Question

Calculate the mass, in grams, of solute present in each of the following solutions. a. 375 g of \(1.51 \%\) ammonium chloride solution b. 125 g of \(2.91 \%\) sodium chloride solution c. \(1.31 \mathrm{~kg}\) of \(4.92 \%\) potassium nitrate solution d. \(478 \mathrm{mg}\) of \(12.5 \%\) ammonium nitrate solution

Short answer

The mass of solute present in each solution is as follows: a. 5.66 g of ammonium chloride b. 3.64 g of sodium chloride c. 64.45 g of potassium nitrate d. 0.0598 g of ammonium nitrate

Step-by-step solution

Determine mass of solute in each solution using percentage concentration

We can use the following formula to calculate the mass of solute: Mass of solute = (Percentage concentration of solute / 100) × Total mass of solution Let's find the mass of the solute in each solution. a. 375 g of 1.51 % ammonium chloride solution: Mass of solute = (1.51 / 100) × 375 g b. 125 g of 2.91 % sodium chloride solution: Mass of solute = (2.91 / 100) × 125 g c. 1.31 kg of 4.92 % potassium nitrate solution (First, we need to convert 1.31 kg to grams): 1.31 kg = 1310 g Mass of solute = (4.92 / 100) × 1310 g d. 478 mg of 12.5 % ammonium nitrate solution (We will convert the mass in the end, first let's calculate in mg): Mass of solute = (12.5 / 100) × 478 mg

Calculate mass of solute in each solution

Perform calculations for each solution: a. Mass of ammonium chloride solute: = (1.51 / 100) × 375 g = 5.6625 g b. Mass of sodium chloride solute: = (2.91 / 100) × 125 g = 3.6375 g c. Mass of potassium nitrate solute: = (4.92 / 100) × 1310 g = 64.452 g d. Mass of ammonium nitrate solute (in mg): = (12.5 / 100) × 478 mg = 59.75 mg Now we need to convert the mass of ammonium nitrate solute from mg to g. 59.75 mg = 0.05975 g

Write the final answer

The mass of solute present in each solution is as follows: a. 5.66 g of ammonium chloride b. 3.64 g of sodium chloride c. 64.45 g of potassium nitrate d. 0.0598 g of ammonium nitrate

Key concepts

Molar Mass

Understanding molar mass is crucial in performing chemical calculations accurately. Molar mass is defined as the mass of one mole of a substance, normally expressed in grams per mole (g/mol). It represents the mass of a given substance divided by the amount of substance. In simpler terms, think of it as the 'weight' of one 'bundle' of atoms or molecules.

For example, the molar mass of water (H₂O) is approximately 18.02 g/mol, which means one mole of water molecules weighs 18.02 grams. Calculating the molar mass involves summing the atomic masses of all the atoms in a molecule. To relate this to our textbook problems, you would first calculate the molar mass of compounds like ammonium chloride (NH₄Cl), sodium chloride (NaCl), potassium nitrate (KNO₃), and ammonium nitrate (NH₄NO₃), using information from the periodic table.

Stoichiometry

Stoichiometry is the method used to calculate the quantities of reactants or products involved in a chemical reaction. It follows the law of conservation of mass, where the mass of the reactants equals the mass of the products. Stoichiometry utilizes balanced chemical equations to allow for the precise calculation of the necessary reactants to ensure a reaction proceeds and to predict the amount of product that will be formed.

In the context of our exercise, stoichiometry would not directly apply as we’re not dealing with a reaction. However, understanding the molar relationships in reactions could help grasp more complex solution concentration problems. But for these percentage concentration calculations, basic algebra suffices.

Solution Concentration

Solution concentration describes the amount of solute that is dissolved in a solvent. It can be expressed in various ways such as molarity, molality, or percent concentration. Percent concentration specifically refers to the ratio of the mass of the solute to the total mass of the solution, multiplied by 100 to get a percentage.

In the provided exercises, percent concentration is used to find the mass of the solute in a solution. For example, a 1.51% ammonium chloride solution indicates that 1.51 grams of ammonium chloride are present in every 100 grams of the solution. Through this information, you can calculate the mass of the solute by using the formula provided in Step 1 of the solution.

Chemical Calculations

Chemical calculations involve a range of mathematical techniques used to solve problems pertaining to chemical substances and their reactions. Key concepts in these calculations often include molar mass, solution concentration, and the Avogadro’s number, which ties into stoichiometry for reaction calculations.

In the context of our textbook problems, the chemical calculations are fairly straightforward. You need to apply the percentage concentration to the total mass of the solution to find out how much of the solute is involved. Units also play a critical role here; conversions between units (e.g. milligrams to grams, kilograms to grams) are often required to ensure that you are working with consistent measures throughout the calculation process, as seen in parts c and d of the problem set.