Question

Which of the following aqueous solutions has the highest concentration of \(\mathrm{K}^{+}\) ? (a) \(0.0850 \mathrm{M} \mathrm{K}_{2} \mathrm{SO}_{4};\) (b) a solution containing \(1.25 \mathrm{g} \mathrm{KBr} / 100 \mathrm{mL} ;\) (c) a solution having \(8.1 \mathrm{mg} \mathrm{K}^{+} / \mathrm{mL}\).

Short answer

The solution having 8.1 mg K+ / mL has the highest concentration of K+.

Step-by-step solution

Calculate the Molar Concentration for Option (a)

For option a: Given that the solution is 0.0850 M K2SO4. Note that each molecule of K2SO4 has two molecules of K+. So, the concentration of K+ in the solution is \(0.0850 M \cdot 2 = 0.170 M\).

Calculate the Molar Concentration for Option (b)

For option b: Convert grams of KBr to moles using the molar mass. Given the volume of the solution is 100 mL, convert this to liters to calculate the molarity (moles per liter). We have \(1.25 g \mathrm{KBr} \times \frac{1 mol \mathrm{KBr}}{119.002 g} = 0.0105 mol \mathrm{KBr}\). Therefore, the concentration of KBr is \(0.0105 mol / 0.1 L = 0.105 M\). There is one mole of Potassium ion in KBr, hence the concentration of K+ is also 0.105 M.

Calculate the Molar Concentration for Option (c)

For option c: Given concentration is 8.1 mg K+ / mL. First, convert mg to g, and mL to L: \(8.1 mg \times \frac{1 g}{1000 mg} = 0.0081 g\) and \(1 mL = \frac{1}{1000} L\). Then convert grams to moles: \(0.0081 g \times \frac{1 mol}{39.098 g} = 0.000207 mol\). Therefore, the molar concentration is \(0.000207 mol / \frac{1}{1000} L = 0.207 M\) for K+.

Compare the Molar Concentrations

The molar concentrations for options (a), (b), and (c) are 0.170 M, 0.105 M, and 0.207 M, respectively. Thus, option c has the highest molar concentration of K+ ions.

Key concepts

Molarity Calculation

Molarity is an essential concept in chemistry that tells us how concentrated a solution is. It is defined as the number of moles of solute (the substance being dissolved) per liter of solution. To calculate molarity, you can use the formula: \[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}} \] Understanding this concept is crucial because it allows us to precisely know how much of a substance is present in a given amount of solution, which is vital for reactions that require specific concentrations to proceed correctly.For example, in the step-by-step solution provided, option (b) requires converting grams of KBr into moles (using its molar mass) and the solution's volume from milliliters to liters. This conversion is performed because the molarity formula requires the volume in liters. By accurately calculating molarity, whether for KBr in option (b) or transforming given parameters in options (a) or (c), we ensure correct determination of the potassium ion concentration.

Ionic Solutions

Ionic solutions are a common type of solution in chemistry where the solute dissociates into ions when dissolved in a solvent, like water. These solutions are essential because ions carry electrical charges, influencing many physical and chemical properties of the solution, such as conductivity and reactivity.When creating an ionic solution, such as potassium sulfate (\(\mathrm{K}_{2} \mathrm{SO}_{4}\)) in option (a), it's important to note that the compound dissociates into more than one type of ion. In the dissolution of \(\mathrm{K}_{2} \mathrm{SO}_{4}\), for example, each formula unit breaks into two \( \mathrm{K}^{+} \) ions and one \( \mathrm{SO}_{4}^{2-} \) ion. This phenomena means a concentration of 0.0850 M \(\mathrm{K}_{2} \mathrm{SO}_{4}\) actually provides double the potassium ion concentration, specifically 0.170 M of \( \mathrm{K}^{+} \).Understanding how substances dissociate in solution and their resultant ionic concentrations can greatly impact calculations, as seen in how we determine the highest potassium ion concentration among the options.

Potassium Ion Concentration

Potassium ions (\( \mathrm{K}^{+} \)) are a vital aspect of many chemical solutions and understanding their concentration is crucial in both chemistry and biology. Accurately determining their concentration in a solution allows for the understanding of the solution's reactivity and potential biological implications.To calculate potassium ion concentration, consider how the initial compound contributes to \( \mathrm{K}^{+} \) ions in the solution. In option (c) of the original problem, you're given the mass of \( \mathrm{K}^{+} \) ions per milliliter. The initial step involves converting this mass to moles and ensuring the volume is converted into liters to finalize the molar concentration calculation. Option (c) shows us that this concentration is 0.207 M, indicating that it's providing a higher amount of \( \mathrm{K}^{+} \) ions compared to the other options presented. Such calculations are essential for effectively comparing different solutions and determining which one might be more potent or reactive based on its ionic makeup.