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Chapter 14: Problem 21

The equilibrium constant \(K_{\mathrm{c}}\) for the reaction $$\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{I}(g)$$ is \(3.8 \times 10^{-5}\) at \(727^{\circ} \mathrm{C} .\) Calculate \(K_{\mathrm{c}}\) and \(K_{P}\) for the equilibrium $$2 \mathrm{I}(g) \rightleftharpoons \mathrm{I}_{2}(g)$$ at the same temperature.

Short Answer

Expert verified
The value of \(K_{c}\) for the reaction 2I(g) \(\rightleftharpoons I_{2}(g)\) is 2.63 \(\times 10^{4}\). The value of \(K_{p}\) for the reaction at the same temperature is 0.32.

Step by step solution

01

Calculate the new \(K_c\)

The reaction we are considering is the reverse of the given reaction. Therefore, the equilibrium constant for our reaction, \(K'_{c}\), is the reciprocal of the given equilibrium constant. That is, \(K'_{c} = 1/K_{c} = 1/(3.8 \times 10^{-5}) = 2.63 \times 10^{4}\).
02

Find the change in moles \(\Delta n\)

Now find \(\Delta n\) for our reaction by subtracting the number of moles of gaseous reactants from the number of moles of gaseous products. For the reaction 2 \(I \rightarrow I_2\), \(\Delta n = n_{products} - n_{reactants} = 1 - 2 = -1\).
03

Convert Celsius to Kelvin

We need to convert the temperature from Celsius to Kelvin because in the formula for \(K_p\), the temperature \(T\) has to be in Kelvin. \(T(K) = T(°C) + 273.15 = 727 + 273.15 = 1000.15 K\).
04

Calculate \(K_p\)

Now we can insert the values into the relationship \(K_p = K_c(RT)^{\Delta n}\) to calculate \(K_p\). Given that \(R = 0.0821 L atm/(mol K)\), we get \(K_p = K'_{c}(RT)^{\Delta n} = (2.63 \times 10^{4})(0.0821 \times 1000.15)^{-1} = 0.32\).

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Most popular questions from this chapter

Based on rate constant considerations, explain why the equilibrium constant depends on temperature.

A 2.50 -mole quantity of \(\mathrm{NOCl}\) was initially in a \(1.50-\mathrm{L}\) reaction chamber at \(400^{\circ} \mathrm{C}\). After equilibrium was established, it was found that 28.0 percent of the NOCl had dissociated: $$2 \mathrm{NOCl}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g)$$ Calculate the equilibrium constant \(K_{\mathrm{c}}\) for the reaction.

The equilibrium constant \(K_{\mathrm{c}}\) for the reaction $$\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g)$$ is 54.3 at \(430^{\circ} \mathrm{C}\). At the start of the reaction there are 0.714 mole of \(\mathrm{H}_{2}, 0.984\) mole of \(\mathrm{I}_{2}\), and 0.886 mole of HI in a 2.40 -L reaction chamber. Calculate the concentrations of the gases at equilibrium.

Define homogeneous equilibrium and heterogeneous equilibrium. Give two examples of each.

Eggshells are composed mostly of calcium carbonate \(\left(\mathrm{CaCO}_{3}\right)\) formed by the reaction $$\mathrm{Ca}^{2+}(a q)+\mathrm{CO}_{3}^{2-}(a q) \rightleftharpoons \mathrm{CaCO}_{3}(s)$$ The carbonate ions are supplied by carbon dioxide produced as a result of metabolism. Explain why eggshells are thinner in the summer when the rate of panting by chickens is greater. Suggest a remedy for this situation.
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