calculate the ph of 20 ml of .1M NaOH to 40 ml of acetic acid
We need the molarity of the acetic acid.
To calculate the pH of a solution resulting from the mixing of a strong base (NaOH) with a weak acid (acetic acid), you'll need to consider the dissociation of the weak acid and the reaction between the acid and the base.
Here's how you can calculate the pH step by step:
1. Calculate the number of moles of acetic acid and sodium hydroxide used:
- Moles of acetic acid = volume (in liters) × concentration (in M) = 0.040 L × 0.1 M = 0.004 moles
- Moles of sodium hydroxide = volume (in liters) × concentration (in M) = 0.020 L × 0.1 M = 0.002 moles
2. Determine the limiting reagent:
The limiting reagent is the one with fewer moles. In this case, sodium hydroxide is limited since it has fewer moles than acetic acid.
3. Find the excess amount of the non-limiting reactant:
Since acetic acid is in excess, the 0.004 moles of acetic acid will not fully react with the 0.002 moles of sodium hydroxide.
4. Calculate the remaining moles of acetic acid:
Since only a portion of the acetic acid reacts, subtract the moles of sodium hydroxide (0.002 moles) from the moles of acetic acid (0.004 moles):
0.004 moles - 0.002 moles = 0.002 moles of acetic acid remaining
5. Calculate the concentration of acetic acid remaining:
The remaining moles of acetic acid divided by the total volume in liters (60 mL = 0.060 L):
Concentration = Remaining moles / Volume
Concentration = 0.002 moles / 0.060 L = 0.0333 M
6. Calculate the dissociation of acetic acid:
Acetic acid is a weak acid, so it partially dissociates in water. The dissociation constant (Ka) for acetic acid is 1.8 × 10^(-5) M at 25 °C. Let's assume x is the amount of acetic acid that dissociates.
Ka = [H+][CH3COO-] / [CH3COOH]
1.8 × 10^(-5) = (x)(x) / (0.0333 - x)
Since the concentration of the undissociated acetic acid decreases by x and the concentration of CH3COO- increases by x (assuming x is small compared to 0.0333 M), we can simplify:
Ka = x^2 / (0.0333 - x)
Rearrange to solve for x:
x^2 = Ka × (0.0333 - x)
x^2 = 1.8 × 10^(-5) × (0.0333 - x)
Solve the quadratic equation to find x.
7. Calculate the concentration of hydrogen ions (H+):
Since x is the amount of acetic acid that dissociates and each acetic acid molecule produces an equal amount of hydrogen ions, the concentration of H+ ions is equal to x.
8. Calculate the pH:
pH = -log[H+]
Plug the concentration of hydrogen ions (H+) into the pH equation to get the final answer.
Note: This calculation assumes all volumes are additive and that the final volume is the sum of the initial volumes.