Problem 18 - Chemical Principles: The Quest for Insight

Question

Describe the preparation of cach solution, starting with the anhydrous solute and warer and using the corrcsponding volumetric flask: (a) \(25.0 \mathrm{~mL}\) of \(6.0 \mathrm{M}\) \(\mathrm{NaOH}(\mathrm{aq}) ;\) (b) \(1.0 \mathrm{~L}\), of \(0.10 \mathrm{M} \mathrm{BaCl}_{2}\) (aq); (c) \(500 \mathrm{~mL}\) of \(0.0010 \mathrm{M} \mathrm{AgNO}_{3}(\mathrm{aq})\).

Step-by-Step Solution

Answer

Part A - Weigh 6.00 g NaOH, dissolve, and add water to 25.0 mL mark. Part B - Weigh 20.82 g BaCl2, dissolve, and add water to 1.0 L mark. Part C - Weigh 0.0849 g AgNO3, dissolve, and add water to 500 mL mark.

Step 1: Part A - Calculate mass of NaOH

To prepare a 25.0 mL of a 6.0 M NaOH solution, calculate the mass of NaOH needed. Molarity (M) is moles of solute per liter of solution. First, determine moles of NaOH required using the molarity and volume of the desired solution: \( n = M \times V = 6.0 \,\text{M} \times 0.025 \,\text{L} = 0.150 \,\text{moles} \). Next, calculate the mass using the molar mass of NaOH (approximately 40.00 g/mol): \( m = n \times \text{molar mass} = 0.150 \,\text{moles} \times 40.00 \,\text{g/mol} = 6.00 \,\text{g} \).

Step 2: Part A - Dissolve and make up to mark

Weigh out 6.00 g of anhydrous NaOH and dissolve it in a small amount of water. After the NaOH has fully dissolved, transfer the solution to a 25.0 mL volumetric flask. Add more water to reach the calibration line on the neck of the flask. Ensure the solution is at room temperature before making up to the mark, as volume is temperature-dependent.

Step 3: Part B - Calculate mass of BaCl2

For a 1.0 L of a 0.10 M BaCl2 solution, calculate the mass of BaCl2 necessary. Use the molarity formula: \( n = M \times V = 0.10 \,\text{M} \times 1.00 \,\text{L} = 0.10 \,\text{moles} \). The molar mass of BaCl2 (Ba:~137.33, Cl:~35.45) is approximately 208.23 g/mol. Calculate the mass: \( m = n \times \text{molar mass} = 0.10 \,\text{moles} \times 208.23 \,\text{g/mol} = 20.82 \,\text{g} \).

Step 4: Part B - Dissolve and make up to mark

Weigh out 20.82 g of anhydrous BaCl2 and dissolve it in a small volume of water. Once completely dissolved, transfer the solution to a 1.0 L volumetric flask. Fill the flask with water up to the calibration line. Ensure to mix thoroughly and that the temperature of the liquid is at room temperature when adjusting the volume.

Step 5: Part C - Calculate mass of AgNO3

For preparing 500 mL of a 0.0010 M AgNO3 solution, determine the mass of AgNO3 needed using molarity: \( n = M \times V = 0.0010 \,\text{M} \times 0.500 \,\text{L} = 0.0005 \,\text{moles} \). With AgNO3 molar mass approximately 169.87 g/mol, the mass needed is: \( m = n \times \text{molar mass} = 0.0005 \,\text{moles} \times 169.87 \,\text{g/mol} = 0.0849 \,\text{g} \).

Step 6: Part C - Dissolve and make up to mark

Weigh out 0.0849 g of anhydrous AgNO3 and dissolve it in a minor quantity of water. Subsequently, transfer this solution to a 500 mL volumetric flask, and fill with water up to the mark. Make sure the final solution is mixed well and the volume is adjusted at room temperature.

Key Concepts

Molarity Calculation

Molarity, symbolized as M, is the cornerstone concept in preparing molar solutions. It is defined as the number of moles of a solute divided by the total volume of the solution in liters. Mathematically, we express molarity as:\[ Molarity (M) = \frac{Number of moles of solute}{Volume of solution in liters} \]

When calculating molarity, first determine the number of moles of solute needed. This can be found by multiplying the desired molarity by the volume of solution (in liters). From there, you can use the molar mass of the compound to convert moles to grams. This value indicates the exact mass of the solute you need to dissolve in water to achieve the required concentration. This calculation is crucial, as ensuring the correct proportions of a substance is key to the effectiveness and reliability of the resulting chemical reactions or solutions.

Volumetric Flask Usage

A volumetric flask is an essential laboratory utensil for creating precise solution concentrations. These flasks are designed to contain a specific volume of liquid, marked by a calibration line on the neck. For accurate result, it’s important to fill the flask to this line and no further.

Volumetric flasks come in various sizes, and choosing the correct size depends on the volume of the solution you are preparing. After calculating the mass of your solute as described in the molarity section, the solute is first dissolved in a minimal amount of water. The solution is then transferred to the volumetric flask, and more water is added until the bottom of the meniscus, the curve seen at the top of a liquid, touches the calibration line. It’s vital to ensure that the temperature of the liquid is at room temperature, as changes in temperature can lead to expansion or contraction, skewing your final solution volume.

Solute Dissolution

The solute dissolution process involves the breaking down of the solid solute into individual particles that are then absorbed by the solvent, typically water, to form a homogenous solution. To properly dissolve a solute, first weigh the appropriate mass based on your molarity calculations. Then, add the measured solute to a container with a small volume of water.

Stirring or gentle shaking is necessary to facilitate the dissolution process, and it might take a while for all of the substance to fully dissolve, especially if the solute is less soluble. It's important not to rush this step to prevent inaccuracies in the final concentration. Once the solute has completely dissolved, you can proceed with the solution preparation as described in the following section.

Solution Preparation

Solution preparation combines accurate molarity calculation, efficient solute dissolution, and proper use of a volumetric flask. After dissolving the calculated mass of solute, transfer the solution into the appropriately sized volumetric flask. Then, complete the solution by slowly adding more water up to the calibration mark. If the solution isn't at room temperature, you'll need to wait or adjust accordingly since temperature affects volume.

Once the water reaches the calibration line, stop filling and mix the solution by inverting the flask multiple times or by using a stirring rod if the opening is wide enough. This ensures uniform distribution of the solute throughout the solvent. It's crucial to employ these steps to guarantee the solution's concentration is accurate and reliable for whatever application it is intended for.