Problem 51 - Chemistry: An Atoms-Focused Approach

Question

What is the difference between molarity and molality?

Step-by-Step Solution

Answer

In summary, molarity (M) is a measure of concentration defined as the number of moles of solute dissolved per liter of solution, while molality (m) is a measure of concentration defined as the number of moles of solute dissolved per kilogram of solvent. The primary difference between them is that molarity considers the total volume of the solution, whereas molality focuses only on the mass of the solvent. In the example provided, a solution of 1 mole of sodium chloride (NaCl) dissolved in 1 liter of water resulted in a molarity of 1 mol/L and a molality of 1 mol/kg, illustrating that these measures can have the same numerical values but different units and meanings in describing a solution's concentration.

Step 1: Definition of Molarity

Molarity (M) is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute (n) dissolved in one liter (1 L) of solution. The formula for molarity is: M = n / V, where "n" is the number of moles of solute and "V" is the volume of the solution in liters.

Step 2: Definition of Molality

Molality (m) is another measure of the concentration of a solute in a solution. It is defined as the number of moles of solute (n) dissolved in one kilogram (1 kg) of solvent. The formula for molality is: m = n / M_s, where "n" is the number of moles of solute and "M_s" is the mass of the solvent in kilograms.

Step 3: An example to compare Molarity and Molality

Let's assume we have a solution prepared by dissolving 1 mole (58.44 g) of sodium chloride (NaCl) in 1 liter of water. We can calculate the molarity as follows: M = number of moles of NaCl / volume of solution in liters M = 1 mol / 1 L M = 1 mol/L Now, let's calculate the molality of the same solution. First, we need to find the mass of the water. Since we know the volume of water is 1 L and the density of water is 1 g/mL, we can convert it to mass: 1 L = 1000 mL 1000 mL * 1 g/mL = 1000 g = 1 kg Now we can calculate the molality: m = number of moles of NaCl / mass of solvent in kg m = 1 mol / 1 kg m = 1 mol/kg In this example, molarity and molality have the same numerical value, but remember that the units are different, and they describe different aspects of the solution concentration. Molarity takes into account the volume of the whole solution, whereas molality only accounts for the mass of the solvent.