Calculate the amount of water (in kilograms) that must be added to 12.0 g of urea, (NH 2 ) 2 CO, in the preparation of a 18.3 percent by mass solution. The molar mass of urea, (NH 2 ) 2 CO, is 60.055 g/mol.

Calculate the amount of water in kilograms that must be added to 12 grams of urea, which has the molecular formula of n h 22 c o, this is yet another way we can write Urea, in the preparation of an 18.3% by mass solution. Here we're told the molar mass of Urea is 60.0 55 grams per mole. Alright. So here we're going to say our mass percent equals the mass of our solute divided by mass of solution. So we're given our mass percent as 18.3%, that's gonna equal, let's see. So here they're asking how much water needs to be added. The 12.0 grams is the is our urea and it represents our solute. So it's 12.0 grams of urea divided by grams of solution, so that's still 12.0 grams of urea, plus our unknown grams of water. What we have to do here is solve for x. So we're gonna cross multiply these here together, so that's 18.3 and that's 12.0 +x. Here, the 18.3 gets distributed, distributed, and that will equal 12. So here when we distribute that's gonna give me 219.6 +18.3x equals equals 12. Oh, and remember there it's times a 100 actually, so that'd be 12 times 100, so that'd be 1200. Alright. So here we have to isolate x so subtract 219.6 from both sides here. So negative two point 219.6. So here I'm gonna bring the math over. So it's gonna give me 18.3 equals 980.4, divide both sides by 18.3 to isolate our x. So x here equals 53 point 57 grams of water, and if we want to change that to kilograms, which we need to, we'd say, remember 1 kilo is equal to 10 to the 3 grams. And when we do that, we get 0.0535 7 kilograms. Here, the best answer available for us would be option b. So option b would be our final answer.

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14. Solutions

Solutions: Mass Percent

General Chemistry

14. Solutions

Solutions: Mass Percent

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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.

0.644 kg

0.0535 kg

6.44 kg

0.0755 kg

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Verified step by step guidance

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.