What is the pH of the buffer solution that results when 58.50 g of sodium acetate (NaCH3CO2) (Formula Mass = 82.02 g mol-1) is added to 1 litre of 0.45 mol L-1 acetic acid (CH3CO2H) ?
Data: Ka for CH3CO2H = 1.8 x 10-5
Use the Henderson-Hasselbalch equation.
To find the pH of the resulting buffer solution, we need to use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
Where:
pH = the pH of the buffer solution
pKa = the negative logarithm of the acid dissociation constant (Ka)
[A-] = concentration of the conjugate base (sodium acetate, NaCH3CO2)
[HA] = concentration of the acid (acetic acid, CH3CO2H)
Let's break down the problem step by step.
Step 1: Convert the mass of sodium acetate (NaCH3CO2) into moles.
We are given the formula mass of sodium acetate, which is 82.02 g/mol. To convert the given mass into moles, divide the given mass by the formula mass:
moles of NaCH3CO2 = 58.50 g / 82.02 g/mol
Step 2: Calculate the concentration of sodium acetate (NaCH3CO2) in the buffer solution.
We are given that 1 liter of the buffer solution contains the calculated moles of sodium acetate. Therefore, the concentration becomes:
concentration of NaCH3CO2 = moles of NaCH3CO2 / volume of solution
Step 3: Calculate the concentration of acetic acid (CH3CO2H) in the buffer solution.
We are given that the concentration of acetic acid is 0.45 mol L-1.
concentration of CH3CO2H = 0.45 mol L-1
Step 4: Calculate the ratio of [A-] (concentration of NaCH3CO2) to [HA] (concentration of CH3CO2H).
Using the concentrations calculated in step 2 and step 3, we can calculate the ratio of [A-] to [HA]:
[A-]/[HA] = (concentration of NaCH3CO2) / (concentration of CH3CO2H)
Step 5: Calculate the pKa.
We are given that the pKa of acetic acid is 1.8 x 10-5.
pKa = -log(Ka)
Step 6: Use the Henderson-Hasselbalch equation to calculate the pH.
Using the calculated pKa and the ratio of [A-] to [HA], we can now substitute these values into the Henderson-Hasselbalch equation to find the pH:
pH = pKa + log([A-]/[HA])
Substitute the values calculated in steps 4 and 5 into the equation to get the final pH value.
And that's how you can find the pH of the buffer solution by using the Henderson-Hasselbalch equation and the given information.