Question

At 500 °C, hydrogen iodide decomposes according to 2HI(g) ↽−−⇀ H₂(g) + I₂(g) For HI(g) heated to 500 °C in a 1.00 L reaction vessel, chemical analysis determined these concentrations at equilibrium: [H₂]=0.307 M , [I₂]=0.307 M , and [HI]=2.59 M . If an additional 1.00 mol of HI(g) is introduced into the reaction vessel, what are the equilibrium concentrations after the new equilibrium has been reached?

Answer 1

Answer:

$[HI]_{eq}=2.902M$

$[I_2]_{eq}=0.344M$

$[H_2]_{eq}=0.344M$

Explanation:

Hello,

At first, with the equilibrium concentrations we compute the equilibrium constant as:

$K=\frac{[H_2]_{eq}[I_2]_{eq}}{[HI]_{eq}^2}=\frac{(0.307M)(0.307M)}{(2.59M)^2} =0.0141$

Now, as 1 mol of HI is added, it has now a 3.59-M concentration, so one modifies the equilibrium based on the new conditions and change, x:

$0.0141=\frac{(x)(x)}{(3.59M-2x)^2} \\0.0141=\frac{x^2}{12.89-3.59x+4x^2} \\0.0141(12.89-14.36x+4x^2)=x^2\\0.1817-0.2025x-0.9436x^2=0\\x_1=-0.559M\\x_2=0.344M$

Finally, the new equilibrium concentrations are:

$[HI]_{eq}=3.59M-2(0.344M)=2.902M$

$[I_2]_{eq}=0.344M$

$[H_2]_{eq}=0.344M$

Best regards.

Answer 2

The equilibrium concentration after the addition of 1 mol HI are, HI = 2.1398 M, hydrogen = 0.2251 M, and iodine = 0.2251 M.

What is an equilibrium constant?

Equilibrium constant is the ratio of the concentration of reactants and products raised to the stoichiometric coefficient at equilibrium.

The equilibrium constant (K) for the decomposition of HI is given as:

$K=\rm \dfrac{[H_2]\;[I_2]}{[HI]^2}$

The substituting the equilibrium concentration for K:

$K=\dfrac{[0.307]\;[0.307]}{[2.59]^2}\\ K=0.014$

The addition of 0.1 mol HI has the change in the equilibrium concentrations. The new equilibrium concentration is given in the ICE table attached below.

Substituting the value of equilibrium concentrations for K:

$0.014=\dfrac{[x]\;[x]}{[2.59-2x]^2}\\ 0.014=\dfrac{x^2}{5.931-10.36x+x^2} \\\\x=0.2251, -0.3709$

The value of concentration is positive, thus x is 0.2251.

The concentration of the compounds at equilibrium is:

• Hydrogen = 0.2251 M
• Iodine = 0.2251 M
• HI= 2.1398 M

Learn more about equilibrium concentration, here:

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