given volume and concentration of base & initial volume and pH of acid, find the Ka of the acid
Initial pH of acid: 2.76
Initial volume of acid: 10.0 mL
Concentration of NaOH: 0.10 M
Volume of NaOH required to reach equivalence: 10.10 mL
To find the Ka of the acid, we need to use titration data. Titration is a chemical technique used to determine the concentration of an unknown acid or base solution by reacting it with a known solution of acid or base.
In this case, you have the initial volume and pH of the acid, as well as the concentration of the base (NaOH) and the volume of base required to reach equivalence. We can use this information to calculate the Ka of the acid.
1. First, convert the initial pH of the acid to its initial concentration of H+ ions. pH is a measure of the concentration of H+ ions in a solution. In this case, the initial pH is 2.76. The concentration of H+ ions in a solution is related to the pH by the equation: [H+] = 10^(-pH). So, calculate [H+] = 10^(-2.76).
2. Determine the number of moles of H+ ions in the initial volume of acid. To do this, multiply the initial concentration of H+ ions (step 1) by the initial volume of acid (10.0 mL) and convert it to moles using the molar volume of a gas at STP (22.4 L/mol).
3. Calculate the number of moles of OH- ions in the volume of base required to reach equivalence. The volume of base is given as 10.10 mL, and the concentration of NaOH is 0.10 M. Use the equation: Moles of solute = concentration × volume. So, calculate the moles of NaOH in the 10.10 mL of solution.
4. Since the reaction between the acid and base is in a 1:1 ratio, the number of moles of H+ ions is equal to the number of moles of OH- ions at equivalence.
5. Use the number of moles of H+ ions (step 2) and OH- ions (step 4) to calculate the concentration of H+ ions at equivalence. Divide the number of moles of H+ ions by the total volume at equivalence (10.0 mL + 10.10 mL) and convert it to molarity.
6. Finally, use the Henderson-Hasselbalch equation to calculate the Ka of the acid. The Henderson-Hasselbalch equation relates the pH of a solution to the ratio of conjugate base to acid, and the pKa (negative logarithm of Ka) to the pH. The equation is: Ka = 10^(pH - pKa). Rearrange the equation to solve for Ka: pKa = pH - log(Ka), then calculate Ka by taking the antilogarithm of (pH - pKa).
By following these steps and plugging in the given values, you should be able to find the Ka of the acid.