Question

Calculate the molarity of a solution prepared by dissolving (a) \(4.00 \mathrm{~g}\) of sodium hydroxide in a total volume of \(100.0 \mathrm{~mL}\) of solution. (b) \(16.0 \mathrm{~g}\) of calcium chloride in a total volume of \(250.0 \mathrm{~mL}\) of solution.

Short answer

The molarity of the NaOH solution is 1.00 M, and the molarity of the CaCl2 solution is 0.576 M.

Step-by-step solution

Calculate the molar mass of sodium hydroxide (NaOH)

The molar mass of a compound is the sum of the masses of all the atoms in a molecule of that compound. Sodium (Na) has a molar mass of approximately 23.0 g/mol, oxygen (O) has a molar mass of 16.0 g/mol, and hydrogen (H) has a molar mass of 1.0 g/mol. Thus, the molar mass of NaOH is calculated as the sum: 23.0 g/mol (Na) + 16.0 g/mol (O) + 1.0 g/mol (H) = 40.0 g/mol.

Convert mass of NaOH to moles

Using the molar mass of NaOH, convert the mass of NaOH to moles using the formula: moles of solute = mass of solute / molar mass of solute. For 4.00 g of NaOH, the calculation is 4.00 g / 40.0 g/mol = 0.100 moles.

Convert the volume of the solution to liters

To find molarity, the volume of the solution must be in liters. Convert 100.0 mL to liters by dividing by 1000: 100.0 mL * (1 L / 1000 mL) = 0.100 L.

Calculate the molarity of the NaOH solution

Molarity is defined as the number of moles of solute per liter of solution. Using the formula molarity (M) = moles of solute / liters of solution, the molarity of the NaOH solution is 0.100 moles / 0.100 L = 1.00 M.

Calculate the molar mass of calcium chloride (CaCl2)

The molar mass of CaCl2 is the sum of the molar masses of calcium (Ca) and chlorine (Cl). Calcium has a molar mass of approximately 40.1 g/mol, and each chlorine atom has a molar mass of approximately 35.5 g/mol. So the molar mass of CaCl2 is 40.1 g/mol (Ca) + 2 * 35.5 g/mol (Cl) = 111.1 g/mol.

Convert mass of CaCl2 to moles

To find the number of moles of CaCl2, use the formula: moles of solute = mass of solute / molar mass of solute. For 16.0 g of CaCl2, the calculation is 16.0 g / 111.1 g/mol = 0.144 moles.

Convert the volume of the CaCl2 solution to liters

The volume of the CaCl2 solution is given in milliliters. Convert it to liters: 250.0 mL * (1 L / 1000 mL) = 0.250 L.

Calculate the molarity of the CaCl2 solution

Calculate the molarity of the CaCl2 solution using the formula: molarity (M) = moles of solute / liters of solution. With 0.144 moles CaCl2 in 0.250 L of solution, the molarity is 0.144 moles / 0.250 L = 0.576 M.

Key concepts

Molar Mass

Understanding molar mass is fundamental when performing molarity calculations. It represents the weight of one mole of a substance, usually expressed in grams per mole (g/mol).

The molar mass is determined by adding together the atomic masses of each element in a compound, as found on the periodic table. For sodium hydroxide (NaOH), this calculation involves the molar masses of sodium (Na), oxygen (O), and hydrogen (H), which amounts to approximately 40.0 g/mol. This figure plays a critical role in Step 2 of the given exercise, where you convert the mass of NaOH to moles by dividing the mass of the compound by its molar mass.

Moles of Solute

In chemistry, the term 'moles of solute' refers to the amount of a substance, in moles, that is dissolved in a solution. It is a measure of the number of particles, such as atoms, ions, or molecules, present in the solution.

One mole is Avogadro's number (\(6.022 \times 10^{23}\) entities) of particles. By dividing the mass of the solute by its molar mass (as demonstrated in Steps 2 and 6 of the exercise), you can calculate the moles of solute, which is a crucial step in determining the molarity of a solution.

Solution Concentration

Molarity as a Measurement of Concentration

Concentration refers to the amount of solute present in a given volume of solvent. One common way to quantify concentration in chemistry is through molarity, which measures the number of moles of solute per liter of solution (mol/L).

High molarity indicates a strong, or concentrated, solution, whereas low molarity corresponds to a weak, or diluted, solution. As shown in the exercise (Step 4 for NaOH and Step 8 for CaCl2), understanding solution concentration is essential when trying to find out how much solute is present in a solution.

Molarity Formula

Calculating Molarity

The molarity formula is straightforward: Molarity (M) = moles of solute / liters of solution. By using this formula, you can find out the molarity of any solution, provided you know the amount of solute in moles and the volume of the solution in liters.

This calculation is exemplified in the given exercise for both NaOH and CaCl2 solutions. It's essential to ensure the volume is converted to liters as the formula requires consistency in units for accurate results.

Stoichiometry

The Role of Stoichiometry in Solutions

Stoichiometry is the area of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It involves using balanced chemical equations to understand the ratio in which compounds react or form.

Even though the original exercise does not involve a reaction, the principles of stoichiometry — such as calculating moles from given masses and understanding molar ratios — are important foundations that enable students to perform molarity calculations effectively.