Questions: What goes in the denominator? 10.2 g sucrose 10.2 solution 100 g sucrose 36 g sucrose 100 g solution What volume of a 10.2% m/v solution of sucrose would be needed to deliver 36 g of sucrose?

What goes in the denominator?
10.2 g sucrose
10.2 solution
100 g sucrose
36 g sucrose
100 g solution

What volume of a 10.2% m/v solution of sucrose would be needed to deliver 36 g of sucrose?

Transcript text: What goes in the denominator? 10.2 g sucrose 10.2 solution 100 g sucrose 36 g sucrose 100 g solution - What volume of a $10.2 \% \mathrm{~m} / \mathrm{v}$ solution of sucrose would be needed to deliver 36 g of sucrose?

Solution

Solution Steps

Step 1: Understand the Problem

We need to find the volume of a 10.2% m/v (mass/volume) sucrose solution that contains 36 g of sucrose.

Step 2: Define the Given Information

The concentration of the solution is 10.2% m/v, which means 10.2 g of sucrose per 100 mL of solution.
We need to find the volume of solution that contains 36 g of sucrose.

Step 3: Set Up the Proportion

We can set up a proportion based on the given concentration: \[ \frac{10.2 \text{ g sucrose}}{100 \text{ mL solution}} = \frac{36 \text{ g sucrose}}{V \text{ mL solution}} \]

Step 4: Solve for the Volume $ V $

Cross-multiply to solve for $ V $: \[ 10.2 \text{ g} \times V \text{ mL} = 36 \text{ g} \times 100 \text{ mL} \] \[ 10.2V = 3600 \] \[ V = \frac{3600}{10.2} \] \[ V \approx 352.9412 \text{ mL} \]

Step 5: Round to Four Significant Digits

Round the volume to four significant digits: \[ V \approx 352.9 \text{ mL} \]