Question

Using concentration as a conversion factor, how many moles of solute are in \(3.44 \mathrm{~L}\) of \(0.753 \mathrm{M}\) \(\mathrm{CaCl}_{2} ?\)

Short answer

2.590 moles of \(\mathrm{CaCl}_2\).

Step-by-step solution

Understand Molarity

Molarity (M) is defined as the number of moles of solute per liter of solution. Therefore, a 0.753 M solution of \(\mathrm{CaCl}_2\) contains 0.753 moles of \(\mathrm{CaCl}_2\) per liter of solution.

Determine the Total Volume in Liters

The volume of the solution is given as \(3.44 \mathrm{~L}\). This is already expressed in liters, so no conversion is required.

Calculate the Total Moles of Solute

Use the formula for molarity to calculate the moles of solute: \[ \text{Moles of } \mathrm{CaCl}_2 = \text{Volume in liters} \times \text{Molarity} \] Substituting the given values, \[ \text{Moles of } \mathrm{CaCl}_2 = 3.44 \text{ L} \times 0.753 \text{ M} = 2.59032 \text{ moles} \]

Present the Result

The number of moles of \(\mathrm{CaCl}_2\) in the solution is approximately \(2.590\) (rounded to three decimal places).

Key concepts

Moles of Solute

When working with solutions in chemistry, understanding the concept of moles is crucial. A mole is a unit used to measure the amount of substance, which is similar to how we use the term dozen to mean twelve items. However, a mole equals approximately 6.022 x 10²³ particles, atoms, or molecules, depending on the substance in question. Knowing the moles of a solute, which is the substance being dissolved, is essential for carrying out chemical reactions and calculations accurately.
In our exercise, the solute in question is calcium chloride, \( \text{CaCl}_2 \). Here, we are tasked with finding out how many moles of \( \text{CaCl}_2 \) exist in a given volume of solution. By multiplying the molarity of the solution by its volume in liters, we can determine the moles of solute present.

Concentration Calculation

Concentration refers to the amount of solute dissolved in a unit volume of solvent, and in this context, molarity is the measure of concentration. Molarity, denoted by \( M \), is equal to the number of moles of solute divided by the volume of the solution in liters.
To calculate the concentration, you can rearrange the formula for molarity:\[\text{Molarity (M)} = \frac{\text{Moles of Solute}}{\text{Volume of Solution in Liters}}\]
In typical exercises, if the molarity and volume of the solution are provided, it's often straightforward to calculate the moles of solute by simply multiplying them. For instance, when given a 0.753 M \( \text{CaCl}_2 \) solution with a volume of 3.44 L, the calculation becomes a matter of simple multiplication: \( 3.44 \, \text{L} \times 0.753 \, \text{M} = 2.59032 \, \text{moles} \). Finally, we round this to three decimal places to get 2.590 moles of \( \text{CaCl}_2 \).
Besides simplifying complex academic topics, understanding concentration helps in various real-world applications like pharmaceuticals, food chemistry, and environmental science.

Solution Volume in Liters

Volume is a basic measure of the amount of space that a substance or object occupies. For solutions, it is usually measured in liters when discussing concentration and molarity. Recognizing the volume of the solution is critical because it directly influences the concentration of the solute.
In this exercise, the volume of the calcium chloride solution is given as 3.44 liters. This value is crucial in calculating the moles of solute because it allows us to utilize the molarity provided. Remember, the standard unit for volume in molarity calculations is liters, so this step ensures that we are working with the correct units. There's no need for unit conversion in this context because the volume was already specified in liters.
In any chemical solution calculation, making sure that the volume is correctly measured and understood ensures accuracy in concentration measurement. This can have implications in laboratory experiments and industrial applications alike, where precision is paramount.