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A buffer solution is prepared by adding 30.0g of pure acetic acid to 41.0g of sodium acetate in water, and then diluting the solution to 1.00L. What is the pH of the buffer solution?
mols HAc = grams/molar mass
M HAc = mols/L soln
mols NaAc = grams/molar mass
M NaAc = mols/L soln
pH = pKa for HAc + log(NaAc)/(HAc)
To determine the pH of the buffer solution, we need to consider the dissociation of acetic acid and its conjugate base, acetate ion, in water. The Henderson-Hasselbalch equation can be used to calculate the pH of a buffer solution and is expressed as:
pH = pKa + log ([A-]/[HA])
Here, pKa is the negative logarithm of the acid dissociation constant, [A-] represents the concentration of the acetate ion, and [HA] represents the concentration of acetic acid.
To use this equation, we first need to calculate the concentrations of acetate and acetic acid in the solution. To do this, we can use the formula:
Concentration (in mol/L) = mass (in g) / molar mass (in g/mol)
The molar mass of acetic acid (CH3COOH) is approximately 60.05 g/mol, and the molar mass of sodium acetate (CH3COONa) is approximately 82.03 g/mol.
First, calculate the moles of acetic acid using its mass:
moles of acetic acid = 30.0 g / 60.05 g/mol
Next, calculate the moles of sodium acetate using its mass:
moles of sodium acetate = 41.0 g / 82.03 g/mol
Since acetic acid and sodium acetate have a 1:1 stoichiometric ratio, the moles of acetate ions will be the same as the moles of sodium acetate.
Therefore, the concentrations of acetate and acetic acid can be calculated as follows:
Concentration of acetate ion = moles of sodium acetate / volume of solution (in L)
Concentration of acetic acid = moles of acetic acid / volume of solution (in L)
Since the solution is diluted to 1.00L, the volume of the solution will be 1.00L.
Now that we have determined the concentrations of acetate and acetic acid, we can use the Henderson-Hasselbalch equation to find the pH of the buffer solution. The pKa value for acetic acid is 4.74.
pH = 4.74 + log ([acetate ion]/[acetic acid])
Finally, substitute the calculated concentrations into the Henderson-Hasselbalch equation to find the pH of the buffer solution.