Question

Calculate the mass fraction and the weight percent of the solute in each of these solutions: (a) \(20.7 \mathrm{~g} \mathrm{NaCl}\) in \(175 \mathrm{~g} \mathrm{H}_{2} \mathrm{O}\). (b) \(1.45 \mathrm{~g}\) ethanol in \(10.0 \mathrm{~g} \mathrm{H}_{2} \mathrm{O}\). (c) \(20.0 \mathrm{~g} \mathrm{CS}_{2}\) in \(45.0 \mathrm{~g} \mathrm{CHCl}_{3} .\) (d) \(4.00 \mathrm{~mL}\) benzene \((d=0.877 \mathrm{~g} / \mathrm{mL})\) in \(120 . \mathrm{g}\) diethyl ether.

Short answer

(a) 10.58%, (b) 12.65%, (c) 30.77%, (d) 2.84%

Step-by-step solution

Understanding the Problem

To solve this problem, we need to calculate the mass fraction and weight percent of the solute for each given solution. The mass fraction is the ratio of the mass of the solute to the total mass of the solution. The weight percent is the mass fraction multiplied by 100%. We'll work through each part separately.

Calculate Mass Fraction and Weight Percent for (a)

For (a) 20.7 g NaCl in 175 g H₂O:1. Total mass of solution = mass of solute + mass of solvent = 20.7 g + 175 g = 195.7 g.2. Mass fraction of NaCl = mass of NaCl / total mass = 20.7 g / 195.7 g.3. Weight percent = mass fraction × 100%. Mass Fraction: \( \frac{20.7}{195.7} \approx 0.1058 \) Weight Percent: \( 0.1058 \times 100 \approx 10.58\% \)

Calculate Mass Fraction and Weight Percent for (b)

For (b) 1.45 g ethanol in 10.0 g H₂O:1. Total mass of solution = 1.45 g + 10.0 g = 11.45 g.2. Mass fraction of ethanol = mass of ethanol / total mass = 1.45 g / 11.45 g.3. Weight percent = mass fraction × 100%. Mass Fraction: \( \frac{1.45}{11.45} \approx 0.1265 \) Weight Percent: \( 0.1265 \times 100 \approx 12.65\% \)

Calculate Mass Fraction and Weight Percent for (c)

For (c) 20.0 g CS₂ in 45.0 g CHCl₃:1. Total mass of solution = 20.0 g + 45.0 g = 65.0 g.2. Mass fraction of CS₂ = mass of CS₂ / total mass = 20.0 g / 65.0 g.3. Weight percent = mass fraction × 100%. Mass Fraction: \( \frac{20.0}{65.0} \approx 0.3077 \) Weight Percent: \( 0.3077 \times 100 \approx 30.77\% \)

Calculate Mass Fraction and Weight Percent for (d)

For (d) 4.00 mL benzene (d = 0.877 g/mL) in 120.0 g diethyl ether:1. Mass of benzene = volume × density = 4.00 mL × 0.877 g/mL = 3.508 g.2. Total mass of solution = 3.508 g + 120.0 g = 123.508 g.3. Mass fraction of benzene = mass of benzene / total mass = 3.508 g / 123.508 g.4. Weight percent = mass fraction × 100%. Mass Fraction: \( \frac{3.508}{123.508} \approx 0.0284 \) Weight Percent: \( 0.0284 \times 100 \approx 2.84\% \)

Key concepts

weight percent

Weight percent is a term commonly used in chemistry to describe the concentration of a solute in a solution. Understanding it is key to solving many chemistry problems. It is expressed as the percentage of the weight of the solute compared to the total weight of the solution. When asked for the weight percent, we are essentially finding out what fraction of the total mass of the solution is made up by the solute, expressed as a percentage.

To calculate the weight percent, follow these simple steps:

• Calculate the total mass of the solution by adding together the mass of the solute and the mass of the solvent.
• Divide the mass of the solute by this total mass to find the mass fraction.
• Finally, multiply the mass fraction by 100 to convert it into a percentage. This is the weight percent.

For example, if you have 20.7 grams of NaCl in 175 grams of water, the total mass of the solution is 195.7 grams. The mass fraction would be approximately 0.1058, so the weight percent is 10.58%. It tells you that 10.58% of the solution's mass is from NaCl.

solute

A solute is the substance that is dissolved in a solvent to form a solution. It can be in various forms – solid, liquid, or gas – depending on the type of solution. The nature of the solute and the solvent determines many of the characteristics of the final solution, such as its boiling point or conductivity.

When performing calculations involving solutions, such as finding the weight percent or mass fraction, it's important to accurately measure the mass of the solute. This value will greatly affect your results.

For instance, in the exercise given, NaCl, ethanol, CS₂, and benzene are used as solutes in their respective solutions. Ensuring accurate weighing of these substances is crucial because errors here will lead to incorrect solutions that affect the entire process of solving the problem. In some solutions, the density might be needed to convert volumes to mass, like with benzene, where density aids in finding the mass necessary for further calculations.

solution

A solution is defined as a homogeneous mixture of two or more substances. In a solution, the solute is the substance present in a lesser amount, dissolved in the solvent, which is the substance present in a greater amount. Solutions can appear in different phases – solid, liquid, or gas – but the most common are liquid solutions.

In scientific terms, solutions are essential because they allow solutes to be evenly dispersed throughout a solvent, making them evenly distributed at the molecular level. This uniformity means any sample of the solution will have the same properties and composition.

When preparing or analyzing a solution, knowing the exact amounts of solute and solvent allows for precise determination of properties such as concentration. This concentration can be expressed in measures such as molarity, molality, volume percent, or weight percent, with weight percent focusing on the mass of the solute relative to the solution's total mass.