Question

For each of the following solutions, the number of moles of solute is given, followed by the total volume of the solution prepared. Calculate the molarity of each solution. a. \(0.754 \mathrm{~mol} \mathrm{KNO}_{3} ; 225 \mathrm{~mL}\) b. \(0.0105 \mathrm{~mol} \mathrm{CaCl}_{2} ; 10.2 \mathrm{~mL}\) c. \(3.15 \mathrm{~mol} \mathrm{NaCl} ; 5.00 \mathrm{~L}\) d. \(0.499 \mathrm{~mol} \mathrm{NaBr} ; 100 . \mathrm{mL}\)

Short answer

The calculated molarities for each solution are approximately: a. 3.35 M (KNO₃) b. 1.03 M (CaCl₂) c. 0.63 M (NaCl) d. 4.99 M (NaBr)

Step-by-step solution

Solution a: Calculate the molarity of the KNO3 solution

First, we need to convert the volume from milliliters (mL) to liters (L): 225 mL * (1 L / 1000 mL) = 0.225 L Now we can use the molarity formula: Molarity = moles of solute / volume of solution (in liters) Molarity = 0.754 mol KNO3 / 0.225 L Molarity = 3.351 mol/L \( \approx 3.35 \:\mathrm{M} \)

Solution b: Calculate the molarity of the CaCl2 solution

Convert the volume from milliliters (mL) to liters (L): 10.2 mL * (1 L / 1000 mL) = 0.0102 L Now we can use the molarity formula: Molarity = moles of solute / volume of solution (in liters) Molarity = 0.0105 mol CaCl2 / 0.0102 L Molarity = 1.029 mol/L \( \approx 1.03 \:\mathrm{M} \)

Solution c: Calculate molarity of the NaCl solution

The volume is already given in liters, so we can directly use the molarity formula: Molarity = moles of solute / volume of solution (in liters) Molarity = 3.15 mol NaCl / 5.00 L Molarity = 0.63 mol/L \( \approx 0.63 \:\mathrm{M} \)

Solution d: Calculate the molarity of the NaBr solution

Convert the volume from milliliters (mL) to liters (L): 100 mL * (1 L / 1000 mL) = 0.100 L Now we can use the molarity formula: Molarity = moles of solute / volume of solution (in liters) Molarity = 0.499 mol NaBr / 0.100 L Molarity = 4.99 mol/L \( \approx 4.99 \:\mathrm{M} \) The calculated molarities are approximately 3.35 M (KNO3), 1.03 M (CaCl2), 0.63 M (NaCl), and 4.99 M (NaBr).

Key concepts

Mole Calculations

Understanding mole calculations is essential in chemistry for determining the amount of a substance. A "mole" is a standard unit in chemistry that represents a specific number of particles, typically atoms or molecules. This number, known as Avogadro's number, is approximately \(6.022 \times 10^{23}\), indicating the vast number of entities in a mole.
To calculate moles, use the formula:

• Moles = (given quantity of substance in grams) / (molar mass of the substance)

The molar mass is the sum of the atomic masses of all atoms in a molecule, measured in grams per mole (g/mol). This basic calculation allows chemists to quantify how much of a substance is needed or available for a reaction.
In the context of the exercise, however, the mole values are already provided. This simplifies the process as the necessary calculations focus primarily on converting the volume and applying the molarity formula.

Solution Concentration

Solution concentration refers to the amount of solute within a given volume of solvent, typically expressed as molarity (M). Molarity is an essential concept in chemistry education. It is defined as the number of moles of solute divided by the number of liters of solution. This quantity helps chemists know how concentrated a solution is, which is crucial for reactions and processes.
The formula for molarity is:

• Molarity (M) = moles of solute / volume of solution in liters

Knowing the molarity of a solution can determine how solutions of different concentrations affect chemical reactions. Higher molarity indicates a more concentrated solution, which can increase the rate of reactions or the intensity of certain properties like conductivity or color.
Understanding solution concentration allows us to prepare a solution accurately by adjusting the amount of solute or solvent to achieve the desired concentration.

Chemistry Education

Chemistry education involves understanding fundamental concepts like moles, molarity, and converting measurements. Learning these basics is crucial for advancing in chemistry. Education in this field reinforces how the microscopic interactions of atoms lead to macroscopic phenomena. Providing students with tools to calculate and understand these concepts greatly improves their ability to predict and manipulate chemical processes.
Students often encounter different contextual applications for concepts like molarity. This enhances their thinking skills and ability to relate theoretical knowledge to practical scenarios. For example, in preparing solutions, understanding molarity helps in determining how much of a substance should be used to make a specific solution concentration.
In addition, technology can aid chemistry education. Interactive software and simulations can make understanding these complex concepts more manageable and engaging, equipping students to tackle real-world scientific challenges.

Volume Conversion

Volume conversion is a common task in chemistry, especially when using formulas like the one for molarity. Chemists often work with measurements in milliliters (mL), which must be converted into liters (L) for calculations. This involves a simple multiplication, as 1 liter equals 1000 milliliters.
Volume conversion formula used is:

• Volume in liters = Volume in milliliters ÷ 1000

Accurate volume conversion is crucial because calculations depend on consistent units. By not converting units properly, the calculated molarity could be far from accurate.
Ensuring that all measurements are in appropriate units before starting calculations is a best practice that ensures precision in experimental and reaction predictions. Continual practice with conversions helps students become quicker and more confident in their chemistry skills.