The equilibrium concentrations in a gas mixture at a particular temperature are

Question

The equilibrium concentrations in a gas mixture at a particular temperature are 0.12 M H2, 0.72 M I2, and 2.0 M HI. What equilibrium concentrations are obtained at the same temperature when 0.22 mol of HI is injected into an empty 500.0 mL container?

Explanation / Answer

The reversible reaction is : H2 + I2 = 2HI I have used the '=' to represent revesible So, K = (2^2)/(0.12*0.72) = 46.2963 When 0.22 mole of HI is injected, the above reaction follows the reverse path Hence, K for that reaction = 1/46.2963 = 0.0216 Let 'x' moles of HI decomposes => '2x' moles each of H2 and I2 is formed => 0.0216 = [(2x/500)(2x/500)]/[(0.22-x)/500]^2 => 0.0216 = (4x^2)/(0.22-x)^2 => 0.14697 = 2x/(0.22-x) => x = 0.0151 moles Hence, final concentration of: HI = (0.22-0.0151)/(500/1000) = 0.4098 M H2 = (2*0.0151)/(500/1000) = 0.0604 M I2 = (2*0.0151)/(500/1000) = 0.0604 M

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