The weak acid HQ has pKa of 4.89. Calculate the [H3O+] of .025 M HQ. when i did this i got 5.2 x 10 ^-14
To calculate the concentration of hydronium ions ([H3O+]) in a solution of a weak acid, you need to use the formula for the acid dissociation constant (Ka) and the equation for the dissociation of the weak acid.
The formula for Ka is as follows:
Ka = [H3O+][A-] / [HA]
Given that pKa = -log10(Ka), you can rearrange this equation to find Ka:
Ka = 10^(-pKa)
Now, let's solve the equation step by step:
1. Calculate Ka:
Ka = 10^(-pKa)
= 10^(-4.89)
= 1.29 × 10^(-5)
2. Since the weak acid, HQ, dissociates according to the following equation:
HQ ⇌ H+ + Q-
The initial concentration of HQ is 0.025 M, and because it's a weak acid, it can be assumed that HA ≈ [HQ]. Therefore, [HA] = 0.025 M.
3. Let [H3O+] be x (as we need to calculate its value).
At equilibrium, [H3O+] = x M, [Q-] = x M, and [HA] = 0.025 - x M.
4. Substitute the values into the equation for Ka:
Ka = [H3O+][Q-] / [HA]
= (x)(x) / (0.025 - x)
5. Substitute the value of Ka we calculated earlier:
1.29 × 10^(-5) = (x)(x) / (0.025 - x)
6. Rearrange the equation:
1.29 × 10^(-5)(0.025 - x) = x^2
7. Solve for x by multiplying and rearranging terms:
1.29 × 10^(-5) × 0.025 - 1.29 × 10^(-5)x = x^2
3.225 × 10^(-7) - 1.29 × 10^(-5)x = x^2
This equation is a quadratic equation, which can be solved by various methods. By solving it, you will find that x ≈ 5.17 × 10^(-4) M.
Therefore, the concentration of [H3O+] in a 0.025 M solution of HQ is approximately 5.17 × 10^(-4) M, which is equivalent to 5.2 × 10^(-4) M.