Question #85a11

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#.