The equilibrium A ? B is first-order in both directions. We will now do a step-by-step derivation of an expression for the concentration of A as a function of time. (i) Given the initial molar concentrations of A and B are [A]0 and [B]0 , derive an expression for d[A]/dt that includes only constants and the variable [A] (ii) Re-arrange this expression so it is of the form dy/dx + yf(x) = g(x) where f(x) and g(x) are constants. Derive an integrated expression for the concentration of A . (iv) Use the boundary condition that at time t = 0, the concentration of [A] = [A]0 in order to determine the constant of integration. (v) Write the simplified final expression for the concentration of A as a function of time. (vi) In order to be confident our answer is correct, determine the final composition of the system (ie, what is [A] as t ? ?)? Consider two limiting scenarios (a) Keq << 1 and (b) Keq >> 1 and show that final composition makes sense.
SEE ATTACHED IMAGE FOR A BETTER DESCRIPTION! Please answer all parts of the question in detail, I am very confused. Thank you!
(17) The equilibrium A B is first-order in both directions. We will now do a step-by-step derivation of an expression for the concentration of A as a function of time. (i) Given the initial molar concentrations of A and B are [Alo and LBJo, derive an expression for dLAJ/dt that includes only constants and the variable [A] (ii Re-arrange this expression so it is of the form dy dx where fx) and g00 are constants. (iii) the solution of such a differential equation is given by eh eha g(x) dx constant h(x) where h(x) j f(x)dx. Derive an integrated expression for the concentration of A (iv) Use the boundary condition that at time t- 0, the concentration of[AF[Alo in order to determine the constant of integration. (v) Write the simplified final expression for the concentration of A as a function of time. (vi In order to be confident our answer is correct, determine the final composition of the system (ie, what is [A] as t oo)? Consider two limiting scenarios (a) Keq 1 and (b) Keq 1 and show that final composition makes sense.
