ivera Suppose A 250mL Flask re httpswwwawhalekscomalekscgi

ivera × Suppose A 250-mL Flask × re https://www-awh.aleks.com/alekscgi/x/lsl.exe/1o_u-lgNslkr7j8P3jH-IQT3rv1gTPrkicRI6pS60AVDiQYFU2vvpW5CMM9duvobhv KINETICS AND EQUILIBRIUM Calculating equilbrium composition from an equilbrium constant Suppose a 500. mL flask is filled with 0.40 mol of H2 and 1.4 mol of HCL. The following reaction becomes possible: H2(g)+CI2(g)2HCI(g) The equilibrium constant K for this reaction is 0.473 at the temperature of the flask. Calculate the equilibrium molarity of H2. Round your answer to two decimal places. Explanation Check

Solution

volume = 500 mL = 0.500 L

initial concentration of H2 = number of mol of H2 / volume
= 0.40 mol / 0.500 L
= 0.80 M

initial concentration of HCl = number of mol of HCl / volume
= 1.4 mol / 0.500 L
= 2.8 M

ICE Table:

                    [H2]                [Cl2]               [HCl]             

initial             0.8                 0                   2.8               

change              +1x                 +1x                 -2x               

equilibrium         0.8+1x              +1x                 2.8-2x            

Equilibrium constant expression is
Kc = [HCl]^2/[H2]*[Cl2]
0.473 = (2.8-2x)^2 / (0.8+x)*x
0.473 = (7.84-11.2*x + 4*x^2)/((0.8 + 1*x)(1*x))
0.473 = (7.84-11.2*x + 4*x^2)/(0.8*x + 1*x^2)
0.3784*x + 0.473*x^2 = 7.84-11.2*x + 4*x^2
-7.84 + 11.5784*x-3.527*x^2 = 0
This is quadratic equation (ax^2+bx+c=0)
a = -3.527
b = 11.58
c = -7.84

Roots can be found by
x = {-b + sqrt(b^2-4*a*c)}/2a
x = {-b - sqrt(b^2-4*a*c)}/2a

b^2-4*a*c = 23.45

roots are :
x = 0.9549 and x = 2.328

x can\'t be 2.328 as this will make the concentration negative.so,
x = 0.9549

At equilibrium:
[H2] = 0.8+1x = 0.8+1*0.95486 = 1.75486 M

Answer: 1.75 M