Problem 68 - Chemistry Matter and Change

Question

How many grams of LiCl are in 275 g of a 15\(\%\) aqueous solution of LiCl?

Step-by-Step Solution

Answer

There are \( 41.25 \) grams of LiCl in the 275 g of a 15% aqueous solution of LiCl.

Step 1: Determine the percentage of LiCl in the solution

In the problem, we're given that the aqueous solution consists of 15% LiCl. This means that 15% of the total mass of the solution (275 g) is LiCl.

Step 2: Calculate the mass of LiCl

Now that we have the percentage of LiCl in the solution, we can calculate the mass of LiCl. To do this, we can use the formula: mass of LiCl = (percentage of LiCl / 100) * total mass of the solution Substitute the given values: mass of LiCl = (15% / 100) * 275 g mass of LiCl = (0.15) * 275 g mass of LiCl = 41.25 g So, there are 41.25 grams of LiCl in the 275 g of a 15% aqueous solution of LiCl.

Key Concepts

Percent Concentration

Understanding percent concentration is crucial when dealing with solutions in chemistry. It's a way of expressing how much solute is present in a solution compared to the total amount of the solution. The percent concentration is calculated by dividing the mass of the solute by the total mass of the solution and then multiplying by 100 to convert the value to a percentage. For example, if you have a solution where 15 grams of salt is dissolved in 100 grams of water, the percent concentration (by mass) of salt is given as:
\[\text{Percent concentration} = \left(\frac{\text{mass of solute}}{\text{total mass of solution}} \right) \times 100\% = \left(\frac{15}{100+15} \right) \times 100\% = 13.04\%\]
When working with percent concentrations, it's also important to note whether the percentage is based on mass or volume, as this can affect the calculation. For aqueous solutions, like the one in our exercise, the percent concentration is typically based on mass, considering the density of water is approximately 1 gram per milliliter, simplifying calculations.

Mass of Solute

The mass of the solute is simply the weight of the substance that is dissolved in a solvent to form a solution. It is usually measured in grams when dealing with solid solutes, and in chemistry, it is a fundamental quantity for preparing solutions with desired properties. In our exercise example, by knowing the percent concentration and the total mass of the solution, we can find the mass of the solute, lithium chloride (LiCl), using the formula given in the step by step solution.
It's essential to always confirm that the units are consistent to avoid errors in the calculation. In this case, since the total mass of the solution is provided in grams and percent concentration is dimensionless, our calculation yields the mass of LiCl in the same units, grams. Grasping this concept enables you to mix solutions of known concentration or to determine the concentration of a pre-existing mixture.

Stoichiometry

Stoichiometry is a section of chemistry that involves calculating the quantities of reactants and products involved in a chemical reaction. It is based on the conservation of mass and the concept of the mole, linking the mass of substances to the number of particles they contain. When you're performing stoichiometry calculations, you start by converting all your measurements into moles, which allows you to use the coefficients in the balanced chemical equation to find the relationships between the substances involved.
In calculations pertaining to solutions, like in our exercise, stoichiometry often comes into play when reacting solutions of known concentrations to create a product. While not directly involved in the calculation of the mass of solute in a given percent concentration, stoichiometry is an overarching concept that ties in mass and molar relationships within chemical reactions, making it an essential tool for any chemist.