Enough of a monoprotic acid is dissolved in water to produce a 1.47 M solution. The pH of the resulting solution is 2.64. Calculate the Ka for the acid.
To calculate the Ka for a monoprotic acid, you can use the equation for acid dissociation:
HA ⇌ H+ + A-
In this equation, HA represents the acid, H+ represents the hydrogen ion, and A- represents the conjugate base.
Given that the pH of the solution is 2.64, we can deduce that the concentration of H+ is 10^-2.64 M. Since the acid is monoprotic, the concentration of HA is equal to the concentration of H+.
So, the concentration of HA is also 10^-2.64 M.
Now, let's define the initial concentration of the conjugate base A-. Since HA fully dissociates into H+ and A-, its initial concentration is 0.
Next, let's define the equilibrium concentrations of H+ and A- as x. At equilibrium, the concentration of HA will be reduced by x and the concentration of A- will increase by x.
The equilibrium expression for the dissociation of HA is:
Ka = [H+][A-] / [HA]
Plugging in the equilibrium concentrations, we get:
Ka = (x)(x) / (10^-2.64 - x)
Since the concentration of A- is x and the concentration of HA is 10^-2.64 M - x, we substitute these values into the equation.
Now, let's assume that x is very small compared to 10^-2.64 M. This assumption is valid because only a small fraction of the acid dissociates, and this value is typically less than 5% for weak acids.
With this assumption, we can simplify the equation to:
Ka ≈ (x)(x) / 10^-2.64
Next, we can make another simplification since x is small compared to 10^-2.64. We can disregard x in the denominator, and the equation becomes:
Ka ≈ x^2 / 10^-2.64
Finally, we can substitute the concentration of H+ (10^-2.64) for x:
Ka ≈ (10^-2.64)^2 / 10^-2.64
Calculating this expression will give you the value of Ka for the acid.