Question

When determining the equilibrium concentrations for the reaction AB(g) = A(g) + B(g) Kc = [A][B] [AB] a simplifying assumption can be used under certain conditions to avoid solving a quadratic equation. Kc = [AB] – [AB] Classify each situation by whether the simplifying assumption can be used or whether the quadratic formula is required. Simplifying assumption can be used Quadratic formula required (AB) - 0.0168 M, K. = 2.26 x 10-6 (AB) = 0.154 M, K. = 2.72 x 10-4 (AB) = 0.00211 M, K. = 1.68 x 10-6 [AB] = 0.0242 M, Ke = 8.48 x 10-5 [AB] = 0.331 M, K. = 1.97 x 10-3

Answer 1

sol:-

we can take assumption only if x < 5% and we can neglect to solve quadratic equation. otherwise we have to solve quadratic equation.

1):- [AB] = 0.0168 , Kc = 2.26 * 10-6

ans. :- let x is less than 5% so we can solve without calculation.

Kc = x2/[AB]

2.26 * 10-6 * [AB] = x2

2.26 * 10-6 * 0.0168 = x2

x = (0.37968 * 10-6)1/2

= 0.194853 * 10-3

x% = (0.194853 * 10-3 / 0.0168)*100

= 0.011598 * 100

= 1.1598 % which is less than 5% so we can solve this without quadratic equation

2):-[AB] =0.00211 , Kc = 1.68 * 10-6

now again let x is less than 5% so we can solve without quadratic equation.

From question,

x2 = Kc * [AB]

x = (Kc * [AB] )1/2

= (1.68 * 10-6 * 0.00211)1/2

= 0.059538 * 10-3

x % = {(0.059538 * 10-3)/0.00211} * 100

= 0.028217 * 100

= 2.8217% which is also less than 5% so we can solve it without quadratic equation.

3):- [ AB] = 0.331 , Kc = 1.97 * 10-3

again let x is less than 5% so,

x =( Kc * [AB])1/2

= (1.97 * 10-3 * 0.331 )1/2

= 0.0255

x% =( 0.0255 /0.331)* 100

= 0.07703 * 100

= 7.703 % this is greater than 5% so we have to  solve this one from quadratic expression.

4):- [AB] = 0.154 , Kc = 2.72 * 10-4

let again x is less than 5% so,

x = (Kc * [AB])1/2

= (2.72 * 10-4 * 0.154)1/2

= 0.64720 * 10-2

x% ={ (0.64720 * 10-2)/0.154} * 100

= 0.04202 * 100

= 4.202 % which is less than 5% so we can solve it without quadratic equation.

5):-[AB] = 0.0242 , Kc = 8.48 * 10-5

again let x is less than 5% so we can use without quadratic equation,

hence

x = (Kc * [AB] )1/2

= (8.48 * 10-5 * 0.0242)1/2

= 0.14325 * 10-2

so x% ={ (0.14325 * 10-2)/0.0242} * 100

= 0.059194 * 100

= 5.9194% which is greater than 5% so we have to solve it from quadratic equation.