Question

An aqueous KNO \(_{3}\) solution is made using 72.5 \(\mathrm{g}\) of KNO \(_{3}\) diluted to a total solution volume of 2.00 L. Calculate the molarity, molality, and mass percent of the solution. (Assume a density of 1.05 \(\mathrm{g} / \mathrm{mL}\) for the solution.)

Short answer

The molarity of the solution is 0.358 M, the mass percent is 3.46%, and the molality is 0.364 m.

Step-by-step solution

Calculate the Number of Moles of KNO3

Use the molar mass of KNO3 to find the number of moles. The molar mass of KNO3 is approximately 101.1 g/mol (39.1 for K, 14.0 for N, and 3*16.0 for the three O atoms). Moles of KNO3 = weight of KNO3 (g) / molar mass of KNO3 (g/mol).

Calculate Molarity

Molarity (M) is defined as the number of moles of solute per liter of solution. Molarity = moles of KNO3 / volume of solution in liters.

Calculate Mass Percent

Mass percent is calculated by dividing the mass of the solute by the total mass of the solution, then multiplying by 100%. Mass percent = (mass of solute (g) / total mass of solution (g)) * 100%

Calculate the Mass of the Solution

First calculate the mass of the solution using its volume and density. Mass of solution = volume of solution (mL) * density (g/mL).

Calculate Molality

Molality (m) is defined as the number of moles of solute per kilogram of solvent. Since the solution is made up of KNO3 and water, and we assume all the excess mass is water, calculate the mass of water, then convert it to kilograms. Molality = moles of KNO3 / mass of water in kilograms.

Key concepts

Molarity

Molarity, often represented by the symbol 'M', is a measure of solution concentration, expressed as the number of moles of a solute in one liter of solution. It informs us how strong or weak a solution is by revealing the amount of substance dissolved in a given volume. Understanding molarity is fundamental for tasks such as diluting solutions to desired concentrations and stoichiometric calculations in chemical reactions.

To calculate molarity, we divide the number of moles of the solute by the volume of the solution in liters. In mathematical terms, the formula for molarity (M) is:
\[ M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]
In the given exercise, once you determine the moles of KNO3 using its molar mass, you simply divide it by the total volume of the solution (2.00 L) to find the molarity.

Molality

Molality, designated as 'm', is another way to express the concentration of a solution. It is defined as the number of moles of solute per kilogram of solvent (not the solution). Unlike molarity, molality is not affected by changes in temperature because it depends on the mass, not volume, which can change with temperature.

The formula for molality is:
\[ m = \frac{\text{moles of solute}}{\text{mass of solvent in kilograms}} \]
To find the molality in our exercise, after calculating the number of moles of KNO3, we subtract the mass of KNO3 from the total mass of the solution to find the mass of the solvent (water). Then we convert this mass from grams to kilograms and divide the moles of KNO3 by this mass to get the molality.

Mass Percent

The mass percent, also known as weight percent or mass fraction, is a concentration metric that compares the mass of the solute to the total mass of the solution, presenting it as a percentage. This measure is useful in pharmacy to prepare solutions or in geochemistry for rock and mineral analysis.

Here's the formula you would use to calculate mass percent:
\[ \text{Mass percent} = \left(\frac{\text{mass of solute (g)}}{\text{total mass of solution (g)}}\right) \times 100\% \]
In the context of our exercise, the mass of KNO3 (72.5 g) and the mass of the solution, which is obtained by multiplying the solution's volume by its density (considering a density of 1.05 g/mL), enable us to find the mass percent of KNO3.

Moles Calculation

Calculating moles is a cornerstone in chemistry for quantifying substances. Moles allow chemists to correlate the number of particles in a given sample with its mass, which is essential for understanding chemical reactions.

The basic formula to calculate moles is:
\[ \text{Moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
For the exercise at hand, the molar mass of KNO3 is found by adding the atomic masses of potassium (K), nitrogen (N), and oxygen (O), which gives us the conversion factor from grams to moles. Once you have the mass of KNO3, you divide it by this molar mass to determine the number of moles present. This moles calculation lays the foundation for finding molarity, molality, and mass percent—crucial steps for this exercise.