How many grams of glucose must be added to 275 g of water in order to prepare percent by mass concentration of aqueous glucose solution 1.30% ?

1 Answer
Apr 18, 2018

"3.62 g"

Explanation:

The idea here is that the solution's percent concentration by mass tells you the number of grams of solute, which in your case is glucose, present for every "100. g" of the solution.

A solution that is "1.30% glucose by mass will contain "1.30 g" of glucose for every "100. g" of the solution.

So the question is actually asking about the number of grams of glucose that must be added to "275 g" of water in order to get "1.30 g" of glucose for every "100. g" of this solution.

If you take x "g" to be the mass of glucose needed to make this solution, you can say that after you add the glucose to the water, the total mass of the solution will be

x quad "g" + "275 g" = (x + 275) quad "g"

So you know that x "g" of glucose in (x + 275) "g" of the solution must be equivalent to "1.30 g" of glucose in "100. g" of the solution.

This means that you have

(x color(red)(cancel(color(black)("g glucose"))))/((x + 275) color(red)(cancel(color(black)("g solution")))) = (1.30 color(red)(cancel(color(black)("g glucose"))))/(100. color(red)(cancel(color(black)("g solution"))))

Rearrange and solve for x to get

100. * x = 1.30 * x + 1.30 * 275

98.7 * x = 357.5 implies x = 357.5/98.7 = 3.6221

Rounded to three sig figs, the number of sig figs you have for your values, the answer will be

color(darkgreen)(ul(color(black)("mass of glucose = 3.62 g")))