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Chapter 17: Problem 34

Calculate \(\Delta S_{\text {surr }}\) for the following reactions at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\). a. \(\mathrm{C}_{3} \mathrm{H}_{8}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 3 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(l)\) \(\begin{array}{ll}\Delta H^{\circ}=-2221 \mathrm{~kJ} \\ \text { b. } 2 \mathrm{NO}_{2}(g) \longrightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) & \Delta H^{\circ}=112 \mathrm{~kJ}\end{array}\)

Short Answer

Expert verified
For the given reactions at 25°C and 1 atm pressure, the change in entropy for the surroundings are: a. ΔS1_surr = 7452.65 J/K b. ΔS2_surr = -375.93 J/K

Step by step solution

01

Convert ΔH to Joules

First, we need to convert the ΔH value from kJ to J. The given ΔH value is -2221 kJ. There are 1000 J in 1 kJ, so we multiply by 1000 to get: ΔH = -2221 kJ × 1000 = -2221000 J
02

Calculate T in Kelvin

We need to convert the given temperature from Celsius to Kelvin. To do this, we add 273.15 to the Celsius temperature: T = 25°C + 273.15 = 298.15 K
03

Calculate ΔSsurr using the formula

Now, we use the formula ΔSsurr = -(ΔH°)/T to calculate the change in entropy for the surroundings: ΔS1_surr = -(-2221000 J) / 298.15 K = 7452.65 J/K #Reaction 2: 2 NO2(g) -> 2 NO(g) + O2(g)#
04

Convert ΔH to Joules

First, we need to convert the ΔH value from kJ to J. The given ΔH value is 112 kJ. There are 1000 J in 1 kJ, so we multiply by 1000 to get: ΔH = 112 kJ × 1000 = 112000 J
05

Calculate T in Kelvin

We have already calculated the temperature in Kelvin which is 298.15 K.
06

Calculate ΔSsurr using the formula

Now, we use the formula ΔSsurr = -(ΔH°)/T to calculate the change in entropy for the surroundings: ΔS2_surr = -(112000 J) / 298.15 K = -375.93 J/K So, the change in entropy for the surroundings for the given reactions at 25°C and 1 atm pressure are: a. ΔS1_surr = 7452.65 J/K b. ΔS2_surr = -375.93 J/K

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Most popular questions from this chapter

For each of the following pairs of substances, which substance has the greater value of \(S^{\circ}\) ? a. \(\mathrm{C}_{\text {graphite }}(s)\) or \(\mathrm{C}_{\text {diamond }}(s)\) b. \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)\) or \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g)\) c. \(\mathrm{CO}_{2}(s)\) or \(\mathrm{CO}_{2}(g)\)

The standard free energies of formation and the standard enthalpies of formation at \(298 \mathrm{~K}\) for difluoroacetylene \(\left(\mathrm{C}_{2} \mathrm{~F}_{2}\right)\) and hexafluorobenzene \(\left(\mathrm{C}_{6} \mathrm{~F}_{6}\right)\) are $$ \begin{array}{|lcc|} & \left.\Delta G_{\mathrm{f}}^{\circ}(\mathrm{k}] / \mathrm{mol}\right) & \Delta H_{\mathrm{f}}^{\circ}(\mathrm{kJ} / \mathrm{mol}) \\ \mathrm{C}_{2} \mathrm{~F}_{2}(g) & 191.2 & 241.3 \\ \mathrm{C}_{6} \mathrm{~F}_{6}(g) & 78.2 & 132.8 \\ \hline \end{array} $$ For the following reaction: $$ \mathrm{C}_{6} \mathrm{~F}_{6}(g) \rightleftharpoons 3 \mathrm{C}_{2} \mathrm{~F}_{2}(g) $$ a. calculate \(\Delta S^{\circ}\) at \(298 \mathrm{~K}\). b. calculate \(K\) at \(298 \mathrm{~K}\). c. estimate \(K\) at \(3000 . \mathrm{K}\), assuming \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) do not depend on temperature.

Which of the following reactions (or processes) are expected to have a negative value for \(\Delta S^{\circ}\) ? a. \(\mathrm{SiF}_{6}(a q)+\mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{HF}(g)+\mathrm{SiF}_{4}(g)\) b. \(4 \mathrm{Al}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3}(s)\) c. \(\mathrm{CO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{COCl}_{2}(g)\) d. \(\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)\) e. \(\mathrm{H}_{2} \mathrm{O}(s) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)\)

Consider the following reaction: $$ \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{Cl}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{HOCl}(g) \quad K_{298}=0.090 $$ For \(\mathrm{Cl}_{2} \mathrm{O}(g)\), $$ \begin{aligned} \Delta G_{\mathrm{f}}^{\circ} &=97.9 \mathrm{~kJ} / \mathrm{mol} \\ \Delta H_{\mathrm{f}}^{\circ} &=80.3 \mathrm{~kJ} / \mathrm{mol} \\ S^{\circ} &=266.1 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol} \end{aligned} $$ a. Calculate \(\Delta G^{\circ}\) for the reaction using the equation \(\Delta G^{\circ}=-R T \ln (K)\) b. Use bond energy values (Table 8.4) to estimate \(\Delta H^{\circ}\) for the reaction. c. Use the results from parts a and \(\mathrm{b}\) to estimate \(\Delta S^{\circ}\) for the reaction. d. Estimate \(\Delta H_{\mathrm{f}}^{\circ}\) and \(S^{\circ}\) for \(\mathrm{HOCl}(g)\). e. Estimate the value of \(K\) at \(500 . \mathrm{K}\). f. Calculate \(\Delta G\) at \(25^{\circ} \mathrm{C}\) when \(P_{\mathrm{H}_{2} \mathrm{O}}=18\) torr, \(P_{\mathrm{Cl}_{2} \mathrm{O}}=\) \(2.0\) torr, and \(P_{\mathrm{HOCl}}=0.10\) torr.

Consider the following reaction at \(25.0^{\circ} \mathrm{C}\) : $$ 2 \mathrm{NO}_{2}(g) \rightleftharpoons \mathrm{N}_{2} \mathrm{O}_{4}(g) $$ The values of \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) are \(-58.03 \mathrm{~kJ} / \mathrm{mol}\) and \(-176.6\) \(\mathrm{J} / \mathrm{K} \cdot \mathrm{mol}\), respectively. Calculate the value of \(\mathrm{K}\) at \(25.0^{\circ} \mathrm{C}\). Assuming \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) are temperature independent, estimate the value of \(K\) at \(100.0^{\circ} \mathrm{C}\).
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