A solution contains \(10.05 \%\) sucrose (cane sugar) by mass. What mass of the solution, in grams, is needed for an application that requires \(1.00 \mathrm{kg}\) sucrose?

Short Answer

Expert verified
The mass of the solution required is 9950 grams.

Step by step solution

01

- Convert Percentage to Decimal

First, convert the percentage of sucrose to decimal by dividing the percentage by 100. So, 10.05% becomes 0.1005.
02

- Identify the Given and Required Values

Identify and collect the data given in the problem. We need to find the total weight of the solution needed, and we know that the weight of sucrose required is 1 kg. Also, collect the percentage of sucrose in the solution in decimal form, which is 0.1005, obtained from step 1.
03

- Calculation

Since we know that the sucrose is 0.1005 of the total solution mass, assign 0.1005x to the mass of sucrose, where x is the total mass of the solution. Since it's required that this mass of sucrose must be 1 kg, we write the equation 0.1005x = 1. Solve for x to obtain the total mass of the solution in kilogram.
04

- Solution Conversion

The answer from the previous step is in kilograms. Convert it to grams (because the problem asks for the weight in grams) by multiplying by 1000 as 1 kilogram is equivalent to 1000 grams.

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