Calculate the pH of the buffer that results from mixing 50.8 mL of a 0.493 M solution of HCHO2 and 13.0 mL of a 0.646 M solution of NaCHO2. The Ka value for HCHO2 is 1.8×10−4
Use the Henderson-Hasselbalch equation.
You can use mols and the answer will be the same as if you had used M.
mols = M x L = ?
To calculate the pH of the buffer, you need to follow a series of steps:
Step 1: Write the balanced equation for the ionization of the weak acid (HCHO2).
HCHO2(aq) ⇌ H+(aq) + CHO2-(aq)
Step 2: Determine the initial moles of both HCHO2 and NaCHO2.
First, calculate the moles of HCHO2:
Moles of HCHO2 = Volume of HCHO2 solution (in L) × Concentration of HCHO2 solution (in mol/L)
= 50.8 mL × (1 L/1000 mL) × 0.493 mol/L
= 0.0250 mol
Next, calculate the moles of NaCHO2 (since it is a sodium salt, it does not react with water):
Moles of NaCHO2 = Volume of NaCHO2 solution (in L) × Concentration of NaCHO2 solution (in mol/L)
= 13.0 mL × (1 L/1000 mL) × 0.646 mol/L
= 0.00840 mol
Step 3: Calculate the moles of CHO2- ion formed.
Since HCHO2 is a weak acid, it will partially ionize in water. The ratio of moles for H+ and CHO2- ions is 1:1 according to the balanced equation.
Moles of CHO2- = Moles of HCHO2
= 0.0250 mol
Step 4: Calculate the total volume of the final solution.
Total volume = Volume of HCHO2 solution + Volume of NaCHO2 solution
= 50.8 mL + 13.0 mL
= 63.8 mL = 0.0638 L
Step 5: Calculate the molarity of the CHO2- ion in the final solution.
Molarity of CHO2- = Moles of CHO2- / Total volume (in L)
= 0.0250 mol / 0.0638 L
= 0.391 mol/L
Step 6: Calculate the pH of the buffer.
The pH of the buffer can be determined using the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
Where pKa is the negative logarithm of the equilibrium constant Ka for the weak acid (HCHO2).
pKa = -log(Ka) = -log(1.8×10^-4) = 3.74
Now, substitute the given values into the Henderson-Hasselbalch equation:
pH = 3.74 + log(0.391/0.0250)
= 3.74 + log(15.64)
= 3.74 + 1.192
= 4.932
Therefore, the pH of the buffer is approximately 4.932.