Problem 65 - General Chemistry: Principles and Modern Applications

Question

A solution of sucrose in water is \(28.0 \%\) sucrose by mass and has a density of \(1.118 \mathrm{g} / \mathrm{mL} .\) What mass of sucrose, in grams, is contained in 3.50 L of this solution?

Step-by-Step Solution

Answer

The mass of sucrose in 3.50 L of this solution is approximately 1096 g.

Step 1: Convert volume to mass

The problem involves using the solution's density to convert the given volume to mass. This is done by multiplying the volume of the solution by its density: \(mass = volume \times density\). Here, the volume is 3.50 L (or 3500 mL, because 1 L = 1000 mL), and the density is 1.118 g/mL. So, the mass of the solution is \(3500 \, \mathrm{mL} \times 1.118 \, \mathrm{g/mL} = 3913 \, \mathrm{g}\).

Step 2: Calculate the mass of sucrose

Next, use the provided concentration of sucrose (28.0% by mass) to find the mass of sucrose in this solution. Keep in mind that the phrase '28.0% by mass' means that 28.0 g of sucrose are in every 100 g of solution. So, to find the mass of sucrose in 3913 g of solution, simply multiply the total mass of the solution by the concentration of sucrose: \(mass \, of \, sucrose = mass \, of \, solution \times concentration = 3913 \, \mathrm{g} \times 0.280 = 1095.64 \, \mathrm{g}\). Therefore, the mass of sucrose in 3.50 L of this solution is roughly 1096 g, assuming that the percentage is accurate to three significant figures.

Key Concepts

Density of Solutions

Density is an important property of solutions that connects mass with volume. When you know the density of a solution, you can use it as a conversion factor to switch between volume and mass. In our exercise, the density given is 1.118 g/mL. This means each milliliter of solution weighs 1.118 grams.

Knowing this, you can easily calculate the mass of a solution when you have the volume. For example, converting 3.50 liters of solution to mass involves multiplying the volume by the density:

• First, change liters to milliliters (since density is in g/mL): 3.50 L = 3500 mL.
• Then, multiply by the density: 3500 mL × 1.118 g/mL = 3913 g.

This conversion is key to solving many concentration and chemical solution problems.

Mass Percent

Mass percent describes how much of one substance is in a solution relative to the total mass of the solution. It is calculated using:\[ \text{Mass Percent} = \left( \frac{\text{Mass of Solute}}{\text{Total Mass of Solution}} \right) \times 100 \% \]In our example, the solution is 28.0% sucrose by mass. This means 28 grams of sucrose are present in every 100 grams of the solution. If you have the total mass of the solution (like 3913 grams in this case), you can find the mass of sucrose.To calculate:

• Find the mass of sucrose by multiplying by the mass percent: 3913 g × 0.280 = 1095.64 g of sucrose.

This percentage helps chemists and students understand the concentration levels in a straightforward manner.

Concentration by Mass

Concentration by mass involves expressing the amount of a substance in a mixture or solution. It is particularly useful for describing the proportion of solute in solutions. Unlike molarity, which uses moles, mass concentration uses mass, such as grams per liter. This approach is straightforward when working with solid solutes like sucrose. In practice:

• Calculate the mass of the solution using its volume and density.
• Determine the mass of the solute using mass percent (as shown previously).

This method clearly outlines how much solute is distributed throughout the solution, an essential part of understanding solution properties and outcomes in experiments.