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Chapter 13: Problem 30

The following equilibrium pressures were observed at a certain temperature for the reaction $$ \begin{array}{c} \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) \\\ P_{\mathrm{NH}_{3}}=3.1 \times 10^{-2} \mathrm{~atm} \\ P_{\mathrm{N}_{2}}=8.5 \times 10^{-1} \mathrm{~atm} \\ P_{\mathrm{H}_{2}}=3.1 \times 10^{-3} \mathrm{~atm} \end{array} $$ Calculate the value for the equilibrium constant \(K_{\mathrm{p}}\) at this temperature. If \(P_{\mathrm{N}_{2}}=0.525 \mathrm{~atm}, P_{\mathrm{NH}_{3}}=0.0167 \mathrm{~atm}\), and \(\underline{P_{\mathrm{H}}}=0.00761\) atm, does this represent a system at equilibrium?

Short Answer

Expert verified
In short, the value of \(K_p\) at this temperature is approximately 23.28. Given the second set of pressures, the calculated \(Q_p\) is approximately 27.50. Since \(Q_p > K_p\), the reaction will shift left (toward reactants), indicating that the system is NOT at equilibrium.

Step by step solution

01

Write the balanced chemical equation

We are given the balanced chemical equation: \[ \mathrm{N}_{2}(g) + 3\mathrm{H}_{2}(g) \rightleftharpoons 2\mathrm{NH}_{3}(g) \]
02

Write the equilibrium expression (reaction quotient)

The equilibrium expression (reaction quotient) for the given reaction is: \[ K_p = \frac{[\mathrm{NH}_3]^2}{[\mathrm{N}_2][\mathrm{H}_2]^3} \]
03

Calculate Kp for the given equilibrium pressures

Using the given equilibrium pressures for N2, H2, and NH3 in the expression: \[ K_p = \frac{(3.1 \times 10^{-2})^2}{(8.5 \times 10^{-1})(3.1 \times 10^{-3})^3} \] Now, solve for Kp: \[ K_p \approx 23.28 \]
04

Calculate Qp using the other set of given pressures

Using the other set of pressures, calculate the reaction quotient Qp for the given reaction: \[ Q_p = \frac{[\mathrm{NH}_3]^2}{[\mathrm{N}_2][\mathrm{H}_2]^3} = \frac{(0.0167)^2}{(0.525)(0.00761)^3} \] Now, solve for Qp: \[ Q_p \approx 27.50 \]
05

Compare Kp and Qp to determine if the system is at equilibrium

Now that we have the calculated values of Kp and Qp, we will compare them to determine if the system is at equilibrium. - If Qp > Kp, the reaction will shift left (toward reactants) - If Qp < Kp, the reaction will shift right (toward products) - If Qp = Kp, the reaction is at equilibrium In this case, since Qp is approximately equal to 27.50 and Kp is approximately equal to 23.28, it implies that Qp > Kp. This means the reaction will shift left (toward reactants). Therefore, given the second set of pressures, the system is NOT at equilibrium.

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Most popular questions from this chapter

Peptide decomposition is one of the key processes of digestion, where a peptide bond is broken into an acid group and an amine group. We can describe this reaction as follows: Peptide \((a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons\) acid \(\operatorname{group}(a q)+\) amine \(\operatorname{group}(a q)\) If we place \(1.0\) mole of peptide into \(1.0 \mathrm{~L}\) water, what will be the equilibrium concentrations of all species in this reaction? Assume the \(K\) value for this reaction is \(3.1 \times 10^{-5}\).

For the reaction $$ \mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{~S}(g) \rightleftharpoons \mathrm{NH}_{4} \mathrm{HS}(s) $$ \(K=400\). at \(35.0^{\circ} \mathrm{C}\). If \(2.00\) moles each of \(\mathrm{NH}_{3}, \mathrm{H}_{2} \mathrm{~S}\), and \(\mathrm{NH}_{4} \mathrm{HS}\) are placed in a \(5.00-\mathrm{L}\) vessel, what mass of \(\mathrm{NH}_{4} \mathrm{HS}\) will be present at equilibrium? What is the pressure of \(\mathrm{H}_{2} \mathrm{~S}\) at equilibrium?

A sample of \(\mathrm{N}_{2} \mathrm{O}_{4}(g)\) is placed in an empty cylinder at \(25^{\circ} \mathrm{C}\). After equilibrium is reached the total pressure is \(1.5\) atm and \(16 \%\) (by moles) of the original \(\mathrm{N}_{2} \mathrm{O}_{4}(g)\) has dissociated to \(\mathrm{NO}_{2}(g)\) a. Calculate the value of \(K_{\mathrm{p}}\) for this dissociation reaction at \(25^{\circ} \mathrm{C} .\) b. If the volume of the cylinder is increased until the total pressure is \(1.0 \mathrm{~atm}\) (the temperature of the system remains constant), calculate the equilibrium pressure of \(\mathrm{N}_{2} \mathrm{O}_{4}(g)\) and \(\mathrm{NO}_{2}(g)\). c. What percentage (by moles) of the original \(\mathrm{N}_{2} \mathrm{O}_{4}(g)\) is dissociated at the new equilibrium position (total pressure = I.00 atm)?

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Consider the reaction $$ \mathrm{Fe}^{3+}(a q)+\mathrm{SCN}^{-}(a q) \rightleftharpoons \mathrm{FeSCN}^{2+}(a q) $$ How will the equilibrium position shift if a. water is added, doubling the volume? b. \(\mathrm{AgNO}_{3}(a q)\) is added? (AgSCN is insoluble.) c. \(\mathrm{NaOH}(a q)\) is added? \(\left[\mathrm{Fe}(\mathrm{OH})_{3}\right.\) is insoluble.] d. \(\mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}(a q)\) is added?
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