A reaction :
A(aq)+B(aq) --> C(aq)
has a standard free-energy change of –4.01 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 used deltaG = -RT(lnK) to find that K= 5.04. Then I wasn't really sure what to do next. Please help.
I don't get 5.04 for K but you're on the right track.
-4010 = 8.413*298*lnK
K = ? I obtained approx 0.2
Then
...........A + B ==> C
I.......0.30.0.40...0.0
C.........-x...-x....x
E.....0.30-x..0.40-x..x
Substitute the E line into Kc expression and solve for x, then evaluate 0.40-x and 0.30-x/
I think it might be because you used 8.413 for R, I think R is supposed to be 8.314. So I think K is right if it is 5.04.
But I seem to be stick on the substitution part because I tried to solve it but I get 5.04 = x/(0.3-x)(0.4-x). Am I supposed to multiply it out and isolate the variable? Because if I was supposed to I got 5.04x^2-4.528x+0.6048=0 and I tried to put it in the quadratic formula to get x=.81 or x =.00612 but they are both wrong
To solve for the concentrations of A, B, and C at equilibrium, you can use the equilibrium constant expression and the stoichiometry of the reaction.
The balanced equation for the reaction is:
A(aq) + B(aq) → C(aq)
Let's use the notation [A], [B], and [C] to represent the concentrations of A, B, and C at equilibrium, respectively.
The equilibrium constant expression for this reaction is:
K = [C] / ([A] * [B])
Given that K = 5.04, we can set up the equation as:
5.04 = [C] / ([A] * [B])
At the beginning of the reaction, the concentrations are as follows:
[A] = 0.30 M
[B] = 0.40 M
[C] = 0 M
Substituting these values into the equation, we have:
5.04 = 0 / (0.30 * 0.40)
Since we cannot divide by zero, it indicates that the reaction has not yet reached equilibrium.
However, you can calculate the concentrations of A, B, and C at equilibrium based on the given K value.
Let's assume the equilibrium concentrations as follows:
[A] = x M
[B] = x M
[C] = y M
Now, substitute these concentrations into the equilibrium constant expression:
5.04 = y / (x * x)
To solve for x and y, rearrange the equation:
y = 5.04 * x^2
Since the stoichiometry of the reaction is 1:1 for A and B, the concentration of C will also be x.
Now, substitute y = x and rearrange the equation to solve for x:
5.04 = x / (x * x)
5.04 = 1 / x
x = 1 / 5.04
The concentration of A, B, and C at equilibrium is 1 / 5.04 M, which is approximately 0.1984 M.
To determine the concentrations of A, B, and C at equilibrium, you can use the equilibrium constant (K) expression and the concept of stoichiometry.
Here's how you can proceed:
1. Write the equilibrium constant expression (K) for the given reaction:
K = [C] / ([A] * [B])
2. Substitute the given values into the equation:
K = [C] / ([A] * [B])
K = [C] / (0.30 M * 0.40 M)
3. Rearrange the equation to solve for [C]:
[C] = K * [A] * [B]
[C] = 5.04 * 0.30 M * 0.40 M
4. Calculate the concentration of C:
[C] = 0.6048 M
So, at equilibrium, the concentration of substance C will be 0.6048 M.
To determine the concentrations of substances A and B, you can use the stoichiometry of the reaction, assuming the reaction goes to completion.
From the balanced equation, we know that for every 1 mole of A reacting, 1 mole of C is produced and 1 mole of B is consumed.
5. Calculate the number of moles of A reacting:
moles of A = initial concentration of A * volume of the solution
Here, we assume that the volume of the solution is 1L:
moles of A = 0.30 M * 1 L
6. Calculate the moles of C produced:
moles of C = moles of A * molar ratio of C to A
From the balanced equation, the molar ratio of C to A is 1:1.
7. Calculate the moles of B consumed:
moles of B = moles of C
8. Calculate the concentration of A at equilibrium:
[A] = (moles of A - moles of C) / volume of the solution
Substitute the calculated values into the equation:
[A] = (0.30 M * 1 L - moles of C) / 1 L
9. Calculate the concentration of B at equilibrium:
[B] = moles of B / volume of the solution
[B] = moles of C / 1 L
10. Substitute the calculated values into the equations to find the concentrations of A and B at equilibrium.
By following these steps, you can determine the concentrations of A, B, and C at equilibrium for the given reaction.