Question
In a closed rigid vessel, the following equilibrium partial pressures are measured, where N2 = 100 mm, H2 = 400 mm and NH3 = 1000 mm. Now, nitrogen is removed from the vessel until the pressure of hydrogen at equilibrium is equal to 700 mm. The new equilibrium partial pressure of N2 is
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Solution
N2 + 3H2 $\rightleftharpoons$ 2NH3
Equ. partial pressure 100 mm 400 mm 1000 mm
New equ. partial pressure 100 – a + x 400 + 3x = 700 mm 1000 – 2x = 800 mm
∴ x = 100 mm
Now, $K_{P} = \frac{1000^{2}}{100 \times 400^{3}} = \frac{800^{2}}{P_{N_{2}} \times 700^{3}} \Rightarrow P_{N_{2}} = 11.94\text{ mm}$
$K_{1} = \frac{\lbrack B\rbrack}{\lbrack A\rbrack},K_{2} = \frac{\lbrack C\rbrack}{\lbrack A\rbrack}$
Now, $X_{A} = \frac{\lbrack A\rbrack}{\lbrack A\rbrack + \lbrack B\rbrack + \lbrack C\rbrack} = \frac{\lbrack A\rbrack}{\lbrack A\rbrack + K_{1}\lbrack A\rbrack + K_{2}\lbrack A\rbrack} = \frac{1}{1 + K_{1} + K_{2}}$
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