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 \(0.250 \mathrm{M} \mathrm{SrBr}\), (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 aqueous solution are: (a) \(0.15 \mathrm{~moles}\) of SrBr in the 600 mL of 0.250 M SrBr solution. (b) \(0.2087 \mathrm{~moles}\) of KCl in the 86.4 g of 0.180 m KCl solution. (c) \(0.0444 \mathrm{~moles}\) of glucose in the 124.0 g of 6.45% glucose by mass solution.

Step 1: Calculate moles of SrBr

For the first solution, we are given the volume (600 mL) and molarity (0.250 M) of SrBr. We can calculate the number of moles using the formula: Moles = Molarity × Volume First, convert the volume from mL to L: \(600 \mathrm{~mL} = 0.6 \mathrm{L}\) Now calculate the number of moles of SrBr: Moles of SrBr = \(0.250 \mathrm{M} × 0.6 \mathrm{L} = 0.15 \mathrm{~moles}\)

Step 2: Calculate moles of KCl

For the second solution, we are given the mass (86.4 g) and molality (0.180 m) of KCl. Molality is defined as the number of moles of solute per kilogram of solvent: Molality = Moles of solute / Mass of solvent (kg) We need the molar mass of KCl to calculate the number of moles. The molar mass of KCl is: Molar mass of KCl = 39.1 g/mol (K) + 35.5 g/mol (Cl) = 74.6 g/mol Now use the molality to find the moles of KCl: Moles of KCl = Molality × Mass of solvent (kg) Moles of KCl = \(0.180 \mathrm{~m} × \dfrac{86.4 \mathrm{~g}}{74.6 \mathrm{~g/mol}} = 0.2087 \mathrm{~moles}\)

Step 3: Calculate moles of glucose

For the third solution, we are given the mass of the solution (124.0 g) and the mass percentage of glucose (6.45%). First, calculate the mass of glucose in the solution: Mass of glucose = % mass of glucose × Total mass of the solution Mass of glucose = \(0.0645 × 124.0 \mathrm{~g} = 8.003 \mathrm{~g}\) We need the molar mass of glucose (C6H12O6) to determine the moles of glucose. The molar mass of glucose is: Molar mass of glucose = 6×12.01 g/mol (C) + 12×1.01 g/mol (H) + 6×16.00 g/mol (O) = 180.18 g/mol Now use the mass of glucose to find the moles of glucose: Moles of glucose = Mass of glucose / Molar mass of glucose Moles of glucose = \(\dfrac{8.003 \mathrm{~g}}{180.18 \mathrm{~g/mol}} = 0.0444 \mathrm{~moles}\) In summary: 1. The number of moles of SrBr in the first solution is 0.15 moles. 2. The number of moles of KCl in the second solution is 0.2087 moles. 3. The number of moles of glucose in the third solution is 0.0444 moles.

Key Concepts

Moles Calculation

Calculating the number of moles in a substance is a foundational skill in chemistry. The mole is a unit that measures the amount of a substance based on the number of atoms or molecules it contains. It's closely linked to Avogadro's number, which is approximately \(6.022 \times 10^{23}\) entities per mole.
To calculate moles, different formulas are used based on the known values.

• For solutions, such as in the case of the SrBr aqueous solution, we derive moles from molarity. The equation is \(\text{Moles} = \text{Molarity} \times \text{Volume in L}\). Being aware that volume needs to be in liters is crucial.
• In situations dealing with mass, such as with glucose or KCl, moles are calculated using \(\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}}\). Here, knowing the molar mass permits the conversion from grams to moles.

Accurately calculating moles requires careful attention to units and the use of precise numerical values.

Aqueous Solutions

Aqueous solutions are a common topic in chemistry, consisting of water (the solvent) and a solute dissolved in it. Their properties depend on the concentration of the solute as well as the interactions between water molecules and solute.
In these solutions, concentration can be expressed in various ways:

• Molarity (M): Defined as the number of moles of solute per liter of solution. Common in laboratory settings for easy calculations.
• Molality (m): Defines concentration as moles of solute per kilogram of solvent. It's beneficial in scenarios where temperature changes because it is not temperature-dependent unlike molarity.

Understanding these metrics is key to measuring how substances behave when dissolved or react within an aqueous solution.

Molar Mass Determination

The molar mass of a substance is the mass of one mole of its entities (atoms, molecules, ions, etc.), expressed in grams per mole (g/mol). Different elements and compounds have unique molar masses.
Molar mass calculations are essential for translating between mass and moles, especially for reactions in chemistry.

• Elemental Molar Mass: Derived directly from the periodic table. Oxygen, for example, has a molar mass of approximately 16.00 g/mol.
• Compound Molar Mass: Calculated by summing up the molar masses of constituent elements. For glucose \(\text{C}_6\text{H}_{12}\text{O}_6\), you add up the molar masses of six carbons, twelve hydrogens, and six oxygens, resulting in \(180.18 \)g/mol.

Acquiring an accurate molar mass is crucial to assessing the quantity of substance involved in reactions or solutions.