Question

Which of the following solutions is more concentrated? (a) \(0.50 M \mathrm{KCl}\) or \(5.0 \%(\mathrm{~m} / \mathrm{v}) \mathrm{KCl}\) (b) \(2.5 \%(\mathrm{~m} / \mathrm{v}) \mathrm{NaHSO}_{4}\) or \(0.025 \mathrm{M} \mathrm{NaHSO}_{4}\)

Short answer

(a) The 5.0% (m/v) solution of KCl is more concentrated. (b) The 2.5% (m/v) solution of NaHSO₄ is more concentrated.

Step-by-step solution

Convert Molarity to Mass/Volume Percent for KCl

To compare the concentration of the two solutions, convert the molarity solution into a percentage solution. We need to find out the percent \((\text{m}/\text{v})\) of the \(0.50\ M\ \mathrm{KCl}\) solution. The molar mass of \(\mathrm{KCl}\) is approximately \(74.55\ \mathrm{g/mol}\).For \(0.50\ M\), there are \(0.50\ \mathrm{moles/L}\), or \(0.50 \times 74.55 = 37.275\ \mathrm{g/L}\).\(37.275\ \mathrm{g/L}\) is equivalent to \(3.7275\%\ (\text{m}/\text{v})\).

Compare KCl Solution Concentrations

(a) Compare the two concentrations: \(3.7275\%\ (\text{m}/\text{v})\ \mathrm{KCl}\)versus \(5.0\%\ (\text{m}/\text{v})\ \mathrm{KCl}\).Clearly, \(5.0\%\ (\text{m}/\text{v})\) is more concentrated than \(3.7275\%\ (\text{m}/\text{v})\).

Convert Mass/Volume Percent to Molarity for NaHSO₄

To compare the concentrations, convert the percent \((\text{m}/\text{v})\) to molarity for \(2.5\%\ (\text{m}/\text{v})\ \mathrm{NaHSO}_{4}\). This concentration corresponds to \(25\ \mathrm{g/L}\). The molar mass of \(\mathrm{NaHSO}_{4}\) is approximately \(120.06\ \mathrm{g/mol}\).To convert to molarity, divide by the molar mass: \( \frac{25 \ \mathrm{g/L}}{120.06\ \mathrm{g/mol}} \approx 0.208\ \mathrm{M}\).

Compare NaHSO₄ Solution Concentrations

(b) Compare \(0.208\ M\ \mathrm{NaHSO}_{4}\) with \(0.025\ M\ \mathrm{NaHSO}_{4}\).Clearly, \(0.208\ M\) is more concentrated than \(0.025\ M\).

Key concepts

Molarity

Molarity is a way to express concentration by indicating the number of moles of a solute present in one liter of solution. It is denoted by the symbol \(M\) and is calculated using the formula:\[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}} \]Molarity helps us understand how concentrated a solution is, as higher molarity indicates a more concentrated solution.
In the exercise, for example, the molarity of \(0.50\ M\ \mathrm{KCl}\) is compared to a \(5.0\%\ \text{m/v}\) solution.Converting molarity to a different concentration unit, like mass/volume percent, allows for easier comparison of the two solutions.

Mass/Volume Percent

Mass/Volume Percent is another way to express concentration, indicating the mass of the solute found in 100 milliliters of solution.It is expressed as \(%\ \text{m/v}\) and calculated using the formula:\[\%\ \text{m/v} = \frac{\text{grams of solute}}{\text{milliliters of solution}} \times 100\]This unit is intuitive because it provides a direct percentage of solute, making it straightforward to compare different solutions.
In the exercise, a \(5.0\%\ \text{m/v}\)\ \mathrm{KCl}\ solution was shown to be more concentrated than a \(3.7275\%\ \text{m/v}\) KCl solution.

Molar Mass

Molar Mass is the mass of one mole of a substance, expressed in grams per mole (g/mol).It is used to convert between the mass of a substance and the number of moles.For instance, in our exercise, the molar mass of \(\mathrm{KCl}\) and \(\mathrm{NaHSO}_{4}\) were critical in converting between molarity and mass/volume percent.

• For \(\mathrm{KCl}\), the molar mass is approximately \(74.55\ \mathrm{g/mol}\).
• For \(\mathrm{NaHSO}_{4}\), it is roughly \(120.06\ \mathrm{g/mol}\).

Understanding the molar mass allows these conversions, which are essential for proper comparison of solution concentrations.

Concentration Conversion

Concentration Conversion involves changing the units of concentration to better compare different solutions.Through conversions, it's easier to understand which solutions are more concentrated than others.
In our exercise, we converted between molarity and mass/volume percent to compare the given solutions:

• For the \(\mathrm{KCl}\) solutions, molarity was converted to \(%\ \text{m/v}\) to enable a straightforward comparison.
• For the \(\mathrm{NaHSO}_{4}\) solutions, \(%\ \text{m/v}\) was converted to molarity.

By mastering concentration conversion, you can compare solutions effectively, regardless of how their concentrations are initially expressed.