Calculate the following problems Round all answers to tenths

Calculate the following problems. Round all answers to tenths. Show all your calculations. How many grams of sucrose must be dissolved in 500 mL of water to make a 75% solution? How many grams of sucrose would be needed to make 1000 mL of 75% solution? How many grams of sucrose would be needed for 250 mL of 75% solution?

Solution

Part 1

Let grams of sucrose required to be added be x. When x grams of sucrose is added to 500 ml of water, the weight of the solution is (500 + x) of which sucrose is x grams. Then, percentage of sucrose in the solution = x/(500 + x). By the problem, this should be 75/100. So, we have x/(500 + x) = 75/100 = 3/4 or 4x = 1500 + 3x or x = 1500.

So, 1500 grams of sucrose when dissolved in 500 ml water would give a 75% sucrose solution - ANSWER

Part 2

Let grams of sucrose required to be added be x. Given that the total quantity of solution is 1000, if the concentration has to be 75%, (quantity of sucrose/1000) must be euual to 75/100 or 3/4. i.e., x/1000 = 3/4 or 4x = 3000 or x = 3000/4 = 750 ANSWER

Part 3

Let grams of sucrose required to be added be x. Given that the total quantity of solution is 250, if the concentration has to be 75%, (quantity of sucrose/250) must be euual to 75/100 or 3/4. i.e., x/250 = 3/4 or 4x = 750 or x = 750/4 = 187.5 ANSWER