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Math Help - Density (check)

  1. #1
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    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.
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  2. #2
    Member pflo's Avatar
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    Quote Originally Posted by hemi View Post
    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!!
    Last edited by pflo; September 15th 2009 at 03:22 PM.
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  3. #3
    Senior Member pacman's Avatar
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    "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?"

    YOUR ANSWER IS CORRECT, though it looks like hurriedly done.

    ================================================== ==

    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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