1L of a .2M solution of butanoic acid is altered by adding 5.00g of sodium butanoate. what is the pH of the new solution?
To calculate the pH of the new solution, we need to determine the concentration of hydrogen ions (H+) in the solution. We can do this by considering the dissociation of butanoic acid (CH3CH2CH2COOH) and sodium butanoate (CH3CH2CH2COONa) in water.
Butanoic acid is a weak acid and undergoes partial dissociation in water:
CH3CH2CH2COOH ⇌ CH3CH2CH2COO- + H+
Sodium butanoate, on the other hand, completely dissociates into its constituent ions:
CH3CH2CH2COONa → CH3CH2CH2COO- + Na+
By adding sodium butanoate to the solution, we are essentially supplying additional CH3CH2CH2COO- ions. These ions react with the H+ ions already present in the solution, resulting in a decrease in the concentration of H+ ions.
To find the new concentration of H+ ions, we need to consider the stoichiometry of the reaction. By adding sodium butanoate, we introduce an equimolar amount of CH3CH2CH2COO- ions. Therefore, the concentration of H+ ions will decrease by the same amount.
Given that the initial concentration of butanoic acid is 0.2 M, the concentration of H+ ions can be approximated as 0.2 M. However, this approximation assumes complete dissociation of the butanoic acid. Since butanoic acid is a weak acid, it does not fully dissociate, and the actual concentration of H+ ions will be slightly lower.
To get a more accurate value, we need to calculate the concentration of H+ ions using the dissociation constant (Ka) of butanoic acid. The Ka value for butanoic acid is 1.5 x 10^-5.
We can set up an equilibrium expression for the dissociation of butanoic acid:
Ka = [CH3CH2CH2COO-][H+] / [CH3CH2CH2COOH]
Since we know the concentration of butanoic acid ([CH3CH2CH2COOH]) is 0.2 M, we can rearrange the equation to solve for [H+]:
[H+] = (Ka * [CH3CH2CH2COOH]) / [CH3CH2CH2COO-]
Substituting the values:
[H+] = (1.5 x 10^-5 * 0.2) / 0.2
[H+] = 1.5 x 10^-5 M
Therefore, the concentration of H+ ions in the new solution is approximately 1.5 x 10^-5 M.
Since pH is defined as the negative logarithm of the hydrogen ion concentration (pH = -log[H+]), we can calculate the pH:
pH = -log(1.5 x 10^-5)
pH = -(-4.82)
pH = 4.82
Therefore, the pH of the new solution is approximately 4.82.