Problem 11 - Chemistry: An Atoms-Focused Approach

Question

Calculate the molarity of each of the following solutions: a. \(0.56 \mathrm{mol} \mathrm{BaCl}_{2}\) in \(100.0 \mathrm{mL}\) of solution b. \(0.200 \mathrm{mol} \mathrm{Na}_{2} \mathrm{CO}_{3}\) in \(200.0 \mathrm{mL}\) of solution c. \(0.325 \mathrm{mol} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) in \(250.0 \mathrm{mL}\) of solution d. \(1.48 \mathrm{mol} \mathrm{KNO}_{3}\) in \(250.0 \mathrm{mL}\) of solution

Step-by-Step Solution

Answer

Answer: The molarities are as follows: a. \(M_{\mathrm{BaCl}_{2}} = 5.60\, \text{M}\) b. \(M_{\mathrm{Na}_{2}\mathrm{CO}_{3}} = 1.00\, \text{M}\) c. \(M_{\mathrm{C}_{6}\mathrm{H}_{12}\mathrm{O}_{6}} = 1.30\, \text{M}\) d. \(M_{\mathrm{KNO}_{3}} = 5.92\, \text{M}\)

Step 1: (Step 1: Convert the volume to liters)

For each solution, convert the given volume from milliliters to liters by dividing by 1000. a. \(100.0 \mathrm{mL} = 0.100\,\text{L}\) b. \(200.0 \mathrm{mL} = 0.200\,\text{L}\) c. \(250.0 \mathrm{mL} = 0.250\,\text{L}\) d. \(250.0 \mathrm{mL} = 0.250\,\text{L}\)

Step 2: (Step 2: Use the molarity formula)

Apply the molarity formula: \(M = \frac{n}{V}\) to calculate the molarity for each solution. a. \(M_{\mathrm{BaCl}_{2}}=\dfrac{0.56 \,\text{mol}}{0.100\,\text{L}} = 5.60\, \text{M}\) b. \(M_{\mathrm{Na}_{2}\mathrm{CO}_{3}}=\dfrac{0.200\, \text{mol}}{0.200\,\text{L}} = 1.00\, \text{M}\) c. \(M_{\mathrm{C}_{6}\mathrm{H}_{12}\mathrm{O}_{6}}=\dfrac{0.325\, \text{mol}}{0.250\, \text{L}} = 1.30\, \text{M}\) d. \(M_{\mathrm{KNO}_{3}}=\dfrac{1.48\, \text{mol}}{0.250\, \text{L}} = 5.92\, \text{M}\)

Step 3: (Step 3: Report the final molarities)

The molarities of the four solutions are: a. \(M_{\mathrm{BaCl}_{2}} = 5.60\, \text{M}\) b. \(M_{\mathrm{Na}_{2}\mathrm{CO}_{3}} = 1.00\, \text{M}\) c. \(M_{\mathrm{C}_{6}\mathrm{H}_{12}\mathrm{O}_{6}} = 1.30\, \text{M}\) d. \(M_{\mathrm{KNO}_{3}} = 5.92\, \text{M}\)

Key Concepts

Solution Preparation

When preparing a chemical solution, understanding the concept and procedure of solution preparation is crucial. This involves measuring the amount of solute and combining it with a solvent to achieve a desired concentration, often expressed as molarity. To begin with, ensure that you have precisely weighed the appropriate number of moles of the solute. For instance, in the provided exercises, we know the moles of solutes like BaCl₂, Na₂CO₃, C₆H₁₂O₆, and KNO₃ beforehand. For more complex situations, you might start by calculating the moles using molar mass and mass of substance. Next, carefully dissolve this solute in a specific volume of solvent—usually water—and ensure it's thoroughly mixed. This might involve using a volumetric flask where you slowly add the solute to the solvent, swirling the mixture until the solute is completely dissolved. The final step involves adjusting the solution to the intended final volume by adding more solvent until the measurement line is reached, ensuring accurate concentration.

Volume Conversion

Converting volume measurements from milliliters (mL) to liters (L) is a small but essential step in molarity calculations, as molarity is defined as moles per liter. The conversion is simple: since there are 1000 milliliters in a liter, you divide the volume in milliliters by 1000. This is because the base SI unit for volume is the liter, and using consistent units avoids miscalculations. For the given exercise:

• 100.0 mL becomes 0.100 L by dividing by 1000 (100.0 ÷ 1000 = 0.100).
• 200.0 mL becomes 0.200 L (200.0 ÷ 1000 = 0.200).
• 250.0 mL becomes 0.250 L (250.0 ÷ 1000 = 0.250).

Accurate volume conversion ensures correct subsequent calculations, like determining the solution's molarity.

Chemical Concentration

Chemical concentration fundamentally describes how much solute is present in a given volume of solution, and understanding this concept is essential for calculating molarity.Molarity (M) is the prevalent way of expressing chemical concentration in solutions. It is defined as the number of moles of solute per liter of solution. This expression provides a clear perspective on how concentrated or diluted a solution is. The formula for calculating molarity is: \[ M = \frac{n}{V} \]where:

• \(n\) = moles of solute,
• \(V\) = volume of the solution in liters.

By using this formula, you can determine the molarity for each solution in the exercise, such as 5.60 M for BaCl₂, indicating a highly concentrated solution, or 1.00 M for Na₂CO₃, which is more moderate. Comprehending concentration, notably molarity, allows chemists to accurately predict how solutions will behave in reactions or practical applications, making it an indispensable concept in chemistry.