Calculating equilibrium concentrations when the net reaction proceeds in reverse

Question

Calculating equilibrium concentrations when the net reaction proceeds in reverse Consider mixture C, which will cause the net reaction to proceed in reverse ? net Concentration (M) XY X] nitia change equilibrium: 0.200 0.300 0.300 0.200 + x 0.300-? 0.300 x The change in concentration, 2, is positive for the reactants because they are produced and negative for the products because they are consumed Part C Based on a Kc value of 0.240 and the data table given, what are the equilibrium concentrations of XY, X, and Y, respectively? Express the molar concentrations numerically View Available Hint(s) XY. [X, [Y]-1.37, -0.87, 0.87 Submit Previous Answers Request Answer Incorrect; Try Again; 3 attempts remaining

Explanation / Answer

sol :-

Because the net reaction proceeds in the reverse direction , therefore given value of Kc get reciprocal for the reverse equation . i.e for the reverse equation Kc = 1 / 0.240

Now , expression of Kc for the reverse reaction will be :

Kc = [XY] / [X] [Y] ................(1)

Kc i.e equilibrium constant is define as the ratio of product of the molar concentration of products to the product of the molar concentration of reactants raised to power their stoichiometric coefficients at equilibrium stage .

therefore , from equation (1) we have

1 / 0.240 = 0.200 + x / (0.300 - x )2 ( here ,x = number of moles dissociated per unit time)

on cross multiplication , we have

(0.300 - x)2 = 0.240(0.200 + x)

(0.300)2 + x2 - 2(0.300)x = 0.048 + 0.240x

0.09 + x2 - 0.6x - 0.240x - 0.048 = 0

x2 - 0.84x + 0.042 = 0

Now , by using Quadratic formula to solve for x i.e

x = - (-0.84) +- ( -0.842 - 4 X1 X 0.042 )1/2 / 2

x = 0.84 +- ( 0.5373)1/2 / 2

x = 0.84 +- 0.733 /2

taking +ve sign , x = 0.84 + 0.733 / 2 = 0.7865 ( which is not possible , because initial concentation of reacting species are less i.e only 0.300 M).

therefore , x = 0.84 - 0.733 /2 ( by taking -ve sign )

= 0.107 / 2

= 0.0535 (possible)

hence, value of x = 0.0535

Therefore , [X] = [Y] = 0.300 - x = 0.300 - 0.0535 = 0.2465M

and [XY] = 0.200 + x = 0.200+ 0.0535 = 0.2535 M

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