Question

Question #5d860

Answer 1

`"pH" = 4.6`

Explanation:

The pH of a solution is simply of measure of how many hydronium cations, `"H"_3"O"^(+)`, it contains.

More specifically, you can find a solution's pH by taking the negative log base `10` of the concentration of hydronium cations present in solution.

`color(blue)(|bar(ul(color(white)(a/a)"pH" = - log( ["H"_3"O"^(+)])color(white)(a/a)|)))`

In your case, the concentration of hydronium cations is said to be equal to

`["H"_3"O"^(+)] = 2.5 * 10^(-5)"M"`

This means that the pH of the solution will be

`"pH" = - log(2.5 * 10^(-5)) = color(green)(|bar(ul(color(white)(a/a)4.6color(white)(a/a)|)))`

Now, is a pH of `4.6` characteristic of an acidic, a neutral, or a basic solution?

Aqueous solutions at room temperature exhibit the following relationship between the concentration of hydronium cations and hydroxide anions, `"OH"^(-)`

`color(blue)(|bar(ul(color(white)(a/a)["H"_3"O"^(+)] * ["OH"^(-)] = 10^(-14)"M"^2color(white)(a/a)|)))`

This relationship is based on the self-ionization of water at room temperature, for which the ionization constant, `K_W`, is equal to

`K_W = 10^(-14)"M"^2`

Now, a neutral solution will always have equal concentrations of hydronium cations and hydroxide anions. For pure water at room temperature, and taking `x` to be the concentration of the two ions, you have

`x * x = 10^(-14)"M"^2 implies x = sqrt(10^(-14)"M"^2) = 10^(-7)"M"`

So, a neutral solution has

`["H"_3"O"^(+)] = ["OH"^(-)] = 10^(-7)"M"`

In your case, you have a higher concentration of hydronium cations than you would have in a neutral solution. This means that the solution will be acidic, since it contains a higher concentration of hydronium cations than of hydroxide anions.

`["OH"^(-)] = (10^(-14)"M"^2)/(["H"_3"O"^(+)])`

In your case, you have

`["OH"^(-)] = (10^(-14)"M"^color(red)(cancel(color(black)(2))))/(2.5 * 10^(-5)color(red)(cancel(color(black)("M")))) = 4.0 * 10^(-10)"M"`

As you can see, you have

`["H"_3"O"^(+)] > ["OH"^(-)] ->` the solution will be acidic