A mixture of 0.438 M H2, 0.444 M I2 , and 0.895 M HI is enclosed in a vessel and heated to 430 °C. H2 (g) + I2 (g) <> 2 HI (g) Kc = 54.3 at 430∘C Calculate the equilibrium concentrations of each gas at 430∘C.

[H₂]  = 0.178 M

[I₂]    = 0.184 M

[HI]   = 1.415 M

Explanation:

For the equilibrium:

H₂(g) + I₂(g) ⇄ 2 HI(g)

the equilibrium constant is given by the equation:

Kc = [ HI]² / [H₂][I₂]

Lets use first the reaction quotient which has the same expression as the equilibrium constant to predict the direction the reaction will take, i.e towards reactants or product side.

Q =( 0.895)²/(0.438)(0.444) = 4.12

Q is less than Kc so the reaction will favor the product side.

We can set up the following table to account for all the species at equilibrium:

                                     H₂             I₂                HI

initial                        0.438        0.444          0.895

change                        -x               -x                +2x

equilibrium              0.438 - x    0.444 - x     0.895 + 2x

Now we are in position to express these concentrations  in terms of the equilibrium conctant, Kc

54.3 = (0.895 + 2x)² / (0.438 -x)(0.444 - x)

performing the calculatiopns will result in a quadratic equation:

0.801 + 3.580x +4x² = (0.194 - 0.882x + x²)x 54.3

Upon rearrangement and some algebra, we have

0.801 + 3.580 x + 4x² = 10.534 - 47.893x + 54.3 x²

0 = 9.733 - 51.473 x + 54.3 x²

This equation has two roots X₁ = 0.687 and X₂ = 0.26

The first is physically impossible since it will imply that more 0.687 will make the quantity at equilibrium for both H₂ and I₂ negative.

Therefore the concentrations at equilibrium of each  gas are:

[H₂] = (0.438 - 0.260)              = 0.178 M

[I₂]   = (0.444 - 0.260) M          = 0.184  M

[HI] = [0.895 + 2x(0.260)] M    = 1.415   M

Note if we plug these values into the equilibrium expression we get 61 which is due to the rounding errors propagating in the quadratic equation.

the ideal gas law equation is as follows

pv = nrt

where p - pressure

v - volume

n - number of moles

r - universal gas constant

t - temperature

so if the pressure, volume and temperature are already known

we are left with n and r

since r is the universal gas constant that has a known fixed value then r too is known

so we are left with 'n'

once we know temperature volume and pressure

we can find the number of moles of gas present using the ideal gas law equation

this is not my own answer, this is an answer for the same question by the user blahblahmali. i do not claim ownership of this account.