Question

Describe how you would prepare each of the following aqueous solutions, starting with solid KBr: (a) \(0.75 \mathrm{~L}\) of \(1.5 \times 10^{-2} M \mathrm{KBr}\), (b) \(125 \mathrm{~g}\) of \(0.180 \mathrm{~m} \mathrm{KBr}\), (c) \(1.85 \mathrm{~L}\) of a solution that is \(12.0 \% \mathrm{KBr}\) by mass (the density of the solution is \(1.10 \mathrm{~g} / \mathrm{mL}\) ), (d) a \(0.150 \mathrm{M}\) solution of \(\mathrm{K} \mathrm{Br}\) that contains just enough \(\mathrm{KBr}\) to precipitate \(16.0 \mathrm{~g}\) of \(\mathrm{AgBr}\) from a solution containing \(0.480 \mathrm{~mol}\) of \(\mathrm{AgNO}_{3}\).

Short answer

To prepare the given aqueous KBr solutions: a) Weigh 1.33875 g of solid KBr, dissolve in distilled water, and adjust the total volume to 0.75 L. b) Weigh 20.32 g of solid KBr, dissolve in distilled water, and adjust the total mass to 125 g. c) Weigh 244.2 g of solid KBr, dissolve in distilled water, and adjust the total mass to 2035 g. d) Weigh 10.1388 g of solid KBr, dissolve in distilled water, adjust the total volume to 0.568 L, and add to the AgNO3 solution to precipitate 16.0 g of AgBr.

Step-by-step solution

Calculate moles of KBr required

To prepare a 0.75 L solution of 1.5x10^{-2} M KBr, we need to calculate the moles of KBr required. The equation to calculate moles (n) is given by n = Molarity (M) × Volume (V) in Liters. Here, M = \(1.5 \times 10^{-2}\) M and V = 0.75 L.\[n = (1.5 \times 10^{-2}) \times 0.75 = 1.125 \times 10^{-2} mol\]

Calculate mass of KBr required

Using the molecular weight of KBr (39.1 g/mol for K + 79.9 g/mol for Br = 119 g/mol), we can calculate the mass required for 1.125x10^{-2} moles.\[mass (KBr) = 1.125 \times 10^{-2} \text{ mol} \times 119 \frac {g}{\text{mol}} = 1.33875 \, g\]

Prepare the solution

Weigh 1.33875 g of solid KBr and dissolve it in distilled water. Add water until the total volume of the solution is 0.75 L. Stir the solution until all the KBr is dissolved. #b) 125 g of 0.180 m KBr#

Calculate moles of KBr required

To prepare a 125 g solution with 0.180 molality (m) KBr, we need to calculate the moles of KBr required. The equation to calculate moles (n) is given by n = Molality (m) × Mass of solvent (in kg). Here, m = 0.180 mol/kg, and we have 125 g solution but we need to find the mass of solvent.\[n = 0.180 \, mol/kg \times mass \, solvent (kg)\]

Calculate mass of KBr and mass of solvent

Let the mass of KBr be x g and mass of solvent be (125-x) g. We have the equation from step 1. Divide both sides by (125-x) to get the mass of KBr required:\[0.180 = \frac{x \, mol}{(125-x) \, g}\] Now, convert the mass of KBr (x) into moles using the molecular weight of KBr (119 g/mol):\[0.180 = \frac{\frac{x \, g}{119 \, g/mol}}{(125-x) \, g}\] Solve for x: x = 20.32 g.

Prepare the solution

Weigh 20.32 g of solid KBr and dissolve it in distilled water. Add water until the total mass of the solution is 125 g. Stir the solution until all the KBr is dissolved. #c) 1.85 L of 12.0% KBr by mass, density=1.10 g/mL#

Calculate mass of KBr required

We need to prepare a 1.85 L solution with 12.0% KBr by mass. Convert the volume to mass using the density: mass = volume × density = 1.85 L × 1000 mL/L × 1.10 g/mL = 2035 g. The mass of KBr in the solution should be 12.0%, so we need 0.12 × 2035 g = 244.2 g of KBr.

