Multiple Choice
What is the mass percent concentration of sugar in a solution if 150 grams of sugar is dissolved in 850 grams of water?
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14. Solutions
Solutions: Mass Percent
Multiple Choice
Calculate the amount of water (in kilograms) that must be added to 12.0 g of urea, (NH2)2CO, in the preparation of a 18.3 percent by mass solution. The molar mass of urea, (NH2)2CO, is 60.055 g/mol.
A
0.644 kg
B
0.0535 kg
C
6.44 kg
D
0.0755 kg
Verified step by step guidance1
Step 1: Understand the concept of percent by mass. Percent by mass is calculated using the formula: \( \text{Percent by mass} = \left( \frac{\text{mass of solute}}{\text{mass of solution}} \right) \times 100 \). In this problem, the solute is urea, and the solution is the mixture of urea and water.
Step 2: Set up the equation for percent by mass. Let \( m_{\text{water}} \) be the mass of water added. The mass of the solution is the sum of the mass of urea and the mass of water: \( \text{mass of solution} = 12.0 \text{ g} + m_{\text{water}} \). The percent by mass of urea in the solution is given as 18.3%.
Step 3: Convert the percent by mass into a decimal for calculation purposes: \( 18.3\% = 0.183 \). Use this to set up the equation: \( 0.183 = \frac{12.0}{12.0 + m_{\text{water}}} \).
Step 4: Solve the equation for \( m_{\text{water}} \). Rearrange the equation to isolate \( m_{\text{water}} \): \( 0.183 \times (12.0 + m_{\text{water}}) = 12.0 \). Expand and solve for \( m_{\text{water}} \).
Step 5: Convert the mass of water from grams to kilograms. Since 1 kg = 1000 g, divide the mass of water in grams by 1000 to find the mass in kilograms.
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