Question

A solution is prepared by adding \(5 \mathrm{~g}\) of a solute \({ }^{\prime} X^{\prime}\) to \(45 \mathrm{~g}\) of solvent ' \(Y\). What is the mass per cent of the solute \({ }^{-} X^{*}\) ? (a) \(10 \%\) (b) \(11.1 \%\) (c) \(90 \%\) (d) \(75 \%\)

Short answer

The mass percent of the solute is 10%.

Step-by-step solution

Understanding Mass Percent

Mass percent is a way of expressing the concentration of a component in a mixture or solution. It is defined as the mass of a specific component divided by the total mass of the mixture or solution, then multiplied by 100 to get a percentage. The formula to calculate mass percent is given by: \[\text{Mass percent} = \left( \frac{\text{Mass of solute}}{\text{Mass of solution}} \right) \times 100\%\]

Calculating Total Mass of the Solution

Calculate the total mass of the solution by adding the mass of the solute to the mass of the solvent. The total mass of the solution is: \[\text{Mass of solution} = \text{Mass of solute} + \text{Mass of solvent}\]

Applying the Formula

Use the provided masses for the solute and solvent to calculate the mass percent of the solute within the solution. We have \(5 \mathrm{~g}\) of solute and \(45 \mathrm{~g}\) of solvent, giving a total mass of \(5 \mathrm{~g} + 45 \mathrm{~g} = 50 \mathrm{~g}\). Applying the formula: \[\text{Mass percent} = \left( \frac{5 \mathrm{~g}}{50 \mathrm{~g}} \right) \times 100\%\]

Performing the Calculation

Compute the mass percent of the solute based on the given values: \[\text{Mass percent} = \left( \frac{5 \mathrm{~g}}{50 \mathrm{~g}} \right) \times 100\% = 10\%\]

Key concepts

Concentration of a Solution

When we talk about the concentration of a solution, we're essentially discussing how much of a specific substance (the solute) is present within a certain amount of another substance (the solvent). It's a way to quantify the ratio of solute to solvent in a mixture. Understanding this concept is fundamental when preparing chemical solutions in labs or following recipes in the kitchen.

What Is Concentration?

Concentration is a measure of the 'amount' of a given substance in a mix. It can be expressed in various forms, like molarity, molality, and mass percent among others. Often in chemistry, we're interested in the mass percent because it doesn't change with temperature, making calculations simpler and more direct.

Relevance in Different Fields

This concept of concentration applies in many areas - from pharmacology, where precise dosages of medication need to be administered, to the food industry, where consistency in flavor and ingredient ratios is key.

Mass Percent Formula

The mass percent formula is a straightforward mathematical expression used to determine the concentration of a solute in a solution.

The Mass Percent Equation

Expressed mathematically: \[\begin{equation}Mass \ percent = \left( \frac{Mass \ of \ solute}{Mass \ of \ solution} \right) \times 100\%\end{equation}\]This formula is a building block in studying chemistry, because it helps relate the masses of substances to their relative proportions.

Practical Use

Let's say you're dissolving salt in water to prepare a saline solution. Using the mass percent formula, you can calculate exactly how much salt is in your solution compared to the total weight of the mixture, ensuring you achieve the desired salinity.

Solute and Solvent Mass

In order to accurately utilize the mass percent formula, it's essential to first comprehend the roles of the solute and the solvent in a solution. The solute is the substance that is being dissolved, while the solvent is the medium that dissolves the solute.

Defining Solute and Solvent

The solute is typically present in a smaller amount and can be a solid, liquid, or a gas. The solvent, usually in a larger quantity, is most often a liquid, but can also be a solid or gas.

Importance of Accurate Measurement

For precise calculations, the mass of the solute and the solvent must be determined accurately. This means weighing them on a scale or balance to ensure that their mass readings are correct for the solution's composition. Inaccuracies can result in an incorrect mass percent, leading to potential errors in whatever task the solution is intended for, be it a chemical reaction or a culinary recipe.