Phosphorous acid, H3PO3, is actually a diprotic acid for which Ka1 = 5.0 × 10-2 and Ka2 = 2.0 × 10-7. What are the values of [H+] and [H2PO3-] in a 2.0 M solution of H3PO3?
Is this correct?
(x ^ 2) / 2.0 = 5.0 x 10 ^ -2
x = 3.162E-1 = [H +] = [H2PO3-]
pH = -log (3.162E-1) = 0.50
...........H3PO3 ==> H^+ + H2PO3^-
I..........2.0.......0......0
C...........-x.......x......x
E..........2.0-x.....x......x
Ignore the contribution to H^+ of k2 then substitute the E line into k1 expression and solve for x = (H^+)=(H2PO3^-)
The problem doesn't ask for pH. I would redo it as a quadratic.
0.316 = (H^+) with the assumption that
2.0-x = 2.0
But it really is 2.0-x and it doesn't appear to me that the x can be ignored with respect to 2.0. That looks like about 15%. I would feel better if the quadratic equation were used.
To find the values of [H+] and [H2PO3-] in a 2.0 M solution of H3PO3, we need to consider the dissociation reactions of phosphorous acid.
The balanced chemical equation for the dissociation reaction of phosphorous acid can be written as follows:
H3PO3 ⇌ H+ + H2PO3-
From the given information, we know the values of Ka1 and Ka2. Ka1 represents the equilibrium constant for the dissociation of the first proton (H+) from phosphorous acid, while Ka2 represents the equilibrium constant for the dissociation of the second proton (H+) from the resulting hydrogen phosphite ion (H2PO3-).
Now, let's use the given data to solve the problem step by step:
1. Calculate the concentration of [H+] using Ka1:
Ka1 = [H+]*[H2PO3-] / [H3PO3]
Since the concentration of [H3PO3] is given as 2.0 M, we can assume that [H+] = [H2PO3-] initially.
Ka1 = [H+]^2 / (2.0 - [H+])
Rearranging the equation and substituting the value of Ka1:
(2.0 - [H+]) * [H+]^2 = Ka1
(2.0 - [H+]) * [H+]^2 = 5.0 × 10^-2
Now, we can solve this equation for [H+]. This can be done using numerical methods or by using a graphing calculator.
2. Calculate the concentration of [H2PO3-] using the value of [H+]:
Since [H+] = [H2PO3-], we can directly substitute the calculated value of [H+] into [H2PO3-].
3. Once you have determined the concentration of [H+] and [H2PO3-], you can convert them into the pH scale if desired.
pH = -log10([H+])
It is important to note that the calculation of [H+] and [H2PO3-] requires solving a quadratic equation. Therefore, it might be easier to use numerical methods or a graphing calculator to find the values accurately.
Remember to always double-check your calculations and ensure that you're using the correct equations and values throughout the process.