What is the pH of a solution of vinegar, which is 5.00% (w/v) acetic acid (CH3COOH, Ka = 1.8 e-5).what is the % dissociation?
5.00% w/v acetic acid means 5.00 g acetic acid per 100 mL solution.
moles acetic acid = grams/molar mass = 15/60 = 0.25 moles/0.1 L = 2.5 M
Then CH3COOH --> H^+ + CH3COO^-
Ka = (H^+)(CH3OO^-)/(CH3COOH)
Set up an ICE chart and solve for H^+, then convert to pH.
%diss = [(H^+)/M]*100 = ??
To find the pH of a solution of acetic acid, we need to calculate the concentration of H+ ions in the solution. The pH is defined as the negative logarithm (base 10) of the H+ concentration.
1. First, calculate the molar concentration of acetic acid (CH3COOH) in the solution:
- Convert the given percentage (w/v) to grams:
- 5.00% (w/v) of acetic acid means there are 5.00 grams of acetic acid in 100.00 mL of solution.
- Convert grams to moles:
- Use the molar mass of acetic acid (CH3COOH), which is approximately 60.05 g/mol.
- Divide the mass in grams by the molar mass to get the number of moles.
- Convert moles to molar concentration:
- Divide the number of moles by the volume of solution in liters (100.00 mL = 0.1000 L).
2. Calculate the concentration of H+ ions that result from the dissociation of acetic acid:
- Since acetic acid is a weak acid, it does not dissociate completely. Only a fraction of acetic acid molecules will produce H+ ions.
- The dissociation constant (Ka) for acetic acid is given as 1.8 × 10^-5.
- The dissociation reaction is: CH3COOH ⇌ H+ + CH3COO-
- Let x be the concentration of H+ ions in moles/liter.
- At equilibrium, the concentration of H+ ions equals x, and the concentration of CH3COO- ions is also x (assuming the concentration of acetic acid is initially 0).
- Write the expression for the dissociation constant:
- Ka = [H+] [CH3COO-] / [CH3COOH]
- Substituting the values, we get: 1.8 × 10^-5 = x * x / 0.1000−x
- Simplifying the equation gives us a quadratic equation.
3. Solve the quadratic equation to find the concentration of H+ ions:
- Solve the quadratic equation using an appropriate method. You can use the quadratic formula or factoring techniques.
- The positive root of the equation will give us the concentration of H+ ions in moles/liter.
4. Calculate the pH of the solution:
- Take the negative logarithm (base 10) of the concentration of H+ ions obtained in step 3.
- Use the formula: pH = -log[H+]
To calculate the % dissociation, we need to compare the concentration of dissociated acetic acid (H+) to the initial concentration of acetic acid (CH3COOH). The % dissociation is given by:
% dissociation = (concentration of dissociated CH3COOH / initial concentration of CH3COOH) x 100
Note: The % dissociation might be small for weak acids such as acetic acid.
Performing these calculations will give us the pH of the acetic acid solution as well as the % dissociation.