Problem 207 - Introductory Chemistry Atoms First

Question

A solution is prepared by dissolving \(5.00 \mathrm{~g}\) of sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\), in \(1.00 \mathrm{~L}\) of water. What is the percent by mass concentration of sucrose? (The density of water is \(1.00 \mathrm{~g} / \mathrm{mL}\) ).

Step-by-Step Solution

Answer

The percent by mass concentration of sucrose in the solution is \(0.498\%\).

Step 1: Find the mass of sucrose

Given, the mass of sucrose is 5.00 g.

Step 2: Find the volume of water

Given, the volume of water is 1.00 L (1000 mL).

Step 3: Calculate the mass of water

The density of water is given as 1.00 g/mL. We can find the mass of water using the formula: Mass = Density × Volume Mass of water = (1.00 g/mL) × (1000 mL) = 1000 g

Step 4: Calculate the total mass of the solution

The total mass of the solution is the sum of the masses of sucrose and water. Total mass = Mass of sucrose + Mass of water Total mass = 5.00 g + 1000 g = 1005 g

Step 5: Calculate the percent by mass concentration of sucrose

Use the formula: Percent by mass = (Mass of solute / Total mass) × 100 Percent by mass of sucrose = (5.00 g / 1005 g) × 100 = 0.498 \%

Key Concepts

Solution Preparation

Understanding solution preparation is a fundamental concept in chemistry and a typical task in many laboratory settings. A solution is a homogeneous mixture composed of two or more substances, where one substance (the solute) is dissolved in another (the solvent). The process of making a solution involves measuring and mixing the solute and solvent in correct proportions to reach a desired concentration.

When preparing a solution with a solid solute like sucrose, the solute is weighed and then added to a pre-measured amount of solvent. In our exercise, sucrose is dissolved in water to create a solution. Accurate measuring of both substances is crucial. Typically, a balance is used for measuring the mass of the solid, and a volumetric flask or cylinder for measuring the liquid volume. The solubility of a substance refers to how well it dissolves in a solvent at a given temperature and pressure, and in this instance, we assume that 5.00 grams of sucrose is entirely soluble in 1.00 liter of water.

Sucrose Solubility

Sucrose, commonly known as table sugar, is a carbohydrate that easily dissolves in water. The solubility of sucrose in water at room temperature is high, making it convenient to prepare solutions of various concentrations for use in food, beverages, and experiments.

The solubility of a substance like sucrose in a solvent depends on temperature, with higher temperatures generally increasing solubility. It is important to note that the solubility limit refers to the maximum amount of solute that can dissolve in a given quantity of solvent at a specific temperature. Exceeding this limit results in an unsaturated, saturated, or supersaturated solution, depending on the amount of solute added relative to its solubility.

Molarity and Dilution

Molarity is a measure of the concentration of a solution, defined as the number of moles of solute per liter of solution. It's expressed with the unit M (molar) and calculated using the equation:

Molarity = \( \frac{moles~of~solute}{liters~of~solution} \)

When preparing a solution from a more concentrated one, a dilution process is involved. Dilution is the addition of solvent to a solution to decrease the concentration of solute. This is often used when a lower concentration is needed for a particular use. The relationship between the initial and final concentrations and volumes is given by the dilution equation:

\( M_1V_1 = M_2V_2 \)

where \(M_1\) and \(V_1\) are the molarity and volume of the initial concentrated solution and \(M_2\) and \(V_2\) are the molarity and volume of the final diluted solution. Understanding this concept is crucial for accurately making solutions in the lab and for adjusting concentrations to fit experimental needs.