Question

(a) Which will have the highest concentration of potassium ion: \(0.20 \mathrm{M} \mathrm{KCl}, 0.15 \mathrm{M} \mathrm{K}_{2} \mathrm{CrO}_{4}\), or \(0.080 \mathrm{M} \mathrm{K}_{3} \mathrm{PO}_{4}\) ? (b) Which will contain the greater number of moles of potassium ion: \(30.0 \mathrm{~mL}\) of \(0.15 \mathrm{M} \mathrm{K}_{2} \mathrm{CrO}_{4}\) or \(25.0 \mathrm{~mL}\) of \(0.080 \mathrm{M} \mathrm{K}_{3} \mathrm{PO}_{4} ?\)

Short answer

(a) The highest concentration of potassium ions is in the 0.15 M K2CrO4 solution, with a concentration of 0.30 M. (b) The 30.0 mL of 0.15 M K2CrO4 solution contains more moles of potassium ions (0.0090 moles) than the 25.0 mL of 0.080 M K3PO4 solution (0.0060 moles).

Step-by-step solution

a) Finding the concentration of potassium ions in each solution

First, let's find the concentration of potassium ions (K+) in each of the given solutions: 1. For 0.20 M KCl, each molecule of KCl releases 1 K+ ion in the solution. So, the concentration of K+ ions will be the same as the concentration of KCl, i.e., 0.20 M. 2. For 0.15 M K2CrO4, each molecule of K2CrO4 releases 2 K+ ions in the solution. So, the concentration of K+ ions will be double the concentration of K2CrO4, i.e., \(0.15 M \times 2 = 0.30 M\). 3. For 0.080 M K3PO4, each molecule of K3PO4 releases 3 K+ ions in the solution. So, the concentration of K+ ions will be triple the concentration of K3PO4, i.e., \(0.080 M \times 3 = 0.240 M\). So, the solution with the highest concentration of potassium ions is the one with K2CrO4, which has a concentration of 0.30 M.

b) Finding the number of moles of potassium ions in 30.0 mL of 0.15 M K2CrO4 and 25.0 mL of 0.080 M K3PO4

Now, let's find the number of moles of potassium ions in each of the given volumes of K2CrO4 and K3PO4 solutions. We'll use the formula: Number of moles = Concentration (M) × Volume (L) First, convert the milliliters (mL) to liters (L): 30.0 mL = 0.030 L 25.0 mL = 0.025 L For 0.15 M K2CrO4 solution: Number of moles = 0.030 L × 0.15 M × 2 (since each molecule of K2CrO4 releases 2 K+ ions) = 0.0090 moles For 0.080 M K3PO4 solution: Number of moles = 0.025 L × 0.080 M × 3 (since each molecule of K3PO4 releases 3 K+ ions) = 0.0060 moles Comparing the two, we find that the 30.0 mL of 0.15 M K2CrO4 solution contains a greater number of moles of potassium ions (0.0090 moles) compared to the 25.0 mL of 0.080 M K3PO4 solution (0.0060 moles).

Key concepts

Molarity Calculations

Understanding molarity is essential for delving into the world of chemistry, especially when dealing with solutions. Molarity, denoted by the symbol 'M', is a measure of concentration that tells us how many moles of a solute are present in a liter of solution. In layman terms, it's like figuring out how much sugar you've dissolved in a jug of lemonade.

To find molarity, simply divide the number of moles of solute by the volume of the solution in liters. The formula looks like this: \[ Molarity (M) = \frac{moles \, of \, solute}{volume \, of \, solution \, in \, liters} \]

When it comes to the exercise at hand, we use molarity to determine the concentration of potassium ions in different solutions. Whether dealing with KCl, K₂CrO₄, or K₃PO₄, we must consider both the molarity of the original compound and the number of potassium ions each unit of that compound will produce when dissolved.

Stoichiometry of Ionic Compounds

The stoichiometry of ionic compounds can seem like a fancy phrase, but it's really just about the relationship between the amounts of reactants and products in a chemical reaction. Each compound has a distinct formula which indicates the ratio of its constituent ions. For example, KCl has a one-to-one ratio of potassium ions to chloride ions.

Why does this matter? Because when you dissolve these compounds in water, they break apart into those ions. For instance, K₂CrO₄ dissociates into two K+ ions and one CrO₄2- ion. If you want to calculate the concentration of just the potassium ions, you have to take this stoichiometry into account. Therefore, if you have a 0.15 M solution of K₂CrO₄, you actually have a 0.30 M concentration of potassium ions since each unit yields two potassium ions. Understanding this concept is critical when solving exercises that require you to find the concentration of a specific ion in a mixture.

Moles and Volume Relationship

The relationship between moles and volume is a cornerstone of chemistry, and grasping it is vital when working with solutions. It's based on the principle that volume is directly proportional to the number of moles: more moles mean more volume, assuming concentration and temperature stay the same.

Using this principle, we can figure out the number of moles in a given volume of solution if we know its molarity. The formula for calculating moles from volume and molarity is: \[ Number \, of \, moles = Molarity (M) \times Volume \, (L) \]

In the exercise we're examining, we convert volumes in milliliters to liters (since 1 L = 1000 mL) and then use the above formula. Remember, though, we must consider the number of potassium ions released per formula unit of the compound, as the exercise deals with K₂CrO₄ and K₃PO₄ releasing multiple K+ ions. This is a clear demonstration of how stoichiometry directly ties into the calculations involving moles and volume.