Question

Question #85a11

Answer 1

`"0.0010 moles HI"`

Explanation:

The idea here is that you need to use the pH of the target solution to figure out the concentration of hydronium cations, `"H"_3"O"^(+)`, it must contain.

Once you know that, you can use the ionization of hydroiodic acid, `"HI"`, and the volume of the solution to figure out the number of moles needed.

So, the pH of a solution is defined as the negative log of the concentration of hydronium cations

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

This means that the concentration of hydronium cations can be found by using the pH of the solution

`color(purple)(|bar(ul(color(white)(a/a)color(black)(["H"_3"O"^(+)] = 10^(-"pH"))color(white)(a/a)|)))`

In your case, the solution is said to have a pH equal to `3`, which means that the concentration of hydronium ions will be

`["H"_3"O"^(+)] = 10^(-3) = "0.0010 mol L"^(-1)`

Now, hydroionic acid is a strong acid, which means that it dissociates completely in aqueous solution to form hydronium cations and iodide anions, `"I"^(-)`, in `1:1` mole ratios

`color(red)("H")"I"_ ((aq)) + "H"_ 2"O"_ ((l)) -> "H"_ 3"O"_ ((aq))^(color(red)(+)) + "I"_((aq))^(-)`

This means that every mole of hydroionic acid placed in aqueous solution will form one mole of hydronium cations. Therefore, you can say that

`["HI"] = ["H"_3"O"^(+)]`

Since you know that the concentration of hydronium cations is given by the pH of the solution, you will have

`["HI"] = "0.0010 mol L"^(-1)`

As you know, a solution's molarity tells you how many moles of solute you get per liter of solution.

In this case, a molarity of `"0.0010 mol L"^(-1)` tells you that one liter of this solution will contain `0.0010` moles of hydroionic acid, your solute.

Since the problem tells you that you're dealing with one liter of this solution, you can say that it will contain

`"no. of moles of HI" = color(green)(|bar(ul(color(white)(a/a)0.0010 color(white)(a/a)|)))`

So, adding `0.0010` moles of `"HI"` in enough water to make one liter of solution will get a solution that has a pH of `3`.