Calculate the new pH after adding 0.050 mol of HBr to 1.0 L of buffer solution containing 0.200 mol HCOOH and 0.200 mol HCOOK. The value of Ka for HCOOH is 1.8 × 10⁻⁴.
To calculate the new pH after adding HBr to the buffer solution, we need to first find the concentration of the components of the buffer solution, then use the Henderson-Hasselbalch equation.
1. Calculate the concentrations of the components of the buffer solution:
[HCOOH] = 0.200 mol/L
[HCOOK] = 0.200 mol/L
2. Calculate the new concentrations after adding HBr:
Since HBr is a strong acid, it will completely dissociate in the buffer solution, reacting with the HCOOK to form HCOOH and KBr. The moles of HBr added are 0.050, so the new concentrations are:
[HCOOH] = 0.200 + 0.050 = 0.250 mol/L
[HCOOK] = 0.200 - 0.050 = 0.150 mol/L
3. Use the Henderson-Hasselbalch equation:
The equation is pH = pKa + log ([A-]/[HA]), where A- is the conjugate base (HCOOK) and HA is the weak acid (HCOOH). We need to find pKa first using the Ka:
Ka = 1.8 × 10⁻⁴
pKa = -log(Ka) = -log(1.8 × 10⁻⁴) = 3.74
Now we can plug in our values into the Henderson-Hasselbalch equation:
pH = 3.74 + log (0.150 / 0.250)
pH = 3.74 + log (0.6)
pH ≈ 3.74 - 0.22
pH ≈ 3.52
The new pH after adding 0.050 mol of HBr to the buffer solution is approximately 3.52.