Question

Dissolving 120g of urea (mol.wt 60) in 1000g of water gave a solution of density 1.15 g/mL. What is the molarity of the solution?

Answer 1

`"2.1 mol L"^(-1)`

Explanation:

The idea here is that a solution's molarity tells you the number of moles of solute present in `"1 L"` of solution.

So in order to calculate a solution's molarity, you essentially need to know the number of moles of solute present in exactly `"1 L" = 10^3` `"mL"` of solution.

Start by using the molar mass of urea to calculate the number of moles present in your sample

`120 color(red)(cancel(color(black)("g"))) * "1 mole urea"/(60color(red)(cancel(color(black)("g")))) = "2 moles urea"`

Now, you know that your solution contains `"120 g"` of urea, the solute, and `"1000 g"` of water, the solvent. This implies that the total mass of the solution

`"mass solution = mass solute + mass solvent"`

will be equal to

`"mass solution" = "120 g + 1000 g" = "1120 g"`

You also know that this solution has a density of `"1.15 g mL"^(-1)`, which means that every `"1 mL"` of solution has a mass of `"1.15 g"`.

Use the density of the solution to calculate its volume

`1120 color(red)(cancel(color(black)("g"))) * "1 mL"/(1.15color(red)(cancel(color(black)("g"))) ) = "973.9 mL"`

Now, your goal is to figure out the number of moles of solute present in `10^3` `"mL"` of solution, so use the known composition of the solution as a conversion factor to get

`10^3 color(red)(cancel(color(black)("mL solution"))) * "2 moles urea"/(973.9color(red)(cancel(color(black)("mL solution")))) = "2.0536 moles urea"`

You can thus say that the molarity of the solution is equal to

`color(darkgreen)(ul(color(black)("molarity = 2.1 mol L"^(-1))))`

I'll leave the answer rounded to two sig figs.