Add 0.010 mol of solid sodium butanate, NaC4H7O2 to 100.0 mL of 1.0 M butanoic acid. No volume change. Ka for HC4H7O2=1x10^5.
I get pH 6. Rught?
No. I could have made a math error. I obtained 4.00.
To determine whether the calculated pH is correct, we need to first understand the reaction that occurs between the sodium butanate (NaC4H7O2) and butanoic acid (HC4H7O2).
Sodium butanate (NaC4H7O2) is a salt and dissociates into sodium ions (Na+) and butanate ions (C4H7O2-) in solution. Butanoic acid (HC4H7O2) is a weak acid that partially dissociates into hydrogen ions (H+) and butanoate ions (C4H7O2-) in solution.
Upon adding sodium butanate to the butanoic acid solution, a neutralization reaction takes place between the sodium ions (Na+) and the hydrogen ions (H+). This results in the formation of water (H2O) and the butanoate ion (C4H7O2-).
Since there is no significant volume change mentioned in the question, we can assume that the final volume remains 100.0 mL.
To determine the pH of the resulting solution, we can use the Henderson-Hasselbalch equation, which relates the pH of a solution to the pKa of the acid and the concentrations of the acid and its conjugate base:
pH = pKa + log([A-]/[HA])
In this case, the acid is butanoic acid (HA) and its conjugate base is butanoate ion (A-).
Given that Ka for butanoic acid (HC4H7O2) is 1x10^5, the pKa can be calculated using the formula:
pKa = -log(Ka)
Therefore, pKa = -log(1x10^5) = 5.
Now, we need to determine the concentrations of the acid (butanoic acid) and its conjugate base (butanoate ion).
We are adding 0.010 mol of sodium butanate (NaC4H7O2) to a 100.0 mL (0.100 L) solution of 1.0 M butanoic acid.
Since 1 mole of NaC4H7O2 produces 1 mole of C4H7O2-, the concentration of butanoate ion is equal to the amount of sodium butanate added, which is 0.010 M.
The concentration of butanoic acid remains constant at 1.0 M.
Using the Henderson-Hasselbalch equation:
pH = 5 + log([0.010]/[1.0])
pH = 5 + log(0.010) - log(1.0)
pH = 5 - 2 = 3
Therefore, the correct pH of the resulting solution is 3, not 6.
It appears there was an error in your calculation, yielding an incorrect pH of 6.