what is solubility of NaOH at pH 5.5 and 8.0 when Ksp for NaOH is 5x 10^-10
To determine the solubility of NaOH at pH 5.5 and 8.0, we need to first understand how pH affects the solubility of a substance. pH is a measure of the acidity or alkalinity of a solution. In the case of NaOH, it is a strong base.
At a low pH, there is an excess of H+ ions which can react with the OH- ions of NaOH and convert them to water. This reaction reduces the concentration of OH- ions in the solution, making NaOH less soluble. As the pH increases, the concentration of H+ ions decreases, allowing more OH- ions to stay in the solution, thus increasing the solubility of NaOH.
Now let's calculate the solubility of NaOH at pH 5.5 and 8.0 using the given Ksp value.
The solubility product constant (Ksp) is an equilibrium constant that relates to the solubility of a sparingly soluble compound. For NaOH, the Ksp is given as 5 x 10^-10.
The Ksp expression for NaOH is:
Ksp = [Na+][OH-]
However, in a neutral solution, the concentration of H+ ions (from water) will also contribute to the overall concentration of OH- ions. Since we have the pH values of the solutions, we can use the concentration of H+ ions in those solutions to calculate the concentration of OH- ions.
To calculate the concentration of OH- ions, we will use the equation Kw = [H+][OH-] where Kw is the ion product of water.
The value of Kw at 25°C is 1x10^-14.
For pH 5.5:
[H+] = 10^(-pH) = 10^(-5.5) = 3.16 x 10^(-6)
[OH-] = Kw/[H+] = (1 x 10^(-14))/(3.16 x 10^(-6)) = 3.16 x 10^(-9)
For pH 8.0:
[H+] = 10^(-pH) = 10^(-8) = 1 x 10^(-8)
[OH-] = Kw/[H+] = (1 x 10^(-14))/(1 x 10^(-8)) = 1 x 10^(-6)
Now we can use the Ksp expression to determine the solubility of NaOH at both pH 5.5 and 8.0.
For pH 5.5:
Ksp = [Na+][OH-]
5 x 10^(-10) = [Na+](3.16 x 10^(-9))
[Na+] = (5 x 10^(-10))/(3.16 x 10^(-9)) = 1.58 x 10^(-1) = 0.158
For pH 8.0:
Ksp = [Na+][OH-]
5 x 10^(-10) = [Na+](1 x 10^(-6))
[Na+] = (5 x 10^(-10))/(1 x 10^(-6)) = 5 x 10^(-4)
Therefore, the solubility of NaOH at pH 5.5 is approximately 0.158 M, and at pH 8.0 is approximately 5 x 10^(-4) M.