# Math Help - Density (check)

1. ## Density (check)

The density of a solution of sucrose is 1.3855 g/cc, and it is 76.00 percent by mass. What volume of the solution (in milliliters) do you need to supply 46.0 g of sucrose?

Here's how I solved this:

0.76 x 1.3855 = 1.05298

46.0g / 1.05298 g = 43.68mL

Is this the correct approach to this problem? Thanks for reading.

2. Originally Posted by hemi
The density of a solution of sucrose is 1.3855 g/cc, and it is 76.00 percent by mass. What volume of the solution (in milliliters) do you need to supply 46.0 g of sucrose?

Here's how I solved this:

0.76 x 1.3855 = 1.05298

46.0g / 1.05298 g = 43.68mL

Is this the correct approach to this problem? Thanks for reading.

Check the units in your calculation. You can't get ml from $g \div g$.

The first calculation gives you 1.05298 what???? Read the equation in words: 76% of the solution is sucrose. Looking at the units (percents have no units): g/cc = g/cc. What this calculation is telling you is that you've got 1.05298 g sugar in each cc of solution.

The proper units for the second calculation are: $g \div g/ml$, which is what gives you ml. THIS is why you're correct!!

3. "The density of a solution of sucrose is 1.3855 g/cc, and it is 76.00 percent by mass. What volume of the solution (in milliliters) do you need to supply 46.0 g of sucrose?"

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1 mL = 1 cc = 0.001 L

Mass of solution of sucrose = 46 g/0.76 = 60.5263 g

Density = Mass/Volume

1.3855 g/cc = Mass/Volume = M/V = 60.5263 g/Volume

cross-multiply,

Volume of sucrose solution = (60.5263 g)/(1.3855 g/cc)

Volume of sucrose solution = 43.6855 cc = 43.6855 mL

since 1 mL = 1 cc = 1 cubic centimeters = 0.001 liter = 0.001 L.

Thus, Volume of sucrose solution = 43.6855 cc = 43.6855 mL

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