Question

Question #bbd91

Answer 1

You need to know the identity of the solute.

Explanation:

You can't provide a numerical answer here because the problem doesn't provide the identity of the solute, which you need in order to convert its mass to moles.

I'm not really sure what you're supposed to solve for here, but I'll show you how to convert the given mass by volume percent concentration, `"% m/v"`, to molarity, `c`, by using a solute that has a molar mass equal to `M_"M" color(white)(.)"g mol"^(-1)`.

So, in order to know the solution's molarity, you need to figure out how many moles of solute you have in `"1 L"` of solution. To make the calculations easier, let's pick a `"1-L"` sample of this solution.

Its mass by volume percent concentration tells you that you get `"5.67 g"` of this unknown solute for every `"100 mL"` of solution.

This means that the sample we've picked will have a total mass of solute equal to

`1 color(red)(cancel(color(black)("L solution"))) * (10^3color(red)(cancel(color(black)("mL"))))/(1color(red)(cancel(color(black)("L")))) * "5.67 g solute"/(100color(red)(cancel(color(black)("mL solution")))) = "56.7 g solute"`

To convert this to moles, use the molar mass of the solute

`M_"M" color(white)(.)"g mol"^(-1) = (M_"M" color(white)(.)"g solute")/"1 mole solute"`

In your case, the sample will contain

`56.7 color(red)(cancel(color(black)("g solute"))) * "1 mole solute"/(M_"M" color(red)(cancel(color(black)("g solute")))) = (56.7/M_"M")" moles solute"`

Since this is the number of moles of solute present in `"1 L"` of solution, you can say that its molarity will be equal to

`color(darkgreen)(ul(color(black)(c_"5.67%" = (56.7/M_"M")color(white)(.)"mol L"^(-1))))`

Notice that you don't need to know the density of the solution in order to figure out its molarity, the mass by volume percent concentration is enough here.