Consider the hypothetical reaction A(g) + 2 B(g) ⇌ 2 C(g), for which Kc = 0.25 at a certain temperature. A1.00-L reaction vessel is loaded with 1.00 mol of compoundC, which is allowed to reach equilibrium. Let thevariable x represent the number of mol/L of compoundA present at equilibrium. (a) In terms of x, what are theequilibrium concentrations of compounds B and C?(b) What limits must be placed on the value of x so thatall concentrations are positive? (c) By putting the equilibriumconcentrations (in terms of x) into the equilibriumconstantexpression, derive an equation that can besolved for x. (d) The equation from part (c) is a cubic equation(one that has the form ax3 + bx2 + cx + d = 0). Ingeneral, cubic equations cannot be solved in closed form.However, you can estimate the solution by plotting thecubic equation in the allowed range of x that you specifiedin part (b). The point at which the cubic equationcrosses the x-axis is the solution. (e) From the plot in part(d), estimate the equilibrium concentrations of A, B, andC. (Hint: You can check the accuracy of your answer bysubstituting these concentrations into the equilibriumexpression.)
Consider the hypothetical reaction A(g) + 2 B(g) ⇌ 2 C(g), for which Kc = 0.25 at a certain temperature. A
1.00-L reaction vessel is loaded with 1.00 mol of compound
C, which is allowed to reach equilibrium. Let the
variable x represent the number of mol/L of compound
A present at equilibrium. (a) In terms of x, what are the
equilibrium concentrations of compounds B and C?
(b) What limits must be placed on the value of x so that
all concentrations are positive? (c) By putting the equilibrium
concentrations (in terms of x) into the equilibriumconstant
expression, derive an equation that can be
solved for x. (d) The equation from part (c) is a cubic equation
(one that has the form ax3 + bx2 + cx + d = 0). In
general, cubic equations cannot be solved in closed form.
However, you can estimate the solution by plotting the
cubic equation in the allowed range of x that you specified
in part (b). The point at which the cubic equation
crosses the x-axis is the solution. (e) From the plot in part
(d), estimate the equilibrium concentrations of A, B, and
C. (Hint: You can check the accuracy of your answer by
substituting these concentrations into the equilibrium
expression.)
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 6 images
