Answer :
To solve for the equilibrium concentrations of PQ and R when given the initial concentrations of reactants P and Q in a chemical equilibrium scenario, we need to follow several steps. However, because we do not have the equilibrium constant (K), we can only set up the equations but cannot find the numerical values of the equilibrium concentrations.
Let's assume the reaction is:
[tex]\[ P + Q \rightleftharpoons PQ + R \][/tex]
### Step-by-Step Solution
1. Initial Concentrations:
- Initial concentration of P: [tex]\( [P]_0 = 0.0833 \)[/tex] M
- Initial concentration of Q: [tex]\( [Q]_0 = 0.0833 \)[/tex] M
- Initial concentration of PQ: [tex]\( [PQ]_0 = 0 \)[/tex] M
- Initial concentration of R: [tex]\( [R]_0 = 0 \)[/tex] M
2. Change in Concentrations:
- As the reaction reaches equilibrium, let's denote the amount of P and Q that react as [tex]\( x \)[/tex] M.
- For each mole of P or Q that reacts, 1 mole of PQ and 1 mole of R is produced.
Therefore, the change in concentrations at equilibrium will be:
- Concentration of P decreases by [tex]\( x \)[/tex] M: [tex]\( [P] = 0.0833 - x \)[/tex] M
- Concentration of Q decreases by [tex]\( x \)[/tex] M: [tex]\( [Q] = 0.0833 - x \)[/tex] M
- Concentration of PQ increases by [tex]\( x \)[/tex] M: [tex]\( [PQ] = x \)[/tex] M
- Concentration of R increases by [tex]\( x \)[/tex] M: [tex]\( [R] = x \)[/tex] M
3. Equilibrium Concentrations:
At equilibrium, the concentrations will be:
- [tex]\( [P] = 0.0833 - x \)[/tex] M
- [tex]\( [Q] = 0.0833 - x \)[/tex] M
- [tex]\( [PQ] = x \)[/tex] M
- [tex]\( [R] = x \)[/tex] M
4. Equilibrium Expression:
The equilibrium expression for the reaction [tex]\( P + Q \rightleftharpoons PQ + R \)[/tex] is given by the equilibrium constant [tex]\( K \)[/tex]:
[tex]\[ K = \frac{[PQ][R]}{[P][Q]} \][/tex]
Substituting the equilibrium concentrations, we get:
[tex]\[ K = \frac{(x)(x)}{(0.0833 - x)(0.0833 - x)} \][/tex]
[tex]\[ K = \frac{x^2}{(0.0833 - x)^2} \][/tex]
Unfortunately, without the value of the equilibrium constant [tex]\( K \)[/tex], we cannot solve for [tex]\( x \)[/tex] and thus cannot determine the numerical values of the equilibrium concentrations.
In summary, the equilibrium concentrations are:
- [tex]\( [P] = 0.0833 - x \)[/tex] M
- [tex]\( [Q] = 0.0833 - x \)[/tex] M
- [tex]\( [PQ] = x \)[/tex] M
- [tex]\( [R] = x \)[/tex] M
To solve for [tex]\( x \)[/tex] and find the exact equilibrium concentrations, the value of the equilibrium constant [tex]\( K \)[/tex] is required.
Let's assume the reaction is:
[tex]\[ P + Q \rightleftharpoons PQ + R \][/tex]
### Step-by-Step Solution
1. Initial Concentrations:
- Initial concentration of P: [tex]\( [P]_0 = 0.0833 \)[/tex] M
- Initial concentration of Q: [tex]\( [Q]_0 = 0.0833 \)[/tex] M
- Initial concentration of PQ: [tex]\( [PQ]_0 = 0 \)[/tex] M
- Initial concentration of R: [tex]\( [R]_0 = 0 \)[/tex] M
2. Change in Concentrations:
- As the reaction reaches equilibrium, let's denote the amount of P and Q that react as [tex]\( x \)[/tex] M.
- For each mole of P or Q that reacts, 1 mole of PQ and 1 mole of R is produced.
Therefore, the change in concentrations at equilibrium will be:
- Concentration of P decreases by [tex]\( x \)[/tex] M: [tex]\( [P] = 0.0833 - x \)[/tex] M
- Concentration of Q decreases by [tex]\( x \)[/tex] M: [tex]\( [Q] = 0.0833 - x \)[/tex] M
- Concentration of PQ increases by [tex]\( x \)[/tex] M: [tex]\( [PQ] = x \)[/tex] M
- Concentration of R increases by [tex]\( x \)[/tex] M: [tex]\( [R] = x \)[/tex] M
3. Equilibrium Concentrations:
At equilibrium, the concentrations will be:
- [tex]\( [P] = 0.0833 - x \)[/tex] M
- [tex]\( [Q] = 0.0833 - x \)[/tex] M
- [tex]\( [PQ] = x \)[/tex] M
- [tex]\( [R] = x \)[/tex] M
4. Equilibrium Expression:
The equilibrium expression for the reaction [tex]\( P + Q \rightleftharpoons PQ + R \)[/tex] is given by the equilibrium constant [tex]\( K \)[/tex]:
[tex]\[ K = \frac{[PQ][R]}{[P][Q]} \][/tex]
Substituting the equilibrium concentrations, we get:
[tex]\[ K = \frac{(x)(x)}{(0.0833 - x)(0.0833 - x)} \][/tex]
[tex]\[ K = \frac{x^2}{(0.0833 - x)^2} \][/tex]
Unfortunately, without the value of the equilibrium constant [tex]\( K \)[/tex], we cannot solve for [tex]\( x \)[/tex] and thus cannot determine the numerical values of the equilibrium concentrations.
In summary, the equilibrium concentrations are:
- [tex]\( [P] = 0.0833 - x \)[/tex] M
- [tex]\( [Q] = 0.0833 - x \)[/tex] M
- [tex]\( [PQ] = x \)[/tex] M
- [tex]\( [R] = x \)[/tex] M
To solve for [tex]\( x \)[/tex] and find the exact equilibrium concentrations, the value of the equilibrium constant [tex]\( K \)[/tex] is required.
