Problem 47 - Chemistry: The Central Science

Question

Calculate the number of moles of solute present in each of the following aqueous solutions: (a) \(600 \mathrm{~mL}\) of \(0.250 \mathrm{M} \mathrm{SrBr}_{2}\), (b) \(86.4 \mathrm{~g}\) of \(0.180 \mathrm{~m} \mathrm{KCl}\), (c) \(124.0 \mathrm{~g}\) of a solution that is \(6.45 \%\) glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) by mass.

Step-by-Step Solution

Answer

(a) \(0.15 \text{ moles of SrBr}_2\) (b) \(0.01275264 \text{ moles of KCl}\) (c) \(0.044388642 \text{ moles of glucose}\)

Step 1: (a) Calculate moles in 600mL of 0.250M SrBr2 solution

To calculate the moles of solute in this solution, we can use the formula: moles = molarity × volume (in liters). We are given the molarity (0.250M) and volume (600mL), so we can plug those values into the formula: moles = 0.250M × (600mL × (1L/1000mL)) moles = 0.250M × 0.6 L moles = 0.15 moles of SrBr2.

Step 2: (b) Calculate moles in 86.4g of 0.180m KCl solution

To calculate the moles of solute in this solution, we can use the formula: moles = molality × kg of solvent. We are given the molality (0.180m) and mass of the solution (86.4g), but we need to find the amount (in kg) of the solvent (water) in the solution: mass of solvent = mass of solution - mass of solute We can find the mass of solute by multiplying the mass of the solution by the molality: mass of solute = molality × kg of solvent mass of solute = 0.180m × (86.4g × (1kg/1000g)) mass of solute = 15.552 g of KCl Now, we can find the mass of the solvent and convert it to kg: mass of solvent = 86.4g - 15.552g = 70.848g mass of solvent = 70.848g × (1kg/1000g) = 0.070848 kg Finally, we can calculate the moles of solute: moles = 0.180m × 0.070848 kg moles = 0.01275264 moles of KCl

Step 3: (c) Calculate moles in 124.0g of a 6.45% glucose (C6H12O6) solution by mass

To calculate the moles of glucose in this solution, we will first find the mass of glucose in the solution, then convert this mass to moles using the molar mass of glucose: mass of glucose = (percentage of glucose in solution) × (total mass of solution) mass of glucose = 0.0645 × 124.0g = 7.998g of glucose Next, we can find the moles of glucose using its molar mass. The molar mass of glucose is: C (x6): 6 × 12.01 g/mol H (x12):12 × 1.01 g/mol O (x6): 6 × 16.00 g/mol Total molar mass = 180.18 g/mol moles of glucose = mass of glucose / molar mass moles of glucose = 7.998g / 180.18 g/mol moles of glucose = 0.044388642 moles of glucose

Key Concepts

Molarity

Molarity is a measure of how concentrated a solution is. It tells you the number of moles of solute (the substance being dissolved) per liter of solution. To calculate molarity, you use the formula:

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

Suppose you have 0.250 M (molar) Strontium bromide (\(\text{SrBr}_2 \)) solution. This means each liter of the solution contains 0.250 moles of \(\text{SrBr}_2 \). To find out how many moles are in 600 mL (0.6 liters) of this solution:

• Convert milliliters to liters: 600 mL × (1 L/1000 mL) = 0.6 L
• Use the molarity formula: Moles = 0.250 M × 0.6 L = 0.15 moles

Thus, there are 0.15 moles of \(\text{SrBr}_2 \) in 600 mL of the solution. It's that simple! Breaking it into smaller calculations can make it easier to follow.

Molality

Molality seems similar to molarity, but it's slightly different. It measures the number of moles of solute per kilogram of solvent (usually water). Molality tells you how many moles of a compound are present in each kilo of solvent, which is handy when temperature changes are involved.
For example, imagine a solution with 0.180 m (molal) of potassium chloride (\(\text{KCl} \)) in a total mass of 86.4 g. Molality can be calculated by the formula:

• Molality (m) = moles of solute / kg of solvent

To find out how many moles are in the solution:

• First, calculate the mass of solute: 0.180 m = mass of solute/0.070848 kg
• Determine mass of solver: 86.4 g - 15.552 g = 70.848 g
• Convert g to kg: 70.848 g = 0.070848 kg
• Therefore, moles = 0.180 m × 0.070848 kg = 0.01275 moles of \(\text{KCl} \)

By understanding these steps, you can easily calculate molality and find the moles of a solute in any solution.

Mass Percent Composition

Mass percent composition is a way to express the concentration of a component in a mixture. It shows the mass of a particular component divided by the total mass of the mixture, then multiplied by 100 to get a percentage.
Let's take an example of glucose, which has a mass percent composition of 6.45% in a solution. To determine the amount of solute (glucose) in 124.0 g of solution:

• Calculate mass of glucose: 0.0645 × 124.0 g = 7.998 g
• Find moles using the molar mass of glucose (\(\text{C}_6\text{H}_{12}\text{O}_6 = 180.18 \text{ g/mol} \)):
• Moles of glucose = 7.998 g / 180.18 g/mol ≈ 0.0444 moles

By breaking down the mass percent to find the actual mass of glucose, you can then easily convert this to moles using the molar mass. Understanding mass percent composition helps in making accurate measurements in chemical reactions.