To calculate the pH and concentrations of H2SO3, HSO3-, and SO32- in NaHSO3, we need to consider the dissociation of NaHSO3 in water. Hence, we will use the given Ka values to calculate the concentrations of the different species.
First, let's write down the dissociation reactions and the corresponding equilibrium constant expressions:
1. NaHSO3 β H2SO3 + Na+
2. H2SO3 β H+ + HSO3-
3. HSO3- β H+ + SO32-
Given that the initial concentration of NaHSO3 is 0.05 M, we assume that there is no H2SO3, HSO3-, or SO32- initially.
Now, let's start by calculating the concentration of H2SO3:
From reaction 1, we know that the initial concentration of NaHSO3 is equal to the initial concentration of H2SO3, i.e., [H2SO3] = 0.05 M.
To calculate the concentrations of HSO3- and SO32-, we need to consider the equilibrium constant expressions for reactions 2 and 3.
For reaction 2:
Ka1 = [H+][HSO3-]/[H2SO3]
Rearranging the equation, we get: [HSO3-] = (Ka1[H2SO3])/[H+]
For reaction 3:
Ka2 = [H+][SO32-]/[HSO3-]
Rearranging the equation, we get: [SO32-] = (Ka2[HSO3-])/[H+]
Now, we can substitute the values into these equations:
[HSO3-] = (Ka1[0.05])/[H+]
[SO32-] = (Ka2[HSO3-])/[H+]
To calculate the concentration of H+ (which is equal to the concentration of [H+) and the pH of the solution), we need to consider that H+ is produced from the dissociation of H2SO3, HSO3-, and NaH2PO4.
[H+] = [H2SO3] + [HSO3-] + [NaH2PO4]
Using these equations, you can calculate the pH and the concentrations of H2SO3, HSO3-, and SO32- in NaHSO3. Try plugging in the given Ka values and the initial concentration of NaHSO3 into the equations, and see if you can reach the provided results.