Final answer:
To determine the pH of a solution of a weak acid, we can use the equation pH = -log[H+]. In this case, using an ICE table and the Ka value, we can calculate the equilibrium concentration of [H+] and then use the pH equation to find the pH of the solution. The pH of the solution is approximately 2.744.
Step-by-step explanation:
To determine the pH of a solution of a weak acid, we can use the equation pH = -log[H+], where [H+] is the concentration of the hydronium ions. In this case, we are given the initial concentration of the weak acid (HA) as 0.856 M and its Ka value as 4.98 x 10⁻⁶.
Since HA is a weak acid, we can assume that it will not dissociate completely in water. Using an ICE table and the Ka value, we can calculate the equilibrium concentration of [H+] and then use the pH equation to find the pH of the solution.
Setting up an ICE table for the dissociation of HA:
[HA] -> [H+] + [A-]
Initial: 0.856 M -> 0 + 0
Change: -x -> +x + +x
Equilibrium: 0.856 - x -> x + x
We know that the initial concentration of [HA] is 0.856 M, so the equilibrium concentration of [HA] is also 0.856 M - x.
Using the Ka expression for the dissociation of HA:
Ka = [H+][A-]/[HA]
Since [H+] = x and [A-] = x, we can substitute these values into the expression.
4.98 x 10⁻⁶ = (x)(x)/(0.856 - x)
Simplifying the equation:
x² = 4.98 x 10⁻⁶(0.856 - x)
x² = 4.98 x 10⁻⁶(0.856) - 4.98 x 10⁻⁶x
x² + 4.98 x 10⁻⁶x - 4.98 x 10⁻⁶(0.856) = 0
Solving the quadratic equation using the quadratic formula, we find that x = 0.0018 M.
Therefore, the concentration of [H+] is 0.0018 M. To calculate the pH, we use the equation pH = -log(0.0018) = 2.744.
Therefore, the pH of the solution is approximately 2.744.