Problem 99 - Introductory Chemistry Atoms First

Question

Give precise instructions to your laboratory assistant as to how to prepare \(1.00 \mathrm{~L}\) of a \(1.00 \mathrm{M}\) aqueous solution of \(\mathrm{CaCl}_{2}\). Remember that your assistant will be measuring out the \(\mathrm{CaCl}_{2}\) in grams. She has available a 1-L volumetric flask.

Step-by-Step Solution

Answer

Weigh 110.98 g of CaCl2 (molar mass = 110.98 g/mol) and transfer it to a 1-L volumetric flask. Fill the flask halfway with distilled water and swirl to dissolve the solid. Fill the flask to the 1.00 L mark with distilled water, ensuring the bottom of the meniscus touches the mark. Place the stopper and invert the flask several times for proper mixing. You now have a 1.00 L of a 1.00 M aqueous solution of CaCl2.

Step 1: Calculate the molar mass of CaCl2

Determine the molar mass of CaCl2 by adding the molar masses of each element in the formula (one Calcium atom and two Chlorine atoms). The molar masses of Calcium and Chlorine are 40.08 g/mol and 35.45 g/mol, respectively. Thus, the molar mass of CaCl2 is: \(Molar~mass~of~CaCl_2 = 40.08 + 2(35.45) = 110.98~g/mol\)

Step 2: Determine the mass of CaCl2 needed for 1.00 L of a 1.00 M solution

Now that we have the molar mass of CaCl2, we can multiply it by the desired molarity (1.00 M) to find the mass of CaCl2 in grams: \(mass~of~CaCl_2 = (1.00~M)(1.00~L)(110.98~g/mol) = 110.98~g\)

Step 3: Prepare the solution using a 1-L volumetric flask

1. Weigh 110.98 g of CaCl2 on a balance and transfer it to the 1-L volumetric flask. 2. Fill the flask approximately halfway with distilled water. 3. Swirl the flask gently to dissolve the CaCl2. Make sure all of the solid is dissolved. 4. Fill the flask to the 1.00 L mark with distilled water. Make sure the bottom of the meniscus is touching the mark. 5. Put the stopper on the flask and invert it several times to ensure proper mixing. The solution is now prepared and contains 1.00 L of a 1.00 M aqueous solution of CaCl2.

Key Concepts

Molar Mass Calculation

Calculating the molar mass is a crucial first step in preparing any chemical solution. It involves finding the mass of one mole of a chemical compound expressed in grams per mole (g/mol). To determine the molar mass of a compound like calcium chloride, we add up the molar masses of its individual elements. Calcium (Ca) has a molar mass of approximately 40.08 g/mol, and chlorine (Cl) is about 35.45 g/mol. Since calcium chloride is represented by the chemical formula \( \mathrm{CaCl}_2 \), we have one calcium atom and two chlorine atoms to consider.

• Calculate the total for calcium: \( 1 \times 40.08 = 40.08 \text{ g/mol} \)
• Calculate the total for chlorine: \( 2 \times 35.45 = 70.90 \text{ g/mol} \)
• Add these values together: \( 40.08 + 70.90 = 110.98 \text{ g/mol} \)

Therefore, the molar mass of \( \mathrm{CaCl}_2 \) is \( 110.98 \text{ g/mol} \). Understanding this calculation helps ensure the correct amount of a compound is used to prepare a solution.

Volumetric Flask Usage

Volumetric flasks are essential tools for preparing solutions with precise concentrations. These flasks have a long neck with a single calibration mark, which signifies the volume of liquid it can hold when filled to that line.Using a volumetric flask properly ensures that your solution is accurate to the degree needed for scientific experiments.
To use a volumetric flask correctly:

• First, ensure that the flask is clean and dry if needed. Residues from previous experiments can affect results.
• After adding your solid (such as \( \mathrm{CaCl}_2 \)), partially fill the flask with distilled water to fully dissolve the compound. Swirl the solution gently to facilitate dissolving.
• Top off with more distilled water, filling exactly to the calibration mark, ensuring accuracy. The meniscus (the curve seen at the top of the liquid) should be at the mark, viewed at eye level.

These flasks are designed to provide precise measurements crucial for consistent results across experiments.

Solution Preparation Steps

Preparing a chemical solution requires careful steps to ensure accuracy and consistency. Following a standardized procedure helps guarantee the desired molarity and solution volume.
For a 1.00 M \( \mathrm{CaCl}_2 \) solution:

• First, calculate and weigh the precise amount of solute needed, \( 110.98 \text{ g} \) in this case, using a balance.
• Transfer the solute to a clean 1-L volumetric flask.
• Half-fill the flask with distilled water to aid in dissolving the solid compound completely.
• Once dissolved, continue to add distilled water until the bottom of the meniscus aligns precisely with the 1.00 L mark on the flask.
• Secure the stopper on the flask and invert it multiple times to ensure even distribution of the solute throughout the solvent.

Following these meticulous steps ensures the solution reaches the correct concentration and is properly mixed.

Chemical Weighing Techniques

Precision in measuring chemical compounds is vital for accurate solution preparation. The right techniques ensure that the calculated amounts align with actual solution needs.
Here are key techniques for weighing chemicals like \( \mathrm{CaCl}_2 \):

• Use a balance that is calibrated and suitable for measuring to the required precision. Ensure it is zeroed before use.
• Place a weighing paper or container on the balance before zeroing again, if necessary, to account for the container's weight.
• Carefully add the compound, picking small amounts at a time to prevent exceeding the required weight. Gradually approach the target weight of \( 110.98 \text{ g} \).
• If the amount exceeds slightly, do not touch the compound with bare hands or directly return it to containers. Use a scrapbook to adjust if needed.

Adhering to these techniques ensures that the desired chemical amount is achieved without compromise, leading to more accurate experimental results.