Calculate the equilibrium concentrations of N2O4 and NO2 at 25 ∘C in a vessel that contains an initial N2O4 concentration of 0.0365 M . The equilibrium constant Kc for the reaction N2O4(g)⇌2NO2(g) is 4.64×10−3 at 25 ∘C.
Express your answers using four decimal places separated by a comma.
ICE Table:
[N2O4] [NO2]
initial 0.0365
change -1x +2x
equilibrium 0.0365-1x +2x
Equilibrium constant expression is
Kc = [NO2]^2/[N2O4]
0.00464 = (4*x^2)/((3.65*10^-2-1*x))
1.694*10^-4-4.64*10^-3*x = 4*x^2
1.694*10^-4-4.64*10^-3*x-4*x^2 = 0
This is quadratic equation (ax^2+bx+c=0)
a = -4
b = -4.64*10^-3
c = 1.694*10^-4
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 = 2.731*10^-3
roots are :
x = -7.113*10^-3 and x = 5.953*10^-3
since x can't be negative, the possible value of x is
x = 5.953*10^-3
At equilibrium:
[N2O4] = 0.0365-1x = 0.0365-1*0.00595 = 0.03055 M
[NO2] = +2x = +2*0.00595 = 0.01191 M
0.0306 , 0.0119 M
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