Prepare the solution

Weigh 244.2 g of solid KBr and dissolve it in distilled water. Add water until the total mass of the solution is 2035 g. Stir the solution until all the KBr is dissolved. #d) 0.150 M KBr solution to precipitate 16.0 g of AgBr from 0.480 mol AgNO3#

Calculate moles of AgBr

Given mass of AgBr is 16.0 g. Calculate the moles of AgBr using the molecular weight of AgBr (107.9 g/mol for Ag + 79.9 g/mol for Br = 187.8 g/mol). Moles (n) = Mass / Molecular weight = 16.0 g / 187.8 g/mol = 0.0852 mol AgBr.

Calculate moles of KBr required

Since the reaction between AgNO3 and KBr (AgNO3 + KBr → AgBr + KNO3) is a 1:1 reaction, we need the same moles of KBr as AgBr required (0.0852 mol) to precipitate 16.0 g of AgBr.

Calculate volume of 0.150 M KBr solution

Using the given molarity (0.150 M), calculate the volume of KBr solution required. Volume (V) = Moles (n) / Molarity (M) = 0.0852 mol / 0.150 M = 0.568 L.

Calculate mass of KBr required

Using the molecular weight of KBr (119 g/mol), calculate the mass required for 0.0852 mol KBr:\[mass(KBr) = 0.0852 \, mol \times 119 \frac{g}{mol} = 10.1388 \, g\]

Prepare the solution

Weigh 10.1388 g of solid KBr and dissolve it in distilled water. Add water until the total volume of the solution is 0.568 L. Stir the solution until all the KBr is dissolved. Add this solution to the AgNO3 solution to precipitate 16.0 g of AgBr.

Key concepts

Molarity

Molarity is a measure of the concentration of a solute in a solution, expressed as the number of moles of solute per liter of solution. To calculate molarity, you need to know the amount of solute (in moles) and the total volume of the solution (in liters). The formula for molarity (M) is:
\[ M = \frac{n}{V} \]
where \( n \) is the number of moles and \( V \) is the volume in liters. This means if you know how much KBr you want to dissolve in water, you can determine the molarity by ensuring the amount of dissolved substance divided by the volume of the solution is consistent with your desired concentration.

• Ensure accurate measurements when weighing KBr and measuring water volume.
• Molarity is temperature-dependent, as volume can change slightly with temperature.

Solution Concentration

Solution concentration is a broad term that can refer to various ways of expressing the amount of solute in a solution. Besides molarity, other metrics for solution concentration include molality, mole fraction, and mass percent.
The choice of concentration expression depends on the chemical process involved and conditions like temperature and pressure.
It's important to note:

• Molarity relates volume to moles, making it common in lab settings for reactions in liquids.
• Molality is based on mass, used when temperature changes, as mass doesn't change with temperature.
• Mass percent gives the ratio of mass of solute to total solution mass, providing a straightforward proportion for mixtures.

Mass Percent

Mass percent is a way to express the concentration by mass of a component within a mixture. It is calculated by dividing the mass of the solute by the total mass of the solution and then multiplying by 100 to convert it to a percentage. The formula is as follows:
\[ \text{Mass Percent} = \left( \frac{\text{mass of solute}}{\text{total mass of solution}} \right) \times 100 \]
This is particularly useful when describing the composition of solutions in terms of the mass composition, and is ideal in cases where the volume may change due to factors like temperature and pressure.
To ensure precision:

• Weigh the solute accurately using a balance.
• Add water slow enough to reach the exact desired mass of the final solution.
• Stir well to ensure the solute is thoroughly dissolved.

Stoichiometry

Stoichiometry involves calculating the amounts of reactants and products in chemical reactions. It applies to solution preparation as it helps determine how much of a substance is required for a given reaction.
In a balanced chemical reaction, stoichiometry can guide you to mix reactants in the correct proportions. This ensures that reactions proceed with maximum efficiency and predictability. The key steps are:

• Balance the chemical equation to know the mole ratio of reactants to products.
• Use molar mass to convert grams to moles when measuring substances.
• Apply the mole ratio to determine how much of a reactant is needed to react with a given amount of another reactant effectively.
• Ensure the complete dissolution of the reactants for a thorough reaction.