Final answer:
After mixing 100 g of a 20% sugar solution with 400 g of a 50% sugar solution, the resulting concentration of the sugar solution is 44%.
Step-by-step explanation:
Calculating the Final Concentration of a Sugar Solution
To calculate the concentration of a mixture of two sugar solutions, we add the mass of sugar from each solution and divide by the total mass of the mixed solution. First, we find the mass of sugar in each solution:
- 100 g of 20% sugar solution contains 20 g of sugar (20% of 100 g).
- 400 g of 50% sugar solution contains 200 g of sugar (50% of 400 g).
The combined mass of sugar is 20 g + 200 g = 220 g. The total mass of the mixed solution is the sum of the masses of the two solutions, which is 100 g + 400 g = 500 g.
The concentration of the mixed solution is calculated by dividing the total mass of sugar by the total mass of the solution:
Concentration = (Mass of Solute / Mass of Solution) x 100%
Concentration = (220 g / 500 g) x 100% = 44%
Therefore, the concentration of the sugar solution, after mixing the two solutions, is 44%.