What mass (in grams) of potassium acetate, KC2H3O2, must be added to 140 mL of 0.010 M acetic acid to form a buffer solution with a pH of 4.5?
(Ka (HC2H3O2)= 1.8 x 10-5)
pH = pKa + log(b/a)
4.5 = 4.74 + log(base)/(acid)
4.5 = 4.74 + log(base)/0.01
Solve for (base) in moles/L.
Convert to moles in 140 mL and convert that to grams KC2H2O2.
To solve this problem, we first need to understand the concept of a buffer solution and how it works. A buffer solution consists of a weak acid and its conjugate base (or a weak base and its conjugate acid) that resists changes in pH when small amounts of an acid or base are added.
In this case, we are given acetic acid, HC2H3O2, and we need to form a buffer solution with a pH of 4.5. The Ka value for acetic acid is provided as 1.8 x 10^-5.
Now, let's break down the steps to solve the problem:
Step 1: Determine the pKa of the weak acid from the given Ka value.
pKa = -log(Ka)
pKa = -log(1.8 x 10^-5)
Step 2: Calculate the ratio of the concentration of the conjugate base to the concentration of the weak acid required to achieve the desired pH.
pH = pKa + log([conjugate base]/[weak acid])
4.5 = pKa + log([conjugate base]/[weak acid])
Step 3: Convert the given volume of acetic acid solution to moles.
Molarity = moles/volume
0.010 M = moles/0.140 L
Step 4: Calculate the concentration of acetic acid using the moles value obtained in step 3.
Concentration of weak acid = moles/volume
Concentration of weak acid = moles/0.140 L
Step 5: Calculate the concentration of the conjugate base using the ratio obtained in step 2.
Concentration of conjugate base = (concentration of weak acid) x 10^(pH - pKa)
Step 6: Calculate the moles of conjugate base using the concentration obtained in step 5.
Moles of conjugate base = (concentration of conjugate base) x (volume of acetic acid solution in liters)
Step 7: Convert the moles of conjugate base to grams using the molar mass of potassium acetate, KC2H3O2.
Mass of potassium acetate = (moles of conjugate base) x (molar mass of KC2H3O2)
By following these steps, you should be able to calculate the mass of potassium acetate needed to form the desired buffer solution with a pH of 4.5.