Problem 15 - Analytical Chemistry

Question

Calculate the molarity of a potassium dichromate solution prepared by placing 9.67 grams of \(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) in a \(100-\mathrm{mL}\) volumetric flask, dissolving, and diluting to the calibration mark.

Step-by-Step Solution

Answer

The molarity of the solution is 0.3285 M.

Step 1: Find the Molar Mass of K2Cr2O7

To find the molarity, we need the molar mass of potassium dichromate, \(\text{K}_2\text{Cr}_2\text{O}_7\). Calculate it by adding the atomic masses of each element: \(2 \times K (39.10\, \text{g/mol}) + 2 \times Cr (51.996\, \text{g/mol}) + 7 \times O (16.00\, \text{g/mol})\). The molar mass is approximately 294.19 g/mol.

Step 2: Calculate Moles of Solute

Use the molar mass from Step 1 to calculate the moles of \(\text{K}_2\text{Cr}_2\text{O}_7\) in the sample. \(\text{Moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{9.67\, \text{g}}{294.19\, \text{g/mol}} \approx 0.03285\, \text{mol}\).

Step 3: Convert Volume from mL to L

Since the molarity is moles per liter, convert 100 mL to liters by dividing by 1000. \(100\, \text{mL} = 0.1\, \text{L}\).

Step 4: Calculate Molarity of the Solution

Now, use the formula for molarity: \(\text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}}\). Substitute the values: \(\text{Molarity} = \frac{0.03285\, \text{mol}}{0.1\, \text{L}} = 0.3285\, \text{M}\).

Key Concepts

Potassium Dichromate

Potassium dichromate, with the chemical formula \( \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7} \), is a bright orange-red crystal that finds extensive use in various industrial and laboratory processes. It acts as a strong oxidizing agent, which means it readily donates oxygen to other substances. This property makes it particularly useful in cleaning laboratory glassware and in photographic processing. However, it's crucial to handle it with care due to its toxic and carcinogenic nature.
Understanding the role of potassium dichromate is important in chemistry, not only because of its applications but also because of its significance in redox reactions. Redox reactions are reactions where the oxidation states of atoms are changed, often leading to energy release or usage.

• Applications: This compound serves as a corrosion inhibitor, in leather tanning, and also as a volumetric solution in titrations.
• Safety: Always use appropriate personal protective equipment (PPE) like gloves and goggles when handling potassium dichromate.

Molar Mass Calculation

Calculating the molar mass of a compound is an essential skill in chemistry. The molar mass indicates how much one mole of a substance weighs, in grams. For potassium dichromate \( (\text{K}_2\text{Cr}_2\text{O}_7) \), this involves adding the atomic masses of all constituent atoms.
To calculate the molar mass, follow these steps:

• Determine the atomic mass of each element in the compound using the periodic table. Here, potassium (K) is 39.10 g/mol, chromium (Cr) is 51.996 g/mol, and oxygen (O) is 16.00 g/mol.
• Multiply the atomic mass by the number of atoms of each element present in the molecule. In \( \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7} \), potassium appears twice, chromium twice, and oxygen seven times.
• Add these values together to get the total molar mass. So, \( 2 \times 39.10 + 2 \times 51.996 + 7 \times 16.00 = 294.19 \text{ g/mol} \).

Calculating molar mass effectively translates into converting mass into moles, a crucial step in finding the molarity of a solution.

Volumetric Flask

A volumetric flask is a type of laboratory glassware used to prepare precise solution concentrations. This pear-shaped vessel is calibrated to hold a specific amount of liquid when filled to a marked line on its neck. The accuracy of these flasks makes them ideal for preparing solutions with a known molarity.
When using a volumetric flask, it's essential to remember:

• Precision: The flask must be filled up to the calibration mark to ensure the exact volume specified is achieved. Even a small deviation can affect the concentration of the solution significantly.
• Mixing: Once the solute is added, and as the solvent is being added, the flask should be swirled to ensure the solute dissolves completely. Adding solvent slowly allows you to approach the calibration mark with precision.
• Volume Conversion: Remember to convert the volume from milliliters to liters when calculating molarity, as molarity is defined in terms of moles of solute per liter of solution.

In our exercise, the use of a 100 mL volumetric flask ensures that the potassium dichromate is dissolved in exactly 0.1 L (100 mL) for calculating its molarity accurately.