Question

For each of the following solutions, the number of moles of solute is given, followed by the total volume of solution prepared. Calculate the molarity. a. 0.10 mol of \(\mathrm{CaCl}_{2} ; 25 \mathrm{mL}\) b. 2.5 mol of \(\mathrm{KBr} ; 2.5 \mathrm{L}\) c. 0.55 mol of \(\mathrm{NaNO}_{3} ; 755 \mathrm{mL}\) d. 4.5 mol of \(\mathrm{Na}_{2} \mathrm{SO}_{4} ; 1.25 \mathrm{L}\)

Short answer

a. \(M = 4 \ \text{M}\) b. \(M = 1 \ \text{M}\) c. \(M = 0.728 \ \text{M}\) d. \(M = 3.6 \ \text{M}\)

Step-by-step solution

Convert volume to liters

First, convert the given volume of 25 mL to liters by dividing by 1000: \(25 \mathrm{mL} = 0.025 \mathrm{L}\)

Calculate the molarity

Now, use the formula to calculate the molarity: \(M = \frac{0.10 \ \text{mol}}{0.025 \ \text{L}} = 4 \ \text{M}\) #b. 2.5 mol of \(\mathrm{KBr} ; 2.5 \mathrm{L}\) #

Calculate the molarity

Since the volume is already given in liters, we can directly use the formula to calculate the molarity: \(M = \frac{2.5 \ \text{mol}}{2.5 \ \text{L}} = 1 \ \text{M}\) #c. 0.55 mol of \(\mathrm{NaNO}_{3} ; 755 \mathrm{mL}\) #

Convert volume to liters

First, convert the given volume of 755 mL to liters by dividing by 1000: \(755 \mathrm{mL} = 0.755 \mathrm{L}\)

Calculate the molarity

Now, use the formula to calculate the molarity: \(M = \frac{0.55 \ \text{mol}}{0.755 \ \text{L}} = 0.728 \ \text{M}\) #d. 4.5 mol of \(\mathrm{Na}_{2} \mathrm{SO}_{4} ; 1.25 \mathrm{L}\) #

Calculate the molarity

Since the volume is already given in liters, we can directly use the formula to calculate the molarity: \(M = \frac{4.5 \ \text{mol}}{1.25 \ \text{L}} = 3.6 \ \text{M}\)

Key concepts

Mole Concept

Understanding the mole concept is foundational to mastering chemistry. A mole is a unit that represents a specific number of particles, typically atoms or molecules. This number, known as Avogadro's number, is approximately \(6.022 \times 10^{23}\) particles. It's akin to a dozen eggs representing 12 eggs; a mole represents \(6.022 \times 10^{23}\) particles.

When you have a substance in a chemical problem, quantifying it in moles allows you to connect the micro world of atoms and molecules with the macro world we can measure. To visualize this, imagine you are given a sample of a pure substance. To determine the number of moles, you would divide the sample's mass by its molar mass (the mass of one mole of that substance). This relationship is essential when moving on to calculate solution concentrations, as seen in the given exercise where the number of moles of solute must be determined to calculate molarity.

Solution Concentration

Solution concentration is a measure of the amount of solute in a given volume of solution. There are various ways to express this, but for chemistry students, molarity is often the most useful. Molarity (\(M\)) is defined as the number of moles of solute per liter of solution.

To calculate the molarity, you need two key pieces of information: the number of moles of the solute and the volume of the solution in liters. A critical step that some students might overlook is ensuring the volume is expressed in liters, which might involve converting from milliliters (mL) to liters, as seen in the exercise. Remember, 1000 mL is equivalent to 1 L. Calculating the molarity then becomes a straightforward division: \[M = \frac{\text{moles of solute}}{\text{liters of solution}}\] It's important to grasp that a higher molarity indicates a more concentrated solution. The concept of molarity extends into various areas of chemistry, from stoichiometry to chemical reactions.

Chemistry Problem Solving

Chemistry problem-solving often requires a methodical approach to dissect complex concepts into manageable parts. The step-by-step solutions provided in textbook exercises model this approach. First, identify the known variables and the units they are expressed in. Next, determine what you are solving for and the most practical formula or principle that applies.

In our exercise, we deal with conversion between units (mL to L) and then use the formula for calculating molarity. Students should always ensure that units are consistent to avoid errors. Moreover, developing a good understanding of dimensional analysis can provide a strong foundation for these conversions.

Finally, the practice of carefully reading the problem, writing down relevant equations, close attention to significant figures and units, and double-checking calculations through estimation or alternative methods forms the bedrock of good chemistry problem-solving.