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Chapter 15: Problem 32

Gaseous hydrogen iodide is placed in a closed container at $450^{\circ} \mathrm{C},\( where it partially decomposes to hydrogen and iodine: \)2 \mathrm{HI}(g) \rightleftharpoons \mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) .$ At equilibrium it is found that $[\mathrm{HI}]=4.50 \times 10^{3} \mathrm{M},\left[\mathrm{H}_{2}\right]=5.75 \times 10^{4} \mathrm{M}$, and \(\left[\mathrm{I}_{2}\right]=5.75 \times 10^{-4} \mathrm{M}\). What is the value of \(K_{c}\) at this temperature?

Short Answer

Expert verified
The value of the equilibrium constant (\(K_c\)) for the decomposition of hydrogen iodide at \(450^{\circ} \mathrm{C}\) is \(1.632 \times 10^{-7}\).

Step by step solution

01

Write the balanced chemical equation

The balanced chemical equation for the decomposition of hydrogen iodide is: \[2\,\mathrm{HI}(g) \rightleftharpoons \mathrm{H}_{2}(g) + \mathrm{I}_{2}(g)\]
02

Write the expression for the equilibrium constant

The equilibrium constant expression for the given reaction is given by: \[K_c = \frac{[\mathrm{H}_2][\mathrm{I}_2]}{[\mathrm{HI}]^2}\]
03

Substitute the given equilibrium concentrations

The given equilibrium concentrations are: \[[\mathrm{HI}] = 4.50 \times 10^3 \mathrm{M}\] \[[\mathrm{H}_2] = 5.75 \times 10^4 \mathrm{M}\] \[[\mathrm{I}_2] = 5.75 \times 10^{-4} \mathrm{M}\] Substitute these values into the equilibrium constant expression: \[K_c = \frac{(5.75 \times 10^4 \mathrm{M})(5.75 \times 10^{-4} \mathrm{M})}{(4.50 \times 10^3 \mathrm{M})^2}\]
04

Calculate \(K_c\)

Now calculate the value of \(K_c\) by performing the arithmetic operations: \[K_c = \frac{(5.75 \times 10^4)(5.75 \times 10^{-4})}{(4.50 \times 10^3)^2} = \frac{3.30625 \times 10^{0}}{2.025 \times 10^7}\] \[K_c = 1.632 \times 10^{-7}\] So, the value of the equilibrium constant (\(K_c\)) for the decomposition of hydrogen iodide at \(450^{\circ} \mathrm{C}\) is \(1.632 \times 10^{-7}\).

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Most popular questions from this chapter

At \(1285^{\circ} \mathrm{C}\), the equilibrium constant for the reaction \(\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{Br}(g)\) is $K_{c}=1.04 \times 10^{-3} .\( A \)1.00-\mathrm{L}$ vessel containing an equilibrium mixture of the gases has \(1.50 \mathrm{~g}\) \(\mathrm{Br}_{2}(g)\) in it. What is the mass of \(\mathrm{Br}(g)\) in the vessel?

(a) If \(Q_{c}>K_{c}\), how must the reaction proceed to reach equilibrium? (b) At the start of a certain reaction, only reactants are present; no products have been formed. What is the value of \(Q_{c}\) at this point in the reaction?

Assume that the equilibrium constant for the dissociation of molecular bromine, \(\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{Br}(g)\), at 800 \(\mathrm{K}\) is \(K_{c}=5.4 \times 10^{-3}\). (a) Which species predominates at equilibrium, \(\mathrm{Br}_{2}\) or Br, assuming that the concentration of \(\mathrm{Br}_{2}\) is larger than $5.4 \times 10^{-3} \mathrm{~mol} / \mathrm{L} ?$ (b) Assuming both forward and reverse reactions are elementary processes, which reaction has the larger numeric value of the rate constant, the forward or the reverse reaction?

Nitric oxide (NO) reacts readily with chlorine gas as follows: $$2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{NOCl}(g)$$ At \(700 \mathrm{~K},\) the equilibrium constant \(K_{p}\) for this reaction is \(2.6 \times 10^{-3}\). Predict the behavior of each of the following mixtures at this temperature and indicate whether or not the mixtures are at equilibrium. If not, state whether the mixture will need to produce more products or reactants to reach equilibrium. (a) $P_{\mathrm{NO}}=20.3 \mathrm{kPa}, P_{\mathrm{Cl}_{2}}=20.3 \mathrm{kPa}, R_{\mathrm{NOCl}}=20.3 \mathrm{kPa}$ (b) $P_{\mathrm{NO}}=25.33 \mathrm{kPa}, P_{\mathrm{Cl}_{2}}=15.2 \mathrm{kPa}, R_{\mathrm{NOCl}}=2.03 \mathrm{kPa}$ (c) $P_{\mathrm{NO}}=15.2 \mathrm{kPa}, P_{\mathrm{Cl}_{2}}=42.6 \mathrm{kPa}, P_{\mathrm{NOCl}}=5.07 \mathrm{kPa}$

If \(K_{c}=1\) for the equilibrium $3 \mathrm{~A}(g) \rightleftharpoons 2 \mathrm{~B}(g)$, what is the relationship between [A] and [B] at equilibrium?
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