Question

Question #5998a

Answer 1

`"molarity" = 14.6` `M`

`"volume" = 13.7` `"mL"`

Explanation:

We're asked to find (a) the molarity of the `"H"_2"SO"_4` solution, and (b) the volume of that acid solution required to make `1` `"L"` of a `0.2` `M` solution.

(a)

To find the molarity of the solution, we can first recognize that in an `80%` by mass solution, and we assume a `100`-`"g"` sample, there would be

• `80.0` `"g H"_2"SO"_4`

• `20.0` `"g H"_2"O"`

Also in a `100`-`"g"` sample, using the given density, the volume (in liters) of the solution is

`V = 100cancel("g soln")((1cancel("mL soln"))/(1.787cancel("g soln")))((1color(white)(l)"L soln")/(10^3cancel("mL soln"))) = color(red)(ul(0.0560color(white)(l)"L soln"`

Remember that the molarity equation is

`ul("molarity" = "mol solute"/"L soln"`

We just found the liters of solution, so let's use the `80` `"g H"_2"SO"_4` and the molar mass of `"H"_2"SO"_4` to find the moles:

`80.0cancel("g H"_2"SO"_4)((1color(white)(l)"mol H"_2"SO"_4)/(98.078cancel("g H"_2"SO"_4))) = color(green)(ul(0.816color(white)(l)"mol H"_2"SO"_4`

The molarity of the solution is thus

`"molarity" = color(green)(0.816color(white)(l)"mol H"_2"SO"_4)/(color(red)(0.0560color(white)(l)"L soln")) = color(blue)(ulbar(|stackrel(" ")(" "14.6color(white)(l)M" ")|)`

(b)

Now, we can use the dilution equation to find the volume of this solution required to make `1` `"L"` of a `0.2` `M` solution.

The dilution equation is

`ul(M_1V_1 = M_2V_2`

where

• `M_1` and `M_2` are the molarities of the two solutions

• `V_1` and `V_2` are the respective volumes of the two solutions

We know:

• `M_1 = color(blue)(14.6color(white)(l)M`

• `V_1 = ?`

• `M_2 = 0.2color(white)(l)M`

• `V_2 = 1color(white)(l)"L"`

Let's rearrange the equation to solve for the unknown volume, `V_1`:

`V_1 = (M_2V_2)/(M_1)`

Plugging in known values:

`V_1 = ((0.2cancel(M))(1color(white)(l)"L"))/(color(blue)(14.6)cancel(color(blue)(M))) = color(blue)(0.0137color(white)(l)"L"` `= color(blue)(ulbar(|stackrel(" ")(" "13.7color(white)(l)"mL"" ")|)`