Question

How many moles of KCl are contained in each solution? a. 0.556 L. of a 2.3 \(\mathrm{M}\) KCl solution b. 1.8 \(\mathrm{L}\) of a 0.85 \(\mathrm{M} \mathrm{KCl}\) solution c. 114 \(\mathrm{mL}\) of a 1.85 \(\mathrm{M} \mathrm{KCl}\) solution

Short answer

a. 1.2788 moles of KCl. b. 1.53 moles of KCl. c. 0.2109 moles of KCl.

Step-by-step solution

Convert volume from liters to milliliters (if necessary)

For parts a and b, the volume is already given in liters, which is the standard unit for molarity calculations, so no conversion is necessary. For part c, convert mililiters to liters by dividing by 1000: 114 mL = 0.114 L.

Calculate moles of KCl using molarity

Use the formula: moles of solute = molarity (M) * volume (L). For part a: Moles of KCl = 2.3 M * 0.556 L. For part b: Moles of KCl = 0.85 M * 1.8 L. For part c: Moles of KCl = 1.85 M * 0.114 L.

Perform the calculations

a. Moles of KCl = 2.3 * 0.556 = 1.2788 moles. b. Moles of KCl = 0.85 * 1.8 = 1.53 moles. c. Moles of KCl = 1.85 * 0.114 = 0.2109 moles.

Key concepts

Moles of Solute

Understanding the concept of 'moles of solute' is key when diving into the world of chemistry and solution preparation. A mole is a unit of measurement that represents a specific number of particles, such as atoms or molecules. This number, known as Avogadro's number, is approximately \(6.022 \times 10^{23}\) particles per mole.

When we refer to 'moles of solute', we are talking about the quantity of a substance (solute) that is dissolved in a solvent to make a solution. It is crucial to be familiar with this concept because it relates directly to how we can replicate results in experiments and how we calculate concentrations. In the textbook exercise, the number of moles of KCl (potassium chloride) present in each solution is determined by the volume of the solution and its molarity, indicating how many 'buckets' of Avogadro’s number of particles are in said volume.

Molar Concentration

Molar concentration, often just called concentration and represented as 'M' for molarity, is another fundamental concept in chemistry that quantifies the amount of a substance in a given volume of solution. It is defined as moles of solute per liter of solution. Thus, a 1 \(\text{M}\) solution contains one mole of solute for every liter of solution.

The molar concentration allows scientists and students alike to prepare solutions with precision. As shown in the exercise solutions, we use the molarity (given as \(2.3 \text{M}\), \(0.85 \text{M}\), and \(1.85 \text{M}\) for KCl) in the calculations to determine the moles of solute. Always remember that molarity is an expression of the ratio of moles to volume, which is a crucial component to predicting the behavior of solutions in chemical reactions.

Volume and Molarity Relationship

The volume of a solution and its molarity are interdependent in calculations involving the concentration of solutions. As shown in the step-by-step solutions for the exercise, to find the moles of solute, you multiply the molarity by the volume in liters:
\[ \text{moles of solute} = \text{molarity (M)} \times \text{volume (L)} \]
For example, in part a of the exercise, a volume of \(0.556 \text{L}\) with a molarity of \(2.3 \text{M}\) indicates a larger number of moles of KCl in solution compared to part c, where a smaller volume of \(0.114 \text{L}\) at a molarity of \(1.85 \text{M}\) is used.

Practical Application

Understanding this relationship is crucial, as it allows us to adjust the amount of solute or solvent to achieve a desired molarity, essential for tasks ranging from buffer preparation in a lab to diluting cleaning chemicals for safe use. Always double-check volume units, converting if necessary, to ensure accuracy in your calculations.