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A buffer was prepared by dissolving 0.100 mol of the weak acid HA (Ka = 1.00 × 10−5) plus 0.050 mol of its conjugate base Na+A− in 1.00 L. Find the pH.
Use the Henderson-Hasselalch equation.
HA is the acid; NaA is the base.
To find the pH of the buffer solution, we need to consider the equilibrium between the weak acid HA and its conjugate base A-. The balanced equation for this equilibrium is as follows:
HA ⇌ H+ + A-
Given that the Ka value of HA is 1.00 × 10^−5, we can set up an expression for the equilibrium constant as follows:
Ka = [H+][A-] / [HA]
Since the initial concentrations of HA and A- are given, we can substitute these values into the equation:
Ka = [H+][0.050 mol] / [0.100 mol]
Now, rearrange the equation to solve for [H+]:
[H+] = (Ka * [HA]) / [A-]
[H+] = (1.00 × 10^-5 * 0.100 mol) / 0.050 mol
[H+] = 2.00 × 10^-5 mol/L
To find the pH, we need to calculate the negative logarithm (base 10) of the hydrogen ion concentration ([H+]).
pH = -log[H+]
pH = -log(2.00 × 10^-5)
pH ≈ 4.70
Therefore, the pH of the buffer solution is approximately 4.70.