Answer:
To determine the pH of a solution with a concentration of 0.0527 M, we need to use the equation:
pH = -log[H3O+]
where [H3O+] is the hydronium ion concentration in moles per liter (M) of the solution.
We first need to find the hydronium ion concentration [H3O+]. In this case, we have not been given the value of [H3O+], but we know that the solution is an aqueous solution. For an aqueous solution, the hydronium ion concentration [H3O+] is related to the concentration of the solute (in this case, the solute is an acid) by the acid dissociation constant (Ka) for the acid.
If we assume that the solute is a weak acid (i.e., it does not dissociate completely), we can use the equilibrium expression for the acid to calculate the value of [H3O+]. For a weak acid HA, the equilibrium expression is:
HA + H2O ⇌ H3O+ + A-
where A- is the conjugate base of the acid. The acid dissociation constant (Ka) for this reaction is:
Ka = [H3O+][A-]/[HA]
At equilibrium, the concentration of the acid [HA] that remains undissociated is equal to the initial concentration of the acid, which is 0.0527 M. Let x be the concentration of [H3O+] that is formed when the acid dissociates. Then, the concentration of [A-] that is formed is also x, since the acid and its conjugate base are in a 1:1 molar ratio. Substituting these values into the equilibrium expression and solving for x, we get:
Ka = x^2 / (0.0527 - x)
Assuming that x is much smaller than 0.0527, we can simplify the expression as follows:
Ka ≈ x^2 / 0.0527
Rearranging the equation to solve for x, we get:
x = √(Ka * 0.0527)
The value of Ka for the acid must be known to calculate x. If we assume that the acid is acetic acid (CH3COOH), we can use its Ka value (1.8 x 10^-5) to calculate the value of x:
x = √(1.8 x 10^-5 * 0.0527)
x ≈ 0.00276 M
Now that we have found the hydronium ion concentration [H3O+] to be 0.00276 M, we can substitute this value into the equation for pH to find the pH of the solution:
pH = -log(0.00276)
pH ≈ 2.56
Therefore, the pH of the 0.0527 M solution of acetic acid is approximately 2.56.