Calculate the pH of a solution that obtained by diluting 0.015 mol acetic acid with water to 250 cm3 (the Ka -
value for acetic acid is 1.74 x 10-5 M).
To calculate the pH of a solution obtained by diluting acetic acid, you need to determine the concentration of the acid after dilution. Then, you can use the dissociation constant (Ka) for acetic acid to calculate the concentration of hydronium ions ([H3O+]) in the solution, which is used to define pH.
Here's how you can solve the problem step-by-step:
1. Find the concentration of acetic acid after dilution:
Volume of solution (V) = 250 cm3 = 0.250 L
Number of moles of acetic acid (n) = 0.015 mol
Concentration of acetic acid (C) = n/V
= 0.015 mol / 0.250 L
= 0.060 M
2. Use the dissociation constant (Ka) equation for acetic acid:
Ka = [H3O+][CH3COO-] / [CH3COOH]
Since acetic acid is a weak acid, it partially dissociates to form hydronium ions ([H3O+]) and acetate ions ([CH3COO-]).
3. Assume that x is the concentration of hydronium ions formed and dissociated from acetic acid. Since acetic acid is weak, the concentration of x compared to the initial concentration of acetic acid is negligible.
The equilibrium expression becomes:
Ka = x * x / (0.060 - x)
4. Solve the quadratic equation:
Input the value of Ka (1.74 x 10^-5) into the equation:
1.74 x 10^-5 = x^2 / (0.060 - x)
Rearrange the equation:
x^2 = 1.74 x 10^-5 * (0.060 - x)
Simplify the equation:
x^2 = 1.044 x 10^-6 - 1.74 x 10^-5x
Set the equation to zero:
x^2 + 1.74 x 10^-5x - 1.044 x 10^-6 = 0
Solve the quadratic equation using the quadratic formula or a calculator to find the value of x. Choose the positive root.
5. Once you find the value of x (which represents the concentration of hydronium ions), use the expression for pH:
pH = -log[H3O+]
Plug in the value of [H3O+] (x) into the equation to calculate the pH of the solution.
Remember to follow these steps carefully and use proper units for accurate results.