Question

How many grams of $\mathrm{NaCl}$ are present in $225\mathrm{mL}$ of a $2.3\mathrm{\%}$ solution by mass? Assume that the density of the solution is $1.0\mathrm{g}/\mathrm{mL}$

Short answer

There are 5.175 grams of NaCl present in 225 mL of a 2.3% solution.

Step-by-step solution

Identify the Mass of the Solution

First, determine the total mass of the solution. Since the density is given as 1.0 g/mL, you can calculate the mass by multiplying the volume of the solution by its density. The mass (m) of the solution is calculated using the formula: m = volume × density.

Calculate the Mass of the Solution

Using the formula from Step 1, compute the mass of 225 mL of solution. m = 225 mL × 1.0 g/mL = 225 g.

Calculate the Mass of NaCl in the Solution

Multiply the total mass of the solution by the percentage (given as 2.3%) to find the mass of NaCl. Convert the percentage to its decimal form by dividing by 100. Mass of NaCl = total mass of solution × (percentage of NaCl / 100).

Find the Mass of NaCl

Now compute the mass of NaCl: Mass of NaCl = 225 g × (2.3/100) = 5.175 g.

Key concepts

Concentration of Solution

Understanding the concentration of a solution is critical when dealing with any mixture of substances. Concentration is a measure of the amount of solute present in a given quantity of solvent or solution. In chemistry, this can often be expressed as a percentage, commonly known as 'mass percent' or 'weight/weight percent'. It is defined as the mass of the solute divided by the total mass of the solution, multiplied by 100%.

For example, a 2.3% NaCl solution means that there are 2.3 grams of NaCl in every 100 grams of the solution. To determine the mass of NaCl in any volume of this solution, one must first know the total mass of the solution and then apply the percentage. This relationship is crucial for many applications, including preparing chemical reagents, cooking recipes, and even in pharmacology for drug preparation.

When dealing with solutions, understanding and calculating concentration allows for accurate control over the properties of the solution, such as its boiling and freezing points, which can be important for a wide range of scientific experiments and industrial processes.

Density and Mass Relationship

Density is a fundamental property of materials that relates mass and volume. It's defined as the mass of an object divided by its volume, usually expressed in grams per milliliter (g/mL) or kilograms per cubic meter (kg/m^3).

The equation to calculate density is simple: $$\text{Density}=\frac{\text{Mass}}{\text{Volume}}$$
When we know the density of a substance and have either the mass or the volume, we can calculate the other. For instance, the density of our NaCl solution is given as 1.0 g/mL. This means that for every milliliter of the solution, the mass is 1 gram. To find the total mass of any volume of solution, multiply the volume by the density.

This concept is not only crucial in chemistry but also in various scientific disciplines. Whether you are an engineer calculating the load structures or a cook measuring ingredients, understanding the relationship between density, mass, and volume is essential.

Stoichiometry

Stoichiometry is a section of chemistry that involves the calculation of the quantities of reactants and products in chemical reactions. It is based on the law of conservation of mass, where the total mass of the reactants equals the total mass of the products.

In the context of our NaCl solution example, stoichiometry isn't directly applied to the calculation since we're not dealing with a reaction. However, stoichiometric principles are implicitly at work when using the percentage concentration to calculate the mass of the solute or when changing the quantities of substances in a preparation. Furthermore, a solid grasp of stoichiometry becomes indispensable when scaling up a reaction from a laboratory to an industrial setting or adjusting recipes for production.

A deeper exploration into stoichiometry would also include topics like the mole concept, molar ratios in balanced equations, and the use of Avogadro's number. These allow chemists to predict the amounts of substances consumed and formed in a reaction, making stoichiometry a powerful tool in the field of chemistry.