Question

Calculate the mass, in grams, of NaCl present in each of the following solutions. a. \(11.5 \mathrm{~g}\) of \(6.25 \% \mathrm{NaCl}\) solution b. \(6.25 \mathrm{~g}\) of \(11.5 \% \mathrm{NaCl}\) solution c. \(54.3 \mathrm{~g}\) of \(0.91 \% \mathrm{NaCl}\) solution d. 452 g of \(12.3 \%\) NaCl solution

Short answer

The mass of NaCl in each solution is: a. \(0.71875\,g\) b. \(0.71875\,g\) c. \(0.49383\,g\) d. \(55.596\,g\)

Step-by-step solution

a. Calculate the mass of NaCl in 11.5 g of 6.25% NaCl solution

To find the mass of NaCl, you multiply the mass of the solution (11.5 g) by the percentage of NaCl in it (6.25%). Make sure to convert the percentage to a decimal by dividing by 100: \( (11.5\,g) * (6.25\% /100) = (11.5\,g) * 0.0625 = 0.71875\,g\)

b. Calculate the mass of NaCtl in 6.25 g of 11.5% NaCl solution

To find the mass of NaCl in this solution, you need to multiply the mass of the solution (6.25 g) by the percentage of NaCl in it (11.5%). Again, make sure to convert the percentage to a decimal by dividing by 100: \( (6.25\,g) * (11.5\% /100) = (6.25\,g) * 0.115 = 0.71875\,g\)

c. Calculate the mass of NaCl in 54.3 g of 0.91% NaCl solution

Finding the mass of NaCl in this solution involves multiplying the mass of the solution (54.3 g) by the percentage of NaCl in it (0.91%). Remember to convert the percentage to a decimal by dividing by 100: \( (54.3\,g) * (0.91\% /100) = (54.3\,g) * 0.0091 = 0.49383\,g\)

d. Calculate the mass of NaCl in 452 g of 12.3% NaCl solution

To find the mass of NaCl in this solution, multiply the mass of the solution (452 g) by the percentage of NaCl in it (12.3%). Don't forget to convert the percentage to a decimal by dividing by 100: \( (452\,g) * (12.3\% /100) = (452\,g) * 0.123 = 55.596\,g\) So, the mass of NaCl in each solution is: a. 0.71875 g b. 0.71875 g c. 0.49383 g d. 55.596 g

Key concepts

Concentration of Solutions

Understanding the concentration of solutions is pivotal in chemistry and plays a crucial role in various real-world applications. Concentration refers to the amount of substance (solute) present in a given volume or mass of solution. There are several ways to express concentration, such as molarity, molality, normality, and mass percent.

For instance, if we have a saline solution (water + salt), the concentration tells us how much salt is dissolved in a certain amount of water. This tells us how 'strong' or 'weak' the solution is. In everyday life, this concept is used when making simple things like lemonade to complex tasks such as preparing intravenous drips for medical use.

Mass Percent

Mass percent is a common way to express the concentration of a solution. It is also known as mass/volume percent when referring to solutions where the concentration is expressed in terms of the volume of the solvent. The mass percent is calculated as the mass of solute (the substance being dissolved) divided by the total mass of the solution, and then multiplied by 100 to convert it to a percentage.

For example, if you dissolve 5 grams of salt in 95 grams of water, the total mass of the solution is 100 grams. The mass percent of salt in this solution would be \( (5/100) \times 100\% = 5\% \) of salt. The modification to a percentage makes it easier to understand and compare concentrations of different solutions.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the relative quantities of reactants and products in chemical reactions. It is a form of bookkeeping for chemistry where the 'coefficients' in chemical equations are used to predict the amount of reactants needed or products formed.

In simple terms, it lets us use balanced chemical equations to scale up reactions from the molecular level to the real world, where we measure substances in grams and liters. It's like a recipe for a reaction that tells you how much of each ingredient you need to produce a certain amount of product.

Chemical Calculations

Chemical calculations encompass a broad range of mathematical operations used to solve problems in chemistry. From the mass-mass relationship in a chemical reaction to the calculations involving the gas laws, chemical calculations allow us to quantitatively understand the underlying stoichiometry in a given problem.

For example, the concentration calculations we performed for NaCl solutions involve taking into account the percentage purity of the compound and its molar mass. It requires an understanding of stoichiometry to determine how much reactant is needed or how much product will be formed under given conditions.