Question

Kp for the decompositions of ammonium hydrogren sulfide is 1.8 x 10^-4 at 25 degrees celcius.

NH₄HS (g) <--> NH₃ (g) + H₂S (g)

When 0.020 atm NH₄HS is placed in a flask and allowed to come to equilibrium, what are the consentrations NH₃ (g) and H₂S (g)?

Please show ICE table and how how quadratic equation is used. Thanks.

Answer 1

Considering the decomposition of ammonium hydrogen sulphide reaction we can draw the ICE table :

                                 NH₄HS_(g)    NH_3(g) +    H₂S(g)

Initial amounts          0.020 M         0               0

change in amounts     -x                      +x              +x

equillibium amounts   (0.020-x)           (0+x)           (0+x)

Now for finding out the concentrations of NH3 and H2S we will find the value of Kc first by the equation :

          Kp = Kc (RT)ⁿ

          Kc = 1.8 x 10^-4[(0.0821L-atm/mole-K) (298K)] ¹

                     = 7.36 x 10^-6

nowsince Kc = [ NH3] [H2S] / [ NH3HS]

putting the ICE table values

          7.36 x 10^-6 = (x) (x) / ( 0.020 - x)

         x² = 7.36 x 10^-6 (0.020 - x)

          x² + (7.36x 10^-6 ) x - (1.472 x 10^-7)

this is a form of quadratic equation ax² + bx + c = 0

here a = 1 , b= 7.36 x 10^-6 , c = - 1.472 x 10^-7

this equation has the solution x = -b b² - 4ac / 2a

by putting the values in the above equation and solving all we get the value of x = 0.00038 M

So at equillibrium the concentrations of NH3 and H2S will be 0.00038M.

How quadratic equation was used you can see in the uploaded picture :