What is the pH of a 2.0 molar solution of acetic acid. Ka acetic acid = 1.810–5

Question

What is the pH of a 2.0 molar solution of acetic acid. Ka acetic acid = 1.810–5

Answer 1

To find the pH of a 2.0 M solution of acetic acid, we need to use the equilibrium constant expression for the dissociation of acetic acid:

CH3COOH + H2O ⇄ CH3COO- + H3O+

Ka = [CH3COO-][H3O+] / [CH3COOH]

We can assume that the initial concentration of acetic acid is 2.0 M, and that at equilibrium, some of it will dissociate to form acetate ions and hydronium ions. Let x be the concentration of H3O+ and CH3COO- ions formed at equilibrium.

Then, we can write:

Ka = x^2 / (2.0 - x)

Since the Ka value is small compared to the initial concentration of acetic acid, we can simplify the expression by assuming that x is much smaller than 2.0. This means that we can ignore the amount of acetic acid that does not dissociate, and consider the concentration of CH3COO- and H3O+ ions to be equal to x.

So, we can write:

Ka = x^2 / 2.0

Rearranging and solving for x, we get:

x = sqrt(Ka * 2.0) = 0.00294 M

The pH of the solution can now be calculated using the definition of pH:

pH = -log[H3O+]

pH = -log(0.00294) = 2.53

Therefore, the pH of a 2.0 M solution of acetic acid is 2.53.

Answer 2

To find the pH of a solution of acetic acid, we need to use the dissociation constant (Ka) and the concentration of the acid. Here's a step-by-step guide:

Step 1: Write the dissociation reaction for acetic acid (CH3COOH):
CH3COOH ⇌ CH3COO- + H+

Step 2: Since acetic acid is a weak acid, we can assume that the dissociation is incomplete. Let's assign x to the concentration of the dissociated ions [CH3COO-] and [H+].

Step 3: The initial concentration of acetic acid ([CH3COOH]) is given as 2.0 M.

Step 4: Use the dissociation constant (Ka) equation to set up the equilibrium expression:
Ka = [CH3COO-] * [H+] / [CH3COOH]

Step 5: Substitute the given values into the equation:
1.8 * 10^-5 = x * x / 2.0

Step 6: Solve for x:
x^2 = 1.8 * 10^-5 * 2.0
x^2 = 3.6 * 10^-5
x ≈ 0.006

Step 7: Since acetic acid is a weak acid and the dissociation is incomplete, we can assume that the concentration of [H+] is equal to the concentration of x, which is approximately 0.006 M.

Step 8: Calculate the pH using the definition of pH:
pH = -log[H+]
pH = -log(0.006)
pH ≈ 2.22

Therefore, the pH of a 2.0 M solution of acetic acid is approximately 2.22.