Can someone please explain how to do this question?
A 0.057M solution of a weak acid has a pH of 4.93. Determine the ionization constant, Ka, of the acid.
a) 2.1 x 10^-4
b) 2.4 x 10^-9
c) 4.1 x 10^-8
d) 2.8 x 10^-7
e) 1.4 x 10^-10
-- Well, to be honest, I skipped this. I know that the Ka = ((H3O^+)(A^-))/(HA), but I didn't know how to find (A^-). Am I approaching this question wrong? Is there a step I missed or can this be solved another way? Perhaps it has something to do with an ICE chart?
Thank you for your time, I really do appreciate your help.
No problem! Let's break down the steps to solve the question.
First, we can start by using the pH of the solution to find the concentration of H3O+ (or [H3O+]). The equation to convert pH to [H3O+] is:
[H3O+] = 10^(-pH)
In this case, [H3O+] = 10^(-4.93) = 1.06 x 10^(-5) M.
Next, we need to determine the initial concentration of the weak acid (HA) in the solution. You are correct that we can use an ICE (Initial, Change, Equilibrium) chart. We assume that the weak acid dissociates partially, so we represent HA as the initial concentration and A^- as the change in concentration.
The ICE chart looks like this:
[HA] --> [H^+ + A^-]
(initial) (change)
Since we have a weak acid, we assume that only a small fraction of HA will dissociate, so we can approximate the change in concentration of HA to be approximately x. Therefore, the concentration of A^- will also be approximately x.
Now, we can write the expression for the ionization constant (Ka):
Ka = ([H3O+][A^-])/[HA]
We can substitute the known values:
Ka = (1.06 x 10^(-5) M)(x)/(0.057 M)
At this point, we can assume that x is small compared to the initial concentration of HA. This assumption allows us to neglect the x value when subtracting it from the initial concentration of HA.
So, we can approximate the expression as:
Ka ≈ (1.06 x 10^(-5) M)(x)/(0.057 M)
The next step is to solve for x. In order to do this, we need to make an assumption about the value of x that will allow us to simplify the expression. One common assumption is that x is much less than the initial concentration of HA. In this case, we can assume that x ≈ 0.
With this approximation, the expression becomes:
Ka ≈ (1.06 x 10^(-5) M)(0)/(0.057 M)
Since the value of x is very small, we can neglect it in the calculation. So, the expression simplifies to:
Ka ≈ 0
Based on this approximation, the value of Ka is very close to zero. None of the given choices for the value of Ka match this result, so none of the provided options are correct.
In conclusion, the ionization constant, Ka, for the weak acid cannot be determined using the given information. It's important to note that this kind of assumption about the value of x is only valid when x is truly small compared to the initial concentration of HA. In other cases, more complex methods, such as solving a quadratic equation, may be needed to find the value of x and determine Ka accurately.
I hope this explanation helps! Let me know if you have any more questions.