What is the concentration of Be(OH)2(aq) in a solution in which the concentrations of Be2+ and OH− are fixed at 2.9×10−5 M? The cumulative formation constant ( β2 ) for Be(OH)2(aq) in water is 2.5×1014 .
To determine the concentration of Be(OH)2(aq) in the solution, we need to consider the equilibrium reaction:
Be(OH)2(aq) ⇌ Be2+(aq) + 2 OH−(aq)
The given information includes the concentrations of Be2+ and OH− ions, as well as the cumulative formation constant (β2) for Be(OH)2(aq) in water.
The equation for the formation constant (Kf) is given by:
Kf = [Be2+][OH−]² / [Be(OH)2(aq)]
Since the concentrations of Be2+ and OH− are fixed, we can substitute their given values into the equation:
2.5×10^14 = (2.9×10^−5)(2.9×10^−5)² / [Be(OH)2(aq)]
Simplifying this equation gives:
[Be(OH)2(aq)] = (2.9×10^−5)(2.9×10^−5)² / 2.5×10^14
Calculating this expression will give us the answer to the concentration of Be(OH)2(aq) in the solution.
To find the concentration of Be(OH)2(aq) in the solution, we need to use the equilibrium constant and the concentrations of Be2+ and OH- ions. Here's the step-by-step process:
1. Write the balanced chemical equation for the formation of Be(OH)2(aq) from Be2+ and OH- ions:
Be2+ + 2OH- -> Be(OH)2(aq)
2. Set up the equation for the equilibrium constant (K) using the concentrations of the reactants and products:
K = [Be(OH)2(aq)] / [Be2+] * [OH-]^2
Note: In this case, the concentration of OH- is squared because the stoichiometric coefficient of OH- in the balanced equation is 2.
3. Plug in the known values:
- [Be2+] = 2.9×10^(-5) M (Given)
- [OH-] = 2.9×10^(-5) M (Given)
- K = 2.5×10^14 (Given)
4. Substitute the values into the equilibrium constant expression:
2.5×10^14 = [Be(OH)2(aq)] / (2.9×10^(-5))^2
5. Rearrange the equation to solve for [Be(OH)2(aq)]:
[Be(OH)2(aq)] = 2.5×10^14 * (2.9×10^(-5))^2
6. Calculate the concentration of Be(OH)2(aq) using a calculator:
[Be(OH)2(aq)] ≈ 1.776 × 10^5 M
Therefore, the concentration of Be(OH)2(aq) in the solution is approximately 1.776 × 10^5 M.