A solution of sugar is obtained by mixing 200 g of its 25 % solution and 500 g of its 40 % solution (both by mass). The mass percentage of the resulting sugar solution is ___________ (Nearest integer)

Solution

Chemistry ma’am · 3 steps

Percentages do not add, but grams of sugar do: total the sugar, then divide by the total mass.

1. Sugar in each. A 25% by mass solution has 25 g sugar in every 100 g. So 200 g of it holds 0.25 × 200 = 50 g sugar, and 500 g of the 40% solution holds 0.40 × 500 = 200 g sugar.
2. Add up. Total sugar is 50 + 200 = 250 g. Total solution mass is 200 + 500 = 700 g.

   mass % = 250/700 × 100 = 35.71%

3. So. The mixed solution is 35.71% sugar by mass, which rounds to 36.

The common slip: 33. Averaging the two percentages, (25 + 40)/2 = 32.5, rounds to 33. That ignores the fact that there is more than twice as much of the 40% solution.

The idea to keep. When you mix solutions, add the solute masses and add the solution masses separately, then divide. Mass is conserved; percentages are not.

Answer from the NTA final answer key. Solution by PrepWiser.