In: Chemistry
Be sure to answer all parts. Phosgene (COCl2) is a toxic substance that forms readily from carbon monoxide and chlorine at elevated temperatures: CO(g) + Cl2(g) ⇌ COCl2(g) If 0.470 mol of each reactant is placed in a 0.500−L flask at 600 K, what are the concentrations of all three substances at equilibrium (Kc = 4.95 at this temperature)?
Initial concentration of CO = mol of CO / volume
= 0.470 mol / 0.500 L
= 0.940 M
Initial concentration of Cl2 = mol of Cl2 / volume
= 0.470 mol / 0.500 L
= 0.940 M
ICE Table:
Equilibrium constant expression is
Kc = [COCl2]/[CO]*[Cl2]
4.95 = (1*x)/((0.94-1*x)(0.94-1*x))
4.95 = (1*x)/(0.8836-1.88*x + 1*x^2)
4.374-9.306*x + 4.95*x^2 = 1*x
4.374-10.31*x + 4.95*x^2 = 0
This is quadratic equation (ax^2+bx+c=0)
a = 4.95
b = -10.31
c = 4.374
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 = 19.61
roots are :
x = 1.488 and x = 0.5937
x can't be 1.488 as this will make the concentration negative.so,
x = 0.5937
At equilibrium:
[CO] = 0.94-1x = 0.94-1*0.5937 = 0.346 M
[Cl2] = 0.94-1x = 0.94-1*0.5937 = 0.346 M
[COCl2] = +1x = +1*0.5937 = 0.594 M
[CO] = 0.346 M
[Cl2] = 0.346 M
[COCl2] = 0.594 M