What is the CHANGE in pH when 0.005 moles of HCl is added to 0.100 L of a buffer solution that is 0.100 M in CH3CO2H and 0.100 M NaCH3CO2? The Ka for acetic acid is 1.8 x 10-5.
To find the change in pH, we first need to calculate the initial pH of the buffer solution before the addition of HCl.
1. Calculate the initial concentration of acetic acid (CH3CO2H) in the buffer solution:
- Initial concentration of acetic acid (CH3CO2H) = 0.100 M
2. Calculate the initial concentration of the acetate ion (CH3CO2-) in the buffer solution:
- Initial concentration of sodium acetate (NaCH3CO2) = 0.100 M
- Since sodium acetate dissociates completely in water to give acetate ions, the initial concentration of acetate ion (CH3CO2-) is also 0.100 M.
3. Calculate the initial moles of acetic acid (CH3CO2H) in the buffer solution:
- Initial moles of acetic acid = initial concentration of acetic acid (CH3CO2H) x volume of buffer solution
- Initial moles of acetic acid = 0.100 M x 0.100 L = 0.0100 moles
4. Calculate the initial moles of acetate ion (CH3CO2-) in the buffer solution:
- Initial moles of acetate ion = initial concentration of acetate ion (CH3CO2-) x volume of buffer solution
- Initial moles of acetate ion = 0.100 M x 0.100 L = 0.0100 moles
5. Calculate the initial moles of H+ ions (from the dissociation of acetic acid) in the buffer solution:
- According to the equation: CH3CO2H ⇌ CH3CO2- + H+
- The molar ratio between acetic acid and H+ ions is 1:1
- Therefore, the initial moles of H+ ions = 0.0100 moles
6. Calculate the initial concentration of H+ ions:
- Initial concentration of H+ ions = initial moles of H+ ions / volume of buffer solution
- Initial concentration of H+ ions = 0.0100 moles / 0.100 L = 0.100 M
7. Calculate the initial pH of the buffer solution using the equation: pH = -log[H+]
- Initial pH = -log(0.100)
- Initial pH ≈ 1.00
Now, let's find the change in pH when 0.005 moles of HCl are added to the buffer solution:
8. Calculate the final moles of acetic acid:
- Final moles of acetic acid = initial moles of acetic acid - moles of HCl added
- Final moles of acetic acid = 0.0100 moles - 0.0050 moles = 0.0050 moles
9. Calculate the final moles of acetate ion:
- Final moles of acetate ion = initial moles of acetate ion
- Final moles of acetate ion = 0.0100 moles
10. Calculate the final moles of H+ ions:
- Final moles of H+ ions = initial moles of H+ ions
- Final moles of H+ ions = 0.0100 moles
11. Calculate the final concentration of H+ ions:
- Final concentration of H+ ions = final moles of H+ ions / volume of buffer solution
- Final concentration of H+ ions = 0.0100 moles / 0.100 L = 0.100 M
12. Calculate the final pH using the equation: pH = -log[H+]
- Final pH = -log(0.100)
- Final pH ≈ 1.00
To find the change in pH, subtract the initial pH from the final pH:
Change in pH = Final pH - Initial pH
Change in pH = 1.00 - 1.00
Change in pH = 0
Therefore, the change in pH when 0.005 moles of HCl is added to the buffer solution is 0.
To calculate the change in pH when a strong acid (HCl) is added to a buffer solution, we need to consider the dissociation of the weak acid (CH3CO2H) in the buffer.
First, let's write the dissociation equation for acetic acid (CH3CO2H):
CH3CO2H ⇌ CH3CO2- + H+
The dissociation constant (Ka) for acetic acid is given as 1.8 x 10^-5, which means that at equilibrium, the ratio of the concentration of products (CH3CO2- and H+) to the concentration of acetic acid (CH3CO2H) will be equal to Ka.
Next, let's consider the initial concentrations of the components in the buffer solution:
[CH3CO2H] = 0.100 M
[CH3CO2-] = 0.100 M
[H+] = 10^(-pH)
Since the buffer capacity is high, we can assume that the concentration of the weak acid and the conjugate base will remain constant after adding the strong acid. Therefore, we can write the final concentrations of the components in the buffer solution after adding HCl as follows:
[CH3CO2H] = 0.100 M
[CH3CO2-] = 0.100 M
[H+] = [CH3CO2H] + moles of HCl / total volume of the solution (0.100 L + volume of HCl)
Now, we can solve for the final concentration of [H+] by taking into account the dissociation of acetic acid and the addition of HCl. We'll use the dissociation constant (Ka) to relate the concentrations.
Ka = [CH3CO2-] * [H+] / [CH3CO2H]
Using the values we know:
1.8 x 10^-5 = (0.100) * (x) / (0.100)
Solving for x (H+ concentration), we get:
x = 1.8 x 10^-5 * 0.100 / 0.100 = 1.8 x 10^-5
Therefore, the final concentration of H+ after adding HCl is 1.8 x 10^-5 M.
To find the change in pH, we need to compare the initial and final concentrations of H+.
Change in pH = -log10([H+]final / [H+]initial)
[H+]initial is the concentration of H+ before adding HCl, which we assumed to be 10^(-pH). Therefore,
[H+]initial = 10^(-pH) = 10^(-pH)
Change in pH = -log10((1.8 x 10^-5) / (10^(-pH)))
Simplifying the equation further, we get:
Change in pH = -log10(1.8 x 10^-5) + log10(10^(-pH))
Change in pH = -(-log10(1.8 x 10^-5)) + pH
Change in pH = log10(1.8 x 10^-5) + pH
Using the given Ka value of acetic acid, we can calculate the change in pH.