Problem 51 - 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

In summary, the number of moles of solute present in each solution is: (a) \(0.150 \mathrm{~mol}\) of SrBr2, (b) \(0.209 \mathrm{~mol}\) of KCl, and (c) \(0.0444 \mathrm{~mol}\) of glucose.

Step 1: Convert mL to L

To make calculations, we first need to convert the volume from milliliters (mL) to liters (L) using the conversion factor 1 L = 1000 mL: \(600 \mathrm{~mL} * \cfrac{1 \mathrm{~L}}{1000 \mathrm{~mL}} = 0.600 \mathrm{~L}\)

Step 2: Calculate moles of solute

We know that molality (M) is equal to moles of solute per liter of solution. To calculate the number of moles, we will use the formula: Moles of solute = M x Volume of solution in L Moles of SrBr2 = \(0.250 \mathrm{~M} * 0.600 \mathrm{~L}\) Moles of SrBr2 = \(0.150 \mathrm{~mol}\) #(b) 86.4 g of 0.180 m KCl#

Step 1: Calculate moles of solute from mass and molality

Given the molality (m) and mass of the solution, we can find the number of moles of solute (KCl) using the formula: Moles of solute = molality x (mass of solution / molecular weight of solute) Molecular weight of KCl = 39.1 (K) + 35.5 (Cl) = 74.6 g/mol Moles of KCl = \(0.180 \mathrm{~m} * \cfrac{86.4 \mathrm{~g}}{74.6 \mathrm{~g/mol}}\) Moles of KCl = \(0.209 \mathrm{~mol}\) #(c) 124.0 g of a solution that is 6.45% glucose (C6H12O6) by mass#

Step 1: Calculate mass of solute

To find the mass of glucose in the solution, we will use the percentage given: Mass of glucose = (percentage of glucose / 100) x mass of solution Mass of glucose = \(\cfrac{6.45}{100} * 124.0 \mathrm{~g}\) Mass of glucose = \(8.00 \mathrm{~g}\)

Step 2: Calculate moles of solute from mass

To find the number of moles of glucose, we will use the molecular weight of glucose and the mass of glucose in the solution: Molecular weight of glucose = 6(12.01) + 12(1.01) + 6(16.00) = 180.18 g/mol Moles of glucose = \(\cfrac{8.00 \mathrm{~g}}{180.18 \mathrm{~g/mol}}\) Moles of glucose = \(0.0444 \mathrm{~mol}\)

Key Concepts

Mole Calculations

Understanding how to calculate the number of moles in a solution is fundamental in solution chemistry. The mole is a unit in chemistry that represents a specific number of atoms or molecules, typically Avogadro's number, which is approximately \(6.022 \times 10^{23}\). To calculate the moles of a solute in a solution, the molarity (M) of the solution is a key element. Molarity is defined as the number of moles of solute divided by the liters of solution.

For example, if we have a solution with a molarity of 0.250 M and a volume of 0.600 L, the number of moles of solute can be calculated using the formula:

• Number of moles = Molarity \(\times\) Volume

Plugging in the numbers:

• Number of moles = \(0.250 \times 0.600\) = \(0.150\) moles

This calculation helps predict how much of a substance is present in the solution, which is crucial for stoichiometry in chemical reactions.

Molality

Molality (\(m\)) is another way to express the concentration of a solution. Unlike molarity, which depends on volume, molality is based on the mass of the solvent and is defined as the number of moles of solute per kilogram of solvent.

This can be especially useful in solutions where temperature changes might alter volume but not mass. Calculating moles from molality involves the following relationship:

• Number of moles = Molality \(\times\) Mass of the solvent (in kg)

In exercises involving solutions with given molality, like 0.180 m KCl, you can determine the moles of solute by:

• Calculating the required mass using the molecular weight of the solute
• Using the formula to obtain moles: \(0.180 \times \frac{86.4}{74.6}\)
• Resulting in approximately \(0.209\) moles of KCl

Remember that molality is temperature-independent and can provide more accurate results in various chemical applications.

Mass Percentage

Mass percentage is a concentration term used to describe how much of a solute is present in a solution based on its mass, represented as a percentage. It's calculated by dividing the mass of the solute by the total mass of the solution and multiplying by 100.

This concept is particularly valuable when dealing with solid mixtures dissolved in a liquid. To find the number of moles from a solution with a known mass percentage:

• First, calculate the actual mass of the solute using the formula:Mass of solute = (Mass percentage / 100) \(\times\) Total mass of solution
• Then, determine the number of moles by dividing the mass of the solute by its molecular weight.

For instance, with 124.0 g of a solution containing 6.45% glucose:

• Mass of glucose = \((6.45/100) \times 124.0 = 8.00\) g
• Calculate moles = \(\frac{8.00}{180.18}\) = 0.0444 moles

Understanding mass percentage aids in converting between mass and moles, critical for preparing solutions and reagents.