The first thing to focus on here is finding the of the solution.
As you know, is defined as mass per unit of volume. You know that your solution has a volume of
Notice that you are given the volume of water and its density. Use this information to find the mass of water used to make the solution - keep in mind that you have
$100.0 color(red)(cancel(color(black)("mL"))) * overbrace("1.00 g"/(1color(red)(cancel(color(black)("mL")))))^(color(purple)("density of water")) = "100.0 g"$
So, the total mass of the solution will be equal to
$m_"sol" = m_(H_3PO_4) + m_"water"$
$m_"sol" = "10.0 g" + "100.0 g" = "110.0 g"$
The density of the solution will thus be
$rho = "110.0 g"/"104 mL" = color(green)("1.06 g mL"^(-1))$
To get the mole fraction of phosphoric acid in this solution, you need to know
- the number of moles of phosphoric acid
- the number of moles of water
Since you have the masses of the two , you can use their molar masses to determine how many moles of each you have present in this solution.
$10.0 color(red)(cancel(color(black)("g"))) * ("1 mole H"_3"PO"_4)/(97.995color(red)(cancel(color(black)("g")))) = "0.10205 moles H"_3"PO"_4$
and
$100.0 color(red)(cancel(color(black)("g"))) * ("1 mole H"_2"O")/(18.015color(red)(cancel(color(black)("g")))) = "5.551 moles H"_2"O"$
The total number of moles in this solution will be
$n_"total" = "0.1025 moles" + "5.551 moles" = "5.6531 moles"$
fraction of phosphoric acid will be
$chi_(H_3PO_4) = (0.10205 color(red)(cancel(color(black)("moles"))))/(5.6531 color(red)(cancel(color(black)("moles")))) = color(green)(0.0181)$
The of the solution is defined as the number of moles of divided by the volume of the solution - expressed in liters.
$color(blue)(c = n_"solute"/V_"solution")$
In your case, you will have
$c = "0.10205 moles"/(104 * 10^(-3)"L") = color(green)("0.981 mol L"^(-1))$
Finally, the of the solution is defined as the number of moles of solute divided by the mass of the - expressed in kilograms.
$color(blue)(b = n_"solute"/m_"solvent")$
Plug in your values to get
$b = "0.10205 moles"/(100.0 * 10^(-3)"kg") = color(green)("1.02 mol kg"^(-1))$