Calculate the pH of a buffer solution that contains 0.60 M NaH2PO4, and 0.26 M Na2HPO4.
To calculate the pH of a buffer solution, you need to consider the acid dissociation constants (Ka) of the acidic and basic components of the buffer. In this case, NaH2PO4 is the acidic component, while Na2HPO4 is the basic component.
Step 1: Write the chemical equation for the dissociation of the acidic component (NaH2PO4):
NaH2PO4 ⇌ H+ + HPO4^2-
Step 2: Write the chemical equation for the dissociation of the basic component (Na2HPO4):
Na2HPO4 ⇌ 2Na+ + HPO4^2-
Step 3: Set up an ICE (Initial, Change, Equilibrium) table to calculate the concentrations of H+ and HPO4^2- ions after the dissociation of the buffer components.
For NaH2PO4:
Initial: 0.60 M NaH2PO4 (acidic component)
Change: -x (decrease in concentration of NaH2PO4)
Equilibrium: 0.60 - x M NaH2PO4, x M H+ and x M HPO4^2-
For Na2HPO4:
Initial: 0.26 M Na2HPO4 (basic component)
Change: -2x (decrease in concentration of Na2HPO4)
Equilibrium: 0.26 - 2x M Na2HPO4, x M H+ and x M HPO4^2-
Step 4: Write the expression for the acid dissociation constant (Ka) of the acidic component (NaH2PO4):
Ka = [H+][HPO4^2-] / [NaH2PO4]
Step 5: Write the expression for the acid dissociation constant (Ka) of the basic component (Na2HPO4):
Ka = [H+][HPO4^2-] / [Na2HPO4]
Step 6: Since NaH2PO4 is a weak acid and Na2HPO4 is its conjugate base, the Ka of NaH2PO4 can be considered as the Kb of Na2HPO4:
Ka = Kw / Kb
Step 7: Calculate the concentration of H+ ion using the equation derived from the ICE table and the expression for Ka:
Ka = [H+][HPO4^2-] / [NaH2PO4]
Ka = x * x / (0.60 - x)
Substitute Ka = Kw / Kb:
(H3O+)(HPO4^2-) / (Na2HPO4) = Kw / Kb
(H3O+)(x) / (0.26 - 2x) = Kw / Kb
Step 8: Calculate the value of x:
Simplify the equation and solve for x using the value of Kw (1.0 x 10^-14) and the value of Kb (Kw / Ka):
(H3O+)(x) / (0.26 - 2x) = (1.0 x 10^-14) / (Kw / Ka)
(H3O+)(x) / (0.26 - 2x) = (1.0 x 10^-14) / (1.0 x 10^-14 / Ka)
Step 9: Calculate the pH:
The pH can be calculated using the concentration of H+ ions using the equation: pH = -log[H+].
I apologize, but without the value of the acid dissociation constant (Ka) for NaH2PO4, I am unable to provide a specific numerical answer to the question. However, by following the steps outlined above and inputting the appropriate values, you should be able to calculate the pH of the buffer solution.