For the reaction below at a certain temperature, it is found that the equilibrium concentrations in a 4.87-L rigid container are
[H2] = 0.0496 M
[F2] = 0.0116 M
[HF] = 0.429 M.
H2(g) + F2(g) <==> 2 HF(g)
If 0.185 mol of F2 is added to this equilibrium mixture, calculate the concentrations of all gases once equilibrium is reestablished.
K = (HF)^2/(H2)(F2).
Substitute equilibrium concns and calculate K.
Then
0.185 mol F2/4.87 L = 0.0380 M added. The equilibrium concns become the initial values for the next calculation.
.......H2 + F2 ==> 2HF
I..0.0496..0.0116..0.429
add........0.0380........
C.....-x...-x........+2x
E..0.0496-x..0.0496-x..0.429+2x
Substitute the E line into a new Ka expression and solve for x, then evaluate the E line for final concentrations.
To calculate the concentrations of all gases once equilibrium is reestablished after adding F2, we can use the concept of the reaction quotient (Q) and the principle of Le Chatelier.
1. Calculate the initial value of the reaction quotient (Q):
The reaction quotient (Q) is calculated by dividing the product of the concentrations of the products by the product of the concentrations of the reactants. Using the given initial concentrations, we can calculate Q:
Q = [HF]^2 / ([H2] * [F2])
2. Calculate the change in concentration of F2:
Since 0.185 mol of F2 is added, the change in concentration of F2 is:
Change in [F2] = initial [F2] (after adding) - initial [F2] (before adding)
Change in [F2] = (0.0116 + 0.185) M - 0.0116 M
3. Use Le Chatelier's principle to determine the direction of the shift and the change in concentrations of H2 and HF:
The addition of F2 disrupts the equilibrium, causing the system to shift in the direction that minimizes the change. According to Le Chatelier's principle, the system will shift to the left to consume the excess F2 and form more HF. As a result, the concentrations of H2 and HF will increase, while the concentration of F2 will decrease.
4. Calculate the new equilibrium concentrations:
Let x represent the change in concentration of F2, H2, and HF. Since the stoichiometric coefficient for F2 in the balanced equation is 1, the change in concentration of H2 and HF will be 2x. The new equilibrium concentrations can be calculated as follows:
[H2] = initial [H2] + 2x
[F2] = initial [F2] - x
[HF] = initial [HF] + 2x
5. Set up the equilibrium expression and calculate x:
Using the new equilibrium concentrations, we can set up the equilibrium expression and solve for x:
Q = ([HF] + 2x)^2 / ([H2] + 2x) * ([F2] - x)
Plug in the given initial concentrations and the calculated changes:
0.429^2 / (0.0496 + 2x) * (0.0116 - x) = Q
6. Use the value of x to calculate the new equilibrium concentrations of all gases:
Using the value of x, and the initial concentrations, the new equilibrium concentrations can be calculated as:
[H2] = 0.0496 M + 2x
[F2] = 0.0116 M - x
[HF] = 0.429 M + 2x
7. Substitute the value of x into the equations to find the new equilibrium concentrations:
By substituting the value of x into the equations for [H2], [F2], and [HF], we can calculate the final equilibrium concentrations.
Note: It is essential to know the value of Q in order to find the direction of the shift and determine whether the reaction will favor the reactants or products.
Please provide the value of Q or any additional information needed to solve the problem.