A reaction: A(aq)+B(aq)<-->C(aq)
has a standard free-energy change of
–4.69 kJ/mol at 25 °C.
What are the concentrations of A, B, and C at equilibrium if, at the beginning of the reaction, their concentrations are 0.30 M, 0.40 M, and 0 M, respectively?
I know you have to calculate K. So I did:
dG = -RT lnK
-4.69=-0.008314x298.15xln(K)
-1.893=ln(K)
e^-1893=K
K=.150
However, I don't know what to do afterwards.
Thanks in advance!
I thought you would just set up an ICE table and subtract .15 from the reactants and add .15 to the product but that is not right.
I figured it out. I got the wrong K value too.
You have to take e^-(-1.893)
so e^(1.893)=6.63
From there,
K=(x)/(.3-x)(.4-x) where K=6.63
Solve for x and you get 0.178
To find the values, plug in 0.178 for x to find values at equilibrium.
You got it. Great! Good work.
To determine the concentrations of A, B, and C at equilibrium, we can use the concept of equilibrium constant, K. The equilibrium constant is a ratio of the concentrations of the products to the concentrations of the reactants, raised to the power of their respective stoichiometric coefficients.
For the given reaction: A(aq) + B(aq) ⇌ C(aq)
The equilibrium constant expression can be written as: K = [C] / [A]^[a] * [B]^[b]
Here, [A], [B], and [C] represent the concentrations of A, B, and C at equilibrium, while [a] and [b] are the stoichiometric coefficients of A and B in the balanced equation.
You correctly calculated the value of K as 0.150. Now, to determine the concentrations at equilibrium, we can set up an ICE (Initial, Change, Equilibrium) table.
At the beginning of the reaction, the concentrations of A, B, and C are given as 0.30 M, 0.40 M, and 0 M, respectively. So, we can fill in the initial row of the table as:
A(aq) + B(aq) ⇌ C(aq)
Initial: 0.30 M 0.40 M 0 M
Let's assume that x represents the change in concentration of A and B that reaches equilibrium. So, the change row in the ICE table will be:
A(aq) + B(aq) ⇌ C(aq)
Change: -x M -x M +x M
The equilibrium row in the ICE table can be obtained by subtracting the changes from the initial concentrations:
A(aq) + B(aq) ⇌ C(aq)
Equilibrium: 0.30 M - x 0.40 M - x x M
At equilibrium, the concentrations of A and B will decrease by x, while the concentration of C will increase by x.
Using the equilibrium expression, we can write:
K = [C] / [A]^[a] * [B]^[b] = x / (0.30 - x)^[a] * (0.40 - x)^[b]
Now, we can substitute the value of K that you calculated earlier (0.150) into the equation:
0.150 = x / (0.30 - x)^[a] * (0.40 - x)^[b]
This equation is non-linear, and it is not straightforward to solve it analytically. However, you can use a numerical method like iteration or use software, such as Excel or Wolfram Alpha, to solve it.
By substituting different values of x into the equation, you can find the value of x that satisfies the equation. Once you have determined the value of x, you can substitute it back into the equilibrium row of the ICE table to find the equilibrium concentrations of A, B, and C.
Note: Keep in mind that, due to the quadratic nature of the equation, there might be two possible solutions. Hence, it's important to check the validity of the solutions to ensure they are physically meaningful for the given context.