Calculate the molality of each of the following solutions: (a) \(0.710 \mathrm{kg}\) of sodium carbonate (washing soda), \(\mathrm{Na}_{2} \mathrm{CO}_{3},\) in \(10.0 \mathrm{kg}\) of water \(-\) a saturated solution at \(0^{\circ} \mathrm{C}\) (b) \(125 \mathrm{g}\) of \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) in \(275 \mathrm{g}\) of water \(-\) a mixture used to make an instant ice pack (c) \(25 \mathrm{g}\) of \(\mathrm{Cl}_{2}\) in \(125 \mathrm{g}\) of dichloromethane, \(\mathrm{CH}_{2} \mathrm{Cl}_{2}\) (d) 0.372 g of tetrahydropyridine, \(\mathrm{C}_{5} \mathrm{H}_{9} \mathrm{N}\), in 125 \(\mathrm{g}\) of chloroform, \(\mathrm{CHCl}_{3}\)

The molar mass of a substance is the weight in grams of one mole of that substance. It represents the collective mass of one mole of atoms, ions, or molecules. Molar mass is measured in units of grams per mole (g/mol).

For example, to calculate the molality of a solution, you first need to know the molar mass of the solute. You can find the molar mass by multiplying the number of atoms of each element in a compound by their atomic masses and summing the results. Atomic masses can be found on the periodic table of elements.

Finding the Molar Mass

Let's take sodium carbonate (\( \text{Na}_2\text{CO}_3 \)) as an instance. The chemical formula indicates it contains two sodium (Na) atoms, one carbon (C) atom, and three oxygen (O) atoms. By using the periodic table, you can find the atomic mass of each atom and then calculate the molar mass:

• Sodium (Na): 22.99 g/mol x 2 = 45.98 g/mol
• Carbon (C): 12.01 g/mol x 1 = 12.01 g/mol
• Oxygen (O): 16.00 g/mol x 3 = 48.00 g/mol

Add these together, and the molar mass of sodium carbonate is 106.99 g/mol. Understanding the molar mass is an essential step towards correct molality calculations.

In chemistry, the mole is a unit that represents a quantity of substance. Specifically, it refers to the number of atoms found in 12 grams of carbon-12, which is approximately 6.022 x 10^23 atoms, known as Avogadro's number.

To calculate the moles of solute in a solution, divide the mass of the solute by its molar mass. This value is crucial in helping to determine the concentration of the solution.

Calculating Moles from Mass

If you have 0.710 kg of sodium carbonate, the number of moles is calculated by dividing this mass by the molar mass found above (\( 106.99 \text{g/mol} \)). Remember to convert kilograms to grams (1 kg = 1000 g) for consistency in units. After calculating the moles of solute, you can then use this value to find the molality of the solution.

The mass of the solvent in a solution is simply the weight of the liquid or solid in which the solute is dissolved. For a precise calculation of molality, the mass of the solvent must be given in kilograms (kg) to match the molality unit definition: moles per kilogram.

When performing a calculation, it's important to be vigilant about the units. If the mass of the solvent is provided in grams (g), you must convert it to kilograms by dividing by 1000.

Understanding the Role of the Solvent

In our given exercise, water is the solvent when sodium carbonate or ammonium nitrate is dissolved. For dichloromethane, the solvent is when chlorine gas is dissolved. For each solution, you would measure the mass of the solvent only, without the solute, for accurate molality calculations.

Molality is a way to express the concentration of a solution. It quantifies how much of a solute is present in a given amount of solvent. Molality is advantageous to use when the solution's temperature is altered, mainly because it doesn't change with temperature, unlike volume-based measurements like molarity.

Since molality is defined as the number of moles of solute per kilogram of solvent, it requires the accurate calculation of both the moles of solute present and the mass of the solvent.

Applying Molality

Knowing the concentration of solutions in molality is essential for tasks across chemistry, including stoichiometry and reactions that depend on the solute concentration. For instance, molality is used in colligative properties calculations, which predict boiling point elevation and freezing point depression of solutions.