Please calculate the pH and [H+] of a 0.30 mol/L solution of butanoic acid,. The Ka of butanoic acid is 1.52 x 10^-5
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To calculate the pH and [H+] of a solution of butanoic acid, we need to use the acid dissociation constant (Ka) of butanoic acid. The Ka value provided is 1.52 x 10^-5.
The formula for calculating the pH of a solution from the concentration of the hydrogen ion ([H+]) is pH = -log[H+].
To determine [H+], we need to calculate the concentration of the hydrogen ions in the butanoic acid solution.
First, we need to determine the degree of dissociation (α) for butanoic acid. This represents the fraction of butanoic acid that dissociates into hydrogen ions and the conjugate base.
The equation for the dissociation of butanoic acid is as follows:
CH3CH2CH2COOH ⇌ CH3CH2CH2COO- + H+
The initial concentration of butanoic acid is 0.30 mol/L. Since it is a weak acid, we can assume that the concentration of the dissociated species is negligible compared to the initial concentration of butanoic acid. Therefore, we can approximate α as the concentration of hydrogen ions ([H+]) divided by the initial concentration of butanoic acid (0.30 mol/L):
α = [H+] / 0.30
Next, we can use the Ka expression for butanoic acid to relate α to the [H+] concentration:
Ka = [H+] * [CH3CH2CH2COO-] / [CH3CH2CH2COOH]
Since the concentration of [CH3CH2CH2COO-] is the same as [H+] (as it is a 1:1 ratio), we can rewrite the equation as:
Ka = [H+]^2 / [CH3CH2CH2COOH]
Rearranging the equation, we get:
[H+]^2 = Ka * [CH3CH2CH2COOH]
Now, we can substitute the known values into the equation. Ka is 1.52 x 10^-5, and the concentration of butanoic acid is 0.30 mol/L:
[H+]^2 = (1.52 x 10^-5) * (0.30)
Solving for [H+], we get:
[H+]^2 = 4.56 x 10^-6
Taking the square root of both sides, we find:
[H+] = √(4.56 x 10^-6)
[H+] = 6.75 x 10^-3 mol/L
Now that we have the concentration of [H+], we can calculate the pH using the formula pH = -log[H+]:
pH = -log(6.75 x 10^-3)
pH = 2.17
Therefore, the pH of the 0.30 mol/L solution of butanoic acid is 2.17, and the concentration of [H+] is 6.75 x 10^-3 mol/L.