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Chapter 15: Problem 34

Phosphorus trichloride gas and chlorine gas react to form phosphorus pentachloride gas: \(\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons\) \(\mathrm{PCl}_{5}(g) .\) A 7.5-L gas vessel is charged with a mixture of \(\mathrm{PCl}_{3}(g)\) and \(\mathrm{Cl}_{2}(g)\), which is allowed to equilibrate at 450 \(\mathrm{K} .\) At equilibrium the partial pressures of the three gases are $P_{\mathrm{PCl}_{3}}=12.56 \mathrm{kPa}, P_{\mathrm{Cl}_{2}}=15.91 \mathrm{kPa},\( and \)P_{\mathrm{PCl}_{5}}=131.7 \mathrm{kPa}$ (a) What is the value of \(K_{p}\) at this temperature? (b) Does the equilibrium favor reactants or products? (c) Calculate \(K_{c}\) for this reaction at \(450 \mathrm{~K}\).

Short Answer

Expert verified
At 450 K, the value of \(K_{p}\) for the given reaction is approximately 0.646, which means the equilibrium favors reactants. The value of \(K_{c}\) at this temperature is approximately 2.41.

Step by step solution

01

Calculate \(K_{p}\)

The expression for \(K_{p}\) is given by: \[K_p = \frac{P_{\mathrm{PCl}_{5}}}{ P_{\mathrm{PCl}_{3}} \cdot P_{\mathrm{Cl}_{2}} }\] Using the given equilibrium partial pressures, we can calculate \(K_{p}\): \[K_p = \frac{131.7}{12.56 \cdot 15.91} \approx 0.646 \]
02

Determine if equilibrium favors reactants or products

A \(K_{p}\) value greater than 1 indicates that the equilibrium favors products, while a value less than 1 indicates it favors reactants. In this case, we found \(K_{p}\) to be approximately 0.646, which means that the equilibrium favors reactants.
03

Calculate \(K_{c}\)

We can use the relationship between \(K_{p}\) and \(K_{c}\) to find the value of \(K_{c}\). The relationship is given by: \[K_p = K_c(RT)^{\Delta n}\] Where \(\Delta n\) is the change in the number of moles of gas in the reaction, \(R\) is the ideal gas constant, and \(T\) is the temperature in Kelvin. In this case, \(\Delta n = 1 - (1 + 1) = -1\), and at 450 K, \[K_p = K_c(8.314 \times 450)^{-1}\] Solving for \(K_c\), we get: \[K_c = K_p \times (8.314 \times 450) \approx 2.41\] So, at 450 K, \(K_{c} \approx 2.41\).

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Most popular questions from this chapter

The equilibrium $2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{NOCl}(g)\( is established at \)550 \mathrm{~K}$. An equilibrium mixture of the three gases has partial pressures of $10.13 \mathrm{kPa}, 20.27 \mathrm{kPa}\(, and \)35.46 \mathrm{kPa}\( for \)\mathrm{NO}, \mathrm{Cl}_{2},$ and \(\mathrm{NOCl}\), respectively.(a) Calculate \(K_{p}\) for this reaction at \(500.0 \mathrm{~K}\). (b) If the vessel has a volume of \(5.00 \mathrm{~L},\) calculate \(K_{c}\) at this temperature.

The equilibrium constant for the reaction $$2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{NOBr}(g)$$ is \(K_{c}=1.3 \times 10^{-2}\) at \(1000 \mathrm{~K}\). (a) At this temperature does the equilibrium favor \(\mathrm{NO}\) and \(\mathrm{Br}_{2}\), or does it favor NOBr? (b) Calculate \(K_{c}\) for $2 \mathrm{NOBr}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) .$ (c) Calculate \(K_{c}\) for $\mathrm{NOBr}(g) \rightleftharpoons \mathrm{NO}(g)+\frac{1}{2} \mathrm{Br}_{2}(g)$.

Consider the reaction $$\begin{aligned} 4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) & \rightleftharpoons \\ & 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g), \Delta H=-904.4 \mathrm{~kJ} \end{aligned}$$ Does each of the following increase, decrease, or leave unchanged the yield of \(\mathrm{NO}\) at equilibrium? (a) increase \(\left[\mathrm{NH}_{3}\right] ;(\mathbf{b})\) increase \(\left[\mathrm{H}_{2} \mathrm{O}\right] ;(\mathbf{c})\) decrease \(\left[\mathrm{O}_{2}\right] ;(\mathbf{d})\) decrease the volume of the container in which the reaction occurs; (e) add a catalyst; (f) increase temperature.

The protein hemoglobin (Hb) transports \(\mathrm{O}_{2}\) in mammalian blood. Each Hb can bind \(4 \mathrm{O}_{2}\) molecules. The equilibrium constant for the \(\mathrm{O}_{2}\) binding reaction is higher in fetal hemoglobin than in adult hemoglobin. In discussing protein oxygen-binding capacity, biochemists use a measure called the \(P 50\) value, defined as the partial pressure of oxygen at which \(50 \%\) of the protein is saturated. Fetal hemoglobin has a \(\mathrm{P} 50\) value of \(2.53 \mathrm{kPa},\) and adult hemoglobin has a P50 value of \(3.57 \mathrm{kPa}\). Use these data to estimate how much larger \(K_{c}\) is for the aqueous reaction $4 \mathrm{O}_{2}(g)+\mathrm{Hb}(a q) \rightleftharpoons\left[\mathrm{Hb}\left(\mathrm{O}_{2}\right)_{4}(a q)\right]\( in a fetus, compared to \)K_{c}$ for the same reaction in an adult.

Methane, \(\mathrm{CH}_{4}\), reacts with \(I_{2}\) according to the reaction $\mathrm{CH}_{4}(g)+\mathrm{I}_{2}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{I}(g)+\mathrm{HI}(g)\(. At \)600 \mathrm{~K}, K_{p}$ for this reaction is \(1.95 \times 10^{-4}\). A reaction was set up at 600 \(\mathrm{K}\) with initial partial pressures of methane of \(13.3 \mathrm{kPa}\) and of $6.67 \mathrm{kPa}\( for \)\mathrm{I}_{2}$. Calculate the pressures, in \(\mathrm{kPa}\), of all reactants and products at equilibrium.
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