Calculate the pH of a solution created by mixing 200.0 mL of 0.400 M acetic acid and 200.0 mL of 1.00 M sodium acetate. Hint: The instant the two solutions are mixed what are the initial concentrations of each?
To calculate the pH of the solution, we need to determine the initial concentrations of acetic acid and sodium acetate when they are mixed.
Since the volume of each solution is given, we can convert them to moles:
For acetic acid:
Moles of acetic acid = Volume (in liters) x Concentration
Moles of acetic acid = 0.200 L x 0.400 M
Moles of acetic acid = 0.080 mol
For sodium acetate:
Moles of sodium acetate = Volume (in liters) x Concentration
Moles of sodium acetate = 0.200 L x 1.00 M
Moles of sodium acetate = 0.200 mol
When acetic acid and sodium acetate react, they form a buffer solution. The equation for the reaction is:
CH3COOH + CH3COONa ↔ CH3COO- + Na+
In this reaction, acetic acid donates a proton (H+) to become acetate ion (CH3COO-). The sodium acetate dissociates into sodium ions (Na+) and acetate ions (CH3COO-).
Since acetic acid is a weak acid, it partially dissociates in water. The acetate (CH3COO-) is a common ion that comes from both the weak acid and its conjugate base (sodium acetate).
Now, let's calculate the initial concentrations of acetic acid and acetate ions.
For acetic acid:
Initial concentration of acetic acid = Moles of acetic acid / Total volume of the solution
Initial concentration of acetic acid = 0.080 mol / (0.200 L + 0.200 L)
Initial concentration of acetic acid = 0.080 mol / 0.400 L
Initial concentration of acetic acid = 0.200 M
For acetate ions:
Initial concentration of acetate ions = Moles of sodium acetate / Total volume of the solution
Initial concentration of acetate ions = 0.200 mol / (0.200 L + 0.200 L)
Initial concentration of acetate ions = 0.200 mol / 0.400 L
Initial concentration of acetate ions = 0.500 M
Now that we have the initial concentrations of acetic acid and acetate ions, we can use the Henderson-Hasselbalch equation to calculate the pH of the solution:
pH = pKa + log([A-] / [HA])
The pKa for acetic acid is 4.75, so:
pH = 4.75 + log(0.500 M / 0.200 M)
pH = 4.75 + log(2.5)
pH = 4.75 + 0.3979
pH ≈ 5.15
Therefore, the pH of the solution created by mixing 200.0 mL of 0.400 M acetic acid and 200.0 mL of 1.00 M sodium acetate is approximately 5.15.
To calculate the pH of the solution, you first need to determine the initial concentrations of acetic acid and sodium acetate when they are mixed.
When the two solutions are mixed, the total volume of the resulting solution will be 200.0 mL + 200.0 mL = 400.0 mL = 0.400 L.
The initial concentration of acetic acid can be calculated using the formula:
Initial concentration of acetic acid (C1) = (Volume of acetic acid solution / Total volume of resulting solution) x Concentration of acetic acid solution
C1 = (200.0 mL / 400.0 mL) x 0.400 M
C1 = 0.200 x 0.400 M
C1 = 0.080 M
Similarly, the initial concentration of sodium acetate can be calculated using the same formula:
Initial concentration of sodium acetate (C2) = (Volume of sodium acetate solution / Total volume of resulting solution) x Concentration of sodium acetate solution
C2 = (200.0 mL / 400.0 mL) x 1.00 M
C2 = 0.200 x 1.00 M
C2 = 0.200 M
Now that you know the initial concentrations, you can use the Henderson-Hasselbalch equation to calculate the pH of the solution:
pH = pKa + log (C2 / C1)
The pKa value for acetic acid is 4.76. Substitute the values into the equation:
pH = 4.76 + log (0.200 M / 0.080 M)
Calculate the ratio of C2/C1:
C2/C1 = 0.200 M / 0.080 M
C2/C1 = 2.5
Take the logarithm of this ratio:
log (2.5) = 0.3979
Add this value to the pKa:
pH = 4.76 + 0.3979
pH = 5.1579
Therefore, the pH of the solution created by mixing 200.0 mL of 0.400 M acetic acid and 200.0 mL of 1.00 M sodium acetate is approximately 5.16.