12 mL of 0.0100 M HCl are added to 25.0 mL of a buffer solution that is 0.010 M HC2H3O2 and 0.11 M C2H3O2-. What is the pH of the resulting solution?
I understand to use the ice method, however, i do understand what to plug into the hh equation.
HC2H3O2 = HAc.
[C2H3O2]^- = Ac^-
It is easier to work in millimoles which I will do. Technically it isn't proper to use mols or millimols in the HH equation; however, since M = millimoles/mL and you have mmols/mL in numerator and denominator of the HH equation, the answer comes out the same because the mL unit cancels.
mmols HAc = mL x M = 25 x 0.01 = 0.25
mmols Ac^- = 25 x 0.11 = 2.75
mmols HCl added = 12 x 0.01 = 0.12
.........Ac^- + H^+ ==> HAc
I.......2.75....0.......0.25
add............0.12.............
C......-0.12..-0.12....+0.12
E......2.63......0......0.27
Plug the E line into the HH equation and solve for pH.
Check these figures, especially the decimal point. The procedure is right but I may have flubbed on the numbers. That's why you need to check them ALL.
To determine the pH of the resulting solution, you can use the Henderson-Hasselbalch equation, which relates the pH of a buffer solution to the components of the buffer system. The Henderson-Hasselbalch equation is given as:
pH = pKa + log([A-] / [HA])
Where:
- pH is the measure of acidity or alkalinity of a solution.
- pKa is the negative logarithm (base 10) of the acid dissociation constant (Ka).
- [A-] represents the concentration of the conjugate base of the acid in the buffer.
- [HA] represents the concentration of the acid in the buffer.
In this case, the acid in the buffer solution is HC2H3O2 (acetic acid), and its conjugate base is C2H3O2- (acetate ion).
To determine the pH of the resulting solution after adding the HCl:
1. First, calculate the new concentrations of the acid and its conjugate base after the addition of the HCl.
- The initial concentration of HC2H3O2 is 0.010 M in 25.0 mL, which means there are (0.010 M) * (0.025 L) = 0.00025 moles of HC2H3O2 initially.
- The initial concentration of C2H3O2- is 0.11 M in 25.0 mL, which means there are (0.11 M) * (0.025 L) = 0.00275 moles of C2H3O2- initially.
- The concentration of HC2H3O2 after adding 12 mL of 0.0100 M HCl can be calculated using stoichiometry:
- The moles of HCl added is (0.0100 M) * (0.012 L) = 0.00012 moles.
- Since the reaction between HCl and HC2H3O2 is a 1:1 ratio, the moles of HC2H3O2 remaining is (0.00025 moles initial) - (0.00012 moles added HCl) = 0.00013 moles.
- The new concentration of HC2H3O2 is (0.00013 moles) / (0.025 L) = 0.0052 M.
- The concentration of C2H3O2- after mixing can be calculated since there is no reaction with HCl. It remains the same:
- The concentration of C2H3O2- remains at 0.11 M.
2. Next, calculate the pKa value for acetic acid (HC2H3O2). The pKa value for HC2H3O2 is 4.76.
3. Substitute the values into the Henderson-Hasselbalch equation:
pH = 4.76 + log([C2H3O2-] / [HC2H3O2])
= 4.76 + log(0.11 M / 0.0052 M)
4. Solve the equation using a calculator:
pH = 4.76 + log(21.15)
= 4.76 + 1.325 (rounded to 3 decimal places)
= 6.085
Therefore, the pH of the resulting solution after adding 12 mL of 0.0100 M HCl to the buffer solution is approximately pH 6.085.