Square Vessel
What is the equilibrium concentration of I2 in the gaseous mixture?
H2(g) + I2(g) ↔ 2HI Temperature = 731K
1.20 mol of H2 and 1.20 mol of I2 are placed in a 1.00 L vessel. What is the equilibrium concentration of I2 in the gaseous mixture?
The equilibrium constant is K = 49.0
HINT Normally you would need to solve a quadratic equation here since K is large.
However, in this case the intial concentrations of the two reactants are the same.
You can set up the equilbirium ratio (products over reactants) in terms of x, set it equal to K in the usual way,
then take the square root of both sides.
Then solve for x in the resulting linear equation.
OR you can solve the quadratic equation, if you prefer.
Let x be the number of moles of I2 that has reacted (out of the original 1.2 moles present) when the system is at equilibrium. From the stoichiometry of the reaction, we know that for every mole of I2 that reacts, one mole of H2 also reacts, so x is also the number of moles of H2 that has reacted when the system is at equilibrium.
Furthermore, we know from the reaction that every mole of O2 that reacts produces two moles of HI, so the amount of HI present at equilibrium is equal to 2x.
We can therefore write the equilibrium concentrations of the reactants and products as:
[H2] = (1.2 mol – x)/1 L
[I2] = (1.2 mol – x)/1 L
[HI] = 2x/1 L
The equilibrium constant for this reaction is given by:
K = 49 = ([HI]^2)/([H2]*[I2])
Plugging in the expressions for the equilibrium concentrations we wrote above, we have:
49 = ((2x)^2)/((1.2 – x)(1.2 – x)) = ((2x)^2)/((1.2 – x)^2)
(I’ve dropped the units here, but x has units of moles)
Take the square root of both sides:
7 = 2x/(1.2 – x)
8.4 – 7x = 2x
8.4 = 9x
0.933 mol = x
Plug this back into the expressions for the concentrations:
[H2] = [I2] = (1.2 mol – 0.933 mol)/1 L = 0.267 mol/L
[HI]= 2*0.933 mol/1 L = 1.867 mol/L
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