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Chapter 15: Problem 34

Gaseous hydrogen iodide is placed in a closed container at \(425^{\circ} \mathrm{C},\) 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 \([\mathrm{HI}]=3.53 \times 10^{-3} \mathrm{M},\left[\mathrm{H}_{2}\right]=4.79 \times 10^{-4} \mathrm{M}\) and \(\left[\mathrm{I}_{2}\right]=4.79 \times 10^{-4} \mathrm{M} .\) What is the value of \(K_{c}\) at this temperature?

Short Answer

Expert verified
The equilibrium constant, \(K_c\), for the reaction \(2HI(g) \rightleftharpoons H_{2}(g) + I_{2}(g)\) at the given temperature and concentrations is approximately 0.035.

Step by step solution

01

1. Write down the balanced chemical equation

First, we write the balanced chemical equation for the given reaction: \[ 2HI(g) \rightleftharpoons H_{2}(g) + I_{2}(g) \]
02

2. Write the expression for the equilibrium constant, \(K_c\)

For the given balanced chemical equation, the equilibrium constant expression is: \[ K_c = \frac{[H_2][I_2]}{[HI]^2} \]
03

3. Substitute the given equilibrium concentrations into the \(K_c\) expression

We are given the equilibrium concentrations of each species: \([HI] = 3.53 \times 10^{-3} M\), \([H_2] = 4.79 \times 10^{-4} M\), and \([I_2] = 4.79 \times 10^{-4} M\). Substitute these values into the \(K_c\) expression: \[ K_c = \frac{(4.79 \times 10^{-4})(4.79 \times 10^{-4})}{(3.53 \times 10^{-3})^2} \]
04

4. Calculate \(K_c\)

Now, simply perform the calculation: \[ K_c = \frac{(4.79 \times 10^{-4})(4.79 \times 10^{-4})}{(3.53 \times 10^{-3})^2} \approx 0.035 \]
05

5. State the final result

The equilibrium constant, \(K_c\), for the given reaction and temperature is approximately 0.035.

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Most popular questions from this chapter

Solid \(\mathrm{NH}_{4} \mathrm{SH}\) is introduced into an evacuated flask at \(24{ }^{\circ} \mathrm{C}\). The following reaction takes place: $$\mathrm{NH}_{4} \mathrm{SH}(s) \rightleftharpoons \mathrm{NH}_{3}(g)+\mathrm{H}_{2} \mathrm{~S}(g)$$ At equilibrium the total pressure (for \(\mathrm{NH}_{3}\) and \(\mathrm{H}_{2} \mathrm{~S}\) taken together) is 0.614 atm. What is \(K_{p}\) for this equilibrium at \(24^{\circ} \mathrm{C}\) ?

\(\mathrm{NiO}\) is to be reduced to nickel metal in an industrial process by use of the reaction $$\mathrm{NiO}(s)+\mathrm{CO}(g) \rightleftharpoons \mathrm{Ni}(s)+\mathrm{CO}_{2}(g)$$ At \(1600 \mathrm{~K}\) the equilibrium constant for the reaction is \(K_{p}=6.0 \times 10^{2}\). If a CO pressure of 150 torr is to be employed in the furnace and total pressure never exceeds 760 torr, will reduction occur?

For the equilibrium $$2 \mathrm{IBr}(g) \rightleftharpoons \mathrm{I}_{2}(g)+\mathrm{Br}_{2}(g)$$ \(K_{p}=8.5 \times 10^{-3}\) at \(150^{\circ} \mathrm{C}\). If 0.025 atm of IBr is placed in a 2.0-L container, what is the partial pressure of all substances after equilibrium is reached?

A mixture of \(\mathrm{CH}_{4}\) and \(\mathrm{H}_{2} \mathrm{O}\) is passed over a nickel catalyst at \(1000 \mathrm{~K}\). The emerging gas is collected in a \(5.00-\mathrm{L}\) flask and is found to contain \(8.62 \mathrm{~g}\) of \(\mathrm{CO}, 2.60 \mathrm{~g}\) of \(\mathrm{H}_{2}, 43.0 \mathrm{~g}\) of \(\mathrm{CH}_{4},\) and \(48.4 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O} .\) Assuming that equilibrium has been reached, calculate \(K_{c}\) and \(K_{p}\) for the reaction.

Calculate \(K_{c}\) at \(303 \mathrm{~K}\) for \(\mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{SO}_{2} \mathrm{Cl}_{2}(g)\) if \(K_{p}=34.5\) at this temperature.
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