Question #e8b23

The first thing to do here is to figure out the density of the solution by using its specific gravity.

The specific gravity of a substance is defined as the density of that substance divided by the density of water at `4^@"C"`, the temperature at which the density of water is maximum.

`color(blue)(ul(color(black)("SG" = rho_"substance"/rho_ ("water at 4"^@"C"))))`

You can approximate the density of water at `4^@"C"` to

`rho_ ("water at 4"^@"C") = "1.00 g mL"^(-1)`

This means that the density of your cinnamaldehyde solution will be equal to

`rho_"cinnamaldehyde" = 1.05 * "1.00 g mL"^(-1)`

`rho_ "cinnamaldehyde" = "1.05 g mL"^(-1)`

Now, molarity is defined as the number of moles of solute present in `"1.0 L"` of solution.

At this point, your strategy will be to pick a `"1.0-L"` sample of this solution and figure out how many moles of cinnamaldehyde, your solute, it contains.

Calculate the mass of the solution first by using its density

`1.0 color(red)(cancel(color(black)("L"))) * (10^3color(red)(cancel(color(black)("mL"))))/(1color(red)(cancel(color(black)("L")))) * "1.05 g"/(1color(red)(cancel(color(black)("mL solution")))) = "1050 g"`

This solution is `98%` cinnamaldehyde by mass, which basically means that you get `"98 g"` of cinnamaldehyde for every `"100 g"` of solution.

In your case, the sample will contain

`1050 color(red)(cancel(color(black)("g solution"))) * "98 g solute"/(100color(red)(cancel(color(black)("g solution")))) = "1029 g solute"`

To convert this to moles of cinnamaldehyde, use the compound's molar mass

`1029 color(red)(cancel(color(black)("g"))) * "1 mole cinnamaldehyde"/(132.16color(red)(cancel(color(black)("g")))) = "7.786 moles cinnamaldehyde"`

Since you know that the solution contains `7.786` moles of solute in `"1.0 L"` of solution, the volume of the sample, you can say that its molarity will be

`color(darkgreen)(ul(color(black)("molarity = 7.8 mol L"^(-1))))`

The answer is rounded to two sig figs, the number of sig figs you have for the solution's percent concentration.