Calculate the pH of 500. mL of 0.100 M acetic acid, CH3COOH, which also contains 0.100 mole of sodium acetate, NaCH3COO.
How do you set this up step by step?
To calculate the pH of the solution, you need to consider the dissociation of acetic acid and the formation of the conjugate base, sodium acetate. Here are the steps to set up the problem:
Step 1: Write the balanced chemical equation for the dissociation of acetic acid:
CH3COOH ⇌ CH3COO- + H+
Step 2: Determine the initial concentrations of acetic acid and sodium acetate. In this case, we are given that the volume of the solution is 500 mL (which is equivalent to 0.500 L) and the concentration of acetic acid is 0.100 M. The concentration of sodium acetate is given as 0.100 mole, which is also equivalent to 0.100 M since the volume was not provided separately for sodium acetate.
Step 3: Set up an ICE (Initial, Change, Equilibrium) table.
CH3COOH: 0.100 M → -x → (0.100 - x) M
CH3COO-: 0 M → +x → x M
H+: 0 M → +x → x M
In the ICE table, x represents the amount of acetic acid that dissociates and also the amount of acetate ion formed.
Step 4: Apply the equilibrium expression for Ka (acid dissociation constant):
Ka = [CH3COO-][H+]/[CH3COOH]
Since acetic acid is a weak acid, it does not dissociate completely. The concentration of acetic acid remaining in the solution is (0.100 - x) M, and the concentration of acetate ion (CH3COO-) and hydrogen ion (H+) is x M.
Step 5: Substitute the values into the equilibrium expression:
Ka = (x)(x)/(0.100 - x)
Step 6: Solve the quadratic equation for x. Rearrange the equation to:
x^2/(0.100 - x) = Ka
Since Ka is a small value for weak acids, we can assume that (0.100 - x) ≈ 0.100. Simplify the equation to:
x^2 = Ka(0.100)
Step 7: Calculate the value of x by taking the square root of both sides:
x = √(Ka(0.100))
Step 8: Convert the value of x into pH. The pH is calculated using the equation:
pH = -log[H+]
Since x represents the concentration of H+, substitute the value of x into the equation:
pH = -log(x)
Step 9: Calculate the final pH by plugging in the value of x into the equation from step 8.
Remember to use the appropriate value of Ka based on the temperature at which the calculation is taking place.