, \Delta H<\Delta E\), or \(\Delta H=\Delta E\) a. \(2 \mathrm{HF}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{F}_{2}(g)\) b. \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\) c. \(4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\)

Short Answer

Expert verified
a. \(\Delta H = \Delta E\) b. \(\Delta H < \Delta E\) c. \(\Delta H > \Delta E\)

Step by step solution

01

Count the moles of gas on both sides of the reaction

Count the number of moles of gaseous reactants and products in the balanced chemical equation.
02

Determine the change in volume

Use the differences in the number of moles of gases on the reactants and products sides to determine the change in volume, \(\Delta V\).
03

Evaluate the relationship between \(\Delta H\) and \(\Delta E\)

Using the equation \(\Delta H = \Delta E + P\Delta V\) and the value of \(\Delta V\), determine whether \(\Delta H > \Delta E\), \(\Delta H < \Delta E\), or \(\Delta H = \Delta E\). a. \(2 \mathrm{HF}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{F}_{2}(g)\)
04

Count the moles of gas on both sides

Reactants: 2 moles of HF (g) Products: 1 mole of H2 (g) + 1 mole of F2 (g)
05

Determine the change in volume

Since the number of gas moles is the same on both sides (2 moles), we have no change in volume: \(\Delta V=0\).
06

Evaluate the relationship between \(\Delta H\) and \(\Delta E\)

Since \(\Delta V = 0\), the equation simplifies to \(\Delta H = \Delta E\). Hence, \(\Delta H = \Delta E\). b. \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2\mathrm{NH}_{3}(g)\)
07

Count the moles of gas on both sides

Reactants: 1 mole of N2 (g) + 3 moles of H2 (g) Products: 2 moles of NH3 (g)
08

Determine the change in volume

There are 4 moles of gas in the reactants and 2 moles of gas in the products, resulting in a decrease in volume: \(\Delta V < 0\).
09

Evaluate the relationship between \(\Delta H\) and \(\Delta E\)

Since \(\Delta V < 0\), then \(\Delta H < \Delta E + P\Delta V\) (with \(P\Delta V<0\)). Hence, \(\Delta H < \Delta E\). c. \(4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4\mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\)
10

Count the moles of gas on both sides

Reactants: 4 moles of NH3 (g) + 5 moles of O2 (g) Products: 4 moles of NO (g) + 6 moles of H2O (g)
11

Determine the change in volume

There are 9 moles of gas in the reactants and 10 moles of gas in the products, resulting in an increase in volume: \(\Delta V > 0\).
12

Evaluate the relationship between \(\Delta H\) and \(\Delta E\)

Since \(\Delta V > 0\), then \(\Delta H > \Delta E + P\Delta V\) (with \(P\Delta V>0\)). Hence, \(\Delta H > \Delta E\).

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Most popular questions from this chapter

Acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) and butane \(\left(\mathrm{C}_{4} \mathrm{H}_{10}\right)\) are gaseous fuels with enthalpies of combustion of \(-49.9 \mathrm{~kJ} / \mathrm{g}\) and \(-49.5 \mathrm{~kJ} / \mathrm{g}\), respectively. Compare the energy available from the combustion of a given volume of acetylene to the combustion energy from the same volume of butane at the same temperature and pressure.

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?

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?

The bomb calorimeter in Exercise 108 is filled with \(987 \mathrm{~g}\) water. The initial temperature of the calorimeter contents is \(23.32^{\circ} \mathrm{C}\). A \(1.056-\mathrm{g}\) sample of benzoic acid \(\left(\Delta E_{\text {comb }}=-26.42 \mathrm{~kJ} / \mathrm{g}\right)\) is combusted in the calorimeter. What is the final temperature of the calorimeter contents?

Consider the dissolution of \(\mathrm{CaCl}_{2}\) : $$ \mathrm{CaCl}_{2}(s) \longrightarrow \mathrm{Ca}^{2+}(a q)+2 \mathrm{Cl}^{-}(a q) \quad \Delta H=-81.5 \mathrm{~kJ} $$ An \(11.0-\mathrm{g}\) sample of \(\mathrm{CaCl}_{2}\) is dissolved in \(125 \mathrm{~g}\) water, with both substances at \(25.0^{\circ} \mathrm{C}\). Calculate the final temperature of the solution assuming no heat loss to the surroundings and assuming the solution has a specific heat capacity of \(4.18 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}\).
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