Calculate the molarity of the following solutions: (a) \(0.50 \mathrm{~mol}\) of solute in \(125 \mathrm{~mL}\) of solution (b) \(2.25 \mathrm{~mol}\) of \(\mathrm{CaCl}_{2}\) in \(1.50 \mathrm{~L}\) of solution (c) \(275 \mathrm{~g} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) in \(775 \mathrm{~mL}\) of solution (d) \(125 \mathrm{~g} \mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O}\) in \(2.50 \mathrm{~L}\) of solution

Molarity is a core concept in chemistry that describes the concentration of a solution. It tells us how many moles of solute are present in one liter of solution. The formula for molarity is quite simple: \[ \text{Molarity (M)} = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}} \] This means that to find molarity, you need two things: the number of moles of the solute and the volume of the solution in liters. For example, if you have 1 mole of salt dissolved in 1 liter of water, the molarity is 1 M. Molarity is essential for preparing solutions, understanding reactions in a solution, and performing concentration calculations. It's one of the most frequent calculations you will do in chemistry. Here's a quick recap on how to use the molarity formula:

• Identify the moles of solute in your solution.
• Measure the volume of your solution in liters.
• Use the formula to calculate the molarity.

Converting units is a fundamental skill in chemistry. Often, you'll need to convert between milliliters and liters, or grams and moles. Accurate conversions are crucial for correct calculations. Let's go through some common conversions:

• Milliliters to Liters: Divide by 1000. For example, 125 mL is converted to 0.125 L.
• Grams to Moles: Use the compound's molar mass (found on the periodic table). For instance, if you have 275 g of glucose (C₆H₁₂O₆), you need its molar mass (180.16 g/mol) to convert it to moles: \[ \text{Moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{275 \text{ g}}{180.16 \text{ g/mol}} \approx 1.526 \text{ mol} \]

Converting units ensures your molarity calculations are accurate. Always double-check your units before plugging values into formulas.

Calculating the concentration of a solution involves understanding how much solute is within a given volume of solvent. This is often expressed as molarity (M). Let's break it down:

• Identify the solute (the substance being dissolved).
• Determine the number of moles of solute.
• Measure the volume of the solution (the solute + solvent) in liters.
• Use the molarity formula to find the concentration.

For example, to find the molarity of a solution with 0.50 moles of solute and 125 mL of solution, convert the volume to liters (0.125 L), then use:\[ M = \frac{0.50 \text{ mol}}{0.125 \text{ L}} = 4.0 \text{ M} \]Knowing the concentration can help predict how a solution will behave in reactions.

The relationship between moles and volume is central to understanding molarity. The number of moles of solute and the volume of the solution are directly proportional to the concentration. This means that as you increase the amount of solute in a fixed volume, the concentration increases. Conversely, if you dilute a solution (increase the volume while keeping the amount of solute constant), the concentration decreases:

• Adding more solute increases molarity.
• Increasing volume decreases molarity.

For instance, adding 2.25 moles of CaCl₂ to 1.50 L of water results in a lower concentration than adding the same amount to 1.0 L:\[ M = \frac{2.25 \text{ mol}}{1.50 \text{ L}} = 1.5 \text{ M} \]Understanding this relationship helps in preparing solutions of desired concentration for various experimental and practical applications.