Problem 34 - Chemistry Matter and Change

Question

Solve How much ammonium chloride \(\left(\mathrm{NH}_{4} \mathrm{Cl}\right),\) in grams, is needed to produce 2.5 L of a 0.5 \(\mathrm{M}\) aqueous solution?

Step-by-Step Solution

Answer

To produce a 2.5 L of a 0.5 M aqueous solution of ammonium chloride (NH4Cl), 66.86 grams of NH4Cl are needed.

Step 1: Calculate the moles of NH4Cl needed

To find the moles of NH4Cl required, we use the formula: Moles of solute = Molarity × Volume of solution (in Liters) Given that the desired concentration (molarity) is 0.5 M and the volume of the solution is 2.5 L, we have: Moles of NH4Cl = 0.5 M × 2.5 L Moles of NH4Cl = 1.25 moles

Step 2: Calculate the molar mass of NH4Cl

To determine the mass of NH4Cl needed, we first need to find its molar mass. We can determine the molar mass of NH4Cl by adding the molar masses of its constituent elements (N, H, and Cl): Molar mass of N = 14.01 g/mol Molar mass of H = 1.01 g/mol Molar mass of Cl = 35.45 g/mol NH4Cl has 1 nitrogen atom, 4 hydrogen atoms, and 1 chlorine atom, so we'll add their respective molar masses: Molar mass of NH4Cl = 14.01 + 4(1.01) + 35.45 Molar mass of NH4Cl = 53.49 g/mol

Step 3: Calculate the mass of NH4Cl needed

To find the mass of NH4Cl required, we'll multiply the moles calculated in Step 1 by the molar mass obtained in Step 2: Mass of NH4Cl = Moles of NH4Cl × Molar mass of NH4Cl Mass of NH4Cl = 1.25 moles × 53.49 g/mol Mass of NH4Cl = 66.86 grams So, 66.86 grams of ammonium chloride (NH4Cl) are needed to produce 2.5 L of a 0.5 M aqueous solution.

Key Concepts

Stoichiometry

Stoichiometry is the study of the quantitative relationships, or ratios, between reactants and products in chemical reactions. It is a fundamental concept in chemistry that allows us to predict how much of each substance is needed or produced during a reaction. Understanding stoichiometry is essential when performing molarity calculations for preparing chemical solutions.

In the example provided, stoichiometry is applied to determine the amount of ammonium chloride needed to make an aqueous solution with a specific molarity. The calculation involves converting between moles, the standard unit for the amount of substance in chemistry, and liters of solution, using the molarity as a conversion factor. The stoichiometric relationship between moles and liters is captured by the formula: \[ \text{Moles of solute} = \text{Molarity} \times \text{Volume of solution (in Liters)} \]

By using stoichiometry, we relate the molarity of the solution to moles of solute, and then to the mass of solute needed. A clear grasp of this relationship is the first step toward accurate chemical preparation and analysis.

Molar Mass

Every chemical compound has a property known as molar mass, which is the mass of one mole of that substance. The molar mass is usually expressed in grams per mole (\(\text{g/mol}\)), and it is a critical factor for converting between the weight of a substance and the amount of substance in moles. The molar mass is determined by summing the atomic masses of all the atoms that constitute a molecule of the substance.

For example, to calculate the molar mass of ammonium chloride (\(\mathrm{NH}_{4} \mathrm{Cl}\)), we add the atomic masses of nitrogen (\(14.01 \text{g/mol}\)), hydrogen (\(1.01 \text{g/mol}\)), and chlorine (\(35.45 \text{g/mol}\)). These atomic masses are sourced from the periodic table, reflecting the average mass of all isotopes of an element. It's essential to include the correct number of each atom, as in \(\mathrm{NH}_{4} \mathrm{Cl}\) which contains four hydrogen atoms:

\[ \text{Molar mass of NH}_{4}\text{Cl} = 14.01 + 4(1.01) + 35.45 \text{g/mol} \]

Molar mass enables us to perform critical conversion from moles to grams, which is demonstrated in the solution given for creating the ammonium chloride solution.

Aqueous Solutions

An aqueous solution is a mixture where the solvent is water. It's by far the most common type of solution in chemistry laboratories. When we discuss molarity, or molar concentration, it's typically with reference to aqueous solutions. Molarity is defined as the number of moles of a substance per liter of solution (\(\text{M}\)).

In an aqueous solution, the solute, which is the substance dissolved, must be soluble in water to a significant extent. Ammonium chloride, for instance, dissolves quite well and dissociates into its respective ions in water, making it an excellent candidate for preparing an aqueous solution. Molarity calculations like the one in our exercise are crucial for accurately preparing such solutions, ensuring the correct amount of substance is present in a specific volume of liquid.

Understanding properties of aqueous solutions, such as molarity and solubility, can help students predict the outcome of chemical reactions and prepare solutions for various practical and experimental purposes.