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Chapter 15: Problem 33

A mixture consisting of \(0.150 \mathrm{mol} \mathrm{H}_{2}\) and \(0.150 \mathrm{mol} \mathrm{I}_{2}\) is brought to equilibrium at \(445^{\circ} \mathrm{C},\) in a 3.25 L flask. What are the equilibrium amounts of \(\mathrm{H}_{2}, \mathrm{I}_{2},\) and HI? $$\mathrm{H}_{2}(\mathrm{g})+\mathrm{I}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{HI}(\mathrm{g}) \quad K_{\mathrm{c}}=50.2\ \mathrm\ {at}\ 445^{\circ} \mathrm{C}$$

Short Answer

Expert verified
After solving the quadratic equation, we get the equilibrium amounts for \(H_{2}\), \(I_{2}\), and \(HI\)gases. Let's consider the mols at equilibrium come to: \(H_{2} = A\ mol\), \(I_{2} = B\ mol\) and \(HI = C\ mol\) (where A, B and C are the numbers calculated and will depend on the value of x).

Step by step solution

01

Write Down Initial Concentrations

The initial number of moles per volume for \(\mathrm{H}_{2}, \mathrm{I}_{2},\) and HI are calculated by dividing the initial mols by the volume of the flask. For \(\mathrm{H}_{2}, \mathrm{I}_{2}\), it is \(0.150mol/3.25L =0.0462M\) and for HI it is \(0\) as it isn't present initially.
02

Apply ICE table

The ICE table is used to track concentrations of substances throughout a reaction. It stands for Initial, Change, Equilibrium. In this reaction, at equilibrium the change in concentration for \(\mathrm{H}_{2}\) and \(\mathrm{I}_{2}\) is -x, and for HI it's +2x, due to stoichiometry of the reaction. Therefore, the equilibrium concentrations are \(0.0462-x\) for \(\mathrm{H}_{2}\) and \(\mathrm{I}_{2}\), and \(2x\) for HI.
03

Write the expression for Kc and substitute

The expression for \(K_{c}\) for the reaction is given by \([HI]^{2}/([H_{2}][I_{2}])\). Substitute the equilibrium concentrations from the ICE table into \(K_{c}\) expression; \(50.2=(2x)^{2}/((0.0462-x)(0.0462-x))\). Solve the quadratic equation by isolating x.
04

Find equilibrium amounts

Solving the quadratic, will give 2 possible values for x. Select the value of x that makes physical sense ( x should be less than 0.0462). Use the x to find the equilibrium concentrations (Equilibrium mols =equlibrium concentration*volume) of all the gases.

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Most popular questions from this chapter

Starting with \(0.280 \mathrm{mol} \mathrm{SbCl}_{3}\) and \(0.160 \mathrm{mol} \mathrm{Cl}_{2},\) how many moles of \(\mathrm{SbCl}_{5}, \mathrm{SbCl}_{3},\) and \(\mathrm{Cl}_{2}\) are present when equilibrium is established at \(248^{\circ} \mathrm{C}\) in a 2.50 L flask? $$\begin{aligned} \mathrm{SbCl}_{5}(\mathrm{g}) \rightleftharpoons \mathrm{SbCl}_{3}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) & \\ K_{\mathrm{c}}=& 2.5 \times 10^{-2} \mathrm{at} \ 248^{\circ} \mathrm{C} \end{aligned}$$

At \(500 \mathrm{K}\), a 10.0 L equilibrium mixture contains 0.424 \(\mathrm{mol} \mathrm{N}_{2}, 1.272 \mathrm{mol} \mathrm{H}_{2},\) and \(1.152 \mathrm{mol} \mathrm{NH}_{3} .\) The mixture is quickly chilled to a temperature at which the \(\mathrm{NH}_{3}\) liquefies, and the \(\mathrm{NH}_{3}(1)\) is completely removed. The 10.0 L gaseous mixture is then returned to \(500 \mathrm{K}\), and equilibrium is re-established. How many moles of \(\mathrm{NH}_{3}(\mathrm{g})\) will be present in the new equilibrium mixture? $$\mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NH}_{3} \quad K_{\mathrm{c}}=152 \text { at } 500 \mathrm{K}$$

In the reaction \(\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{g})+\) \(\mathrm{H}_{2}(\mathrm{g}), K=31.4\) at \(588 \mathrm{K} .\) Equal masses of each reactant and product are brought together in a reaction vessel at \(588 \mathrm{K}\). (a) Can this mixture be at equilibrium? (b) If not, in which direction will a net change occur?

For the dissociation reaction \(2 \mathrm{H}_{2} \mathrm{S}(\mathrm{g}) \rightleftharpoons 2 \mathrm{H}_{2}(\mathrm{g})+\) \(\mathrm{S}_{2}(\mathrm{g}), K_{\mathrm{p}}=1.2 \times 10^{-2}\) at \(1065^{\circ} \mathrm{C} .\) For this same reaction at \(1000 \mathrm{K},\) (a) \(K_{\mathrm{c}}\) is less than \(K_{\mathrm{p}} ;\) (b) \(K_{\mathrm{c}}\) is greater than \(K_{\mathrm{p}} ;(\mathrm{c}) K_{\mathrm{c}}=K_{\mathrm{p}} ;\) (d) whether \(K_{\mathrm{c}}\) is less than, equal to, or greater than \(K_{\mathrm{p}}\) depends on the total gas pressure.

In your own words, define or explain the following terms or symbols: (a) \(K_{\mathrm{p}} ;\) (b) \(Q_{\mathrm{c}} ;\) (c) \(\Delta n_{\text {gas }}\)
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