a chemist has 200 ml of a 10% sucrose solution. if she adds x milliliters of a 40% sucrose solution, what is…

a chemist has 200 ml of a 10% sucrose solution. if she adds x milliliters of a 40% sucrose solution, what is the percent concentration of the final mixture? final concentration = \\(\\frac{total\\ mass\\ of\\ sucrose}{total\\ volume\\ of\\ solution}\\cdot100\\) which expression represents the total mass, in grams, of sucrose in the final mixture? which expression represents the total volume, in milliliters, of the final mixture? done

a chemist has 200 ml of a 10% sucrose solution. if she adds x milliliters of a 40% sucrose solution, what is the percent concentration of the final mixture? final concentration = \\(\\frac{total\\ mass\\ of\\ sucrose}{total\\ volume\\ of\\ solution}\\cdot100\\) which expression represents the total mass, in grams, of sucrose in the final mixture? which expression represents the total volume, in milliliters, of the final mixture? done

Answer

Explanation:

Step1: Calculate mass of sucrose in 10% solution

The initial 200 - mL 10% sucrose solution has mass of sucrose $0.1\times200$ grams. Since we have two 200 - mL 10% solutions, the total mass of sucrose from these is $2\times0.1\times200$ grams. The $x$ milliliters of 40% sucrose solution has mass of sucrose $0.4x$ grams. So the total mass of sucrose in the final mixture is $2\times0.1\times200 + 0.4x=40 + 0.4x$ grams.

Step2: Calculate total volume of final mixture

The initial two 200 - mL solutions have a combined volume of $2\times200$ mL, and then we add $x$ mL of the 40% solution. So the total volume of the final mixture is $2\times200+x = 400 + x$ mL.

Answer:

Total mass of sucrose in final mixture: $40 + 0.4x$ Total volume of final mixture: $400 + x$