Question

What mass of sugar is needed to prepare 400 g. of 10% solution of sugar?

Answer 1

Answer:

A solution's percent concentration by mass,

% w/w

, basically tells you what mass of solute you get per

100 g

of solution.

In your case, sugar is the solute and water is the solvent. A solution is formed when you dissolve a solute in a solvent.

Here's how to solve this problem without using the formula for percent concentration by mass, which is given to you as

% w/w

=

mass of solute

mass of solution

×

100

You know that your target sugar solution must be

7% w/w

. This means that every

100 g

of this solution must contain

7 g

of sugar.

This ratio between sugar and water is the same regardless of the mass of solution. In your case, you want the solution to have a mass of

235 g

. Since it must contain

7 g

of sugar for every

100 g

of solution, you can say that

235

g solution

⋅

= 7% w/w



7 g sugar

100

g solution

=

16.45 g sugar

You should round this off to one sig fig, since that's how many sig figs you have for the percent by mass, but I'll leave it rounded to two sig figs, just for good measure

m

sugar

=

16 g

This is what the formula for percent concentration by mass actually means. If you start with

% w/w

=

m

solute

m

solution

×

100

you can rearrange to solve for

m

solute

, which is the mass of sugar

% w/w

⋅

m

solution

=

m

solute

⋅

100

m

solute

=

% w/w

⋅

m

solution

100

Now plug in your values to get

m

solute

=

7

⋅

235 g

100

=

16 g

Explanation:

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