Problem 40 - Chemistry The Central Science

Question

(a) What is the mass percentage of iodine in a solution containing 0.035 \(\mathrm{mol}_{2}\) in 125 \(\mathrm{g}\) of \(\mathrm{CCl}_{4} ?\) (b) Seawater contains 0.0079 \(\mathrm{g}\) of Sr \(^{2+}\) per kilogram of water. What is the concentration of \(\mathrm{Sr}^{2+}\) in ppm?

Step-by-Step Solution

Answer

The mass percentage of iodine in the solution is 6.64%, and the concentration of Sr²⁺ ions in seawater is 7.9 ppm.

Step 1: (Part a: Calculate the mass of iodine)

First, we need to calculate the mass of iodine in grams given the number of moles (0.035 moles). The molecular weight of iodine is approximately 254 g/mol. So, to find the mass of iodine in grams, we use the formula: mass (g) = number of moles x molecular weight mass (g) = 0.035 mol x 254 g/mol mass (g) = 8.89 g So, the mass of iodine in the solution is 8.89 g.

Step 2: (Part a: Calculate the mass percentage of iodine)

Now that we know the mass of iodine, we can find the mass percentage of iodine in the solution using the formula: mass percentage = (mass of solute / mass of solution) x 100 The solution is made up of iodine (8.89 g) and CCl4 (125 g). Therefore, the mass of the solution is: mass of solution = 8.89 g (iodine) + 125 g (CCl4) = 133.89 g Now we can calculate the mass percentage: mass percentage = (8.89 g / 133.89 g) x 100 = 6.64% So, the mass percentage of iodine in the solution is 6.64%.

Step 3: (Part b: Convert grams per kilogram to ppm)

In this part, we have 0.0079 g of Sr²⁺ ions per kilogram of seawater. To convert it to ppm (parts per million), we can use the following conversion: 1 g/kg = 1,000 ppm So, we can multiply the concentration in g/kg by 1,000 to find the concentration in ppm: concentration of Sr²⁺ (ppm) = 0.0079 g/kg x 1,000 = 7.9 ppm Thus, the concentration of Sr²⁺ ions in seawater is 7.9 ppm.

Key Concepts

Molecular Weight

Understanding molecular weight is crucial in chemistry, especially when dealing with processes like calculating the mass of a substance. Molecular weight refers to the mass of a given molecule based on the sum of the atomic masses of all the atoms it contains. This is typically expressed in grams per mole (g/mol).
For example, iodine (\(\mathrm{I_2}\)) has a molecular weight of approximately 254 g/mol, meaning one mole of iodine molecules weighs 254 grams.

To find the mass of a substance using its molecular weight:

• Determine the number of moles of the substance you have.
• Multiply the number of moles by the molecular weight of the substance.

This calculation lets you convert from the number of moles to the mass in grams, a crucial step in determining mass percentages in solutions.

Conversion to ppm

Parts per million (ppm) is a concentration metric, expressing the number of parts of a substance per million parts of a whole. It is especially used for very dilute solutions, such as impurities in water.
Think of ppm as a way to scale down the concentration, similar to percentages but a thousand times smaller since 1 percent is equal to 10,000 ppm.

To convert a concentration from grams per kilogram (g/kg) to ppm:

• Understand that 1 g/kg is equivalent to 1,000 ppm.
• Multiply the concentration in g/kg by 1,000 to find the value in ppm.

For instance, a concentration of 0.0079 g of \(\mathrm{Sr^{2+}}\) per kilogram of seawater is equivalent to 7.9 ppm.
This conversion helps in quantifying elements or compounds within a solution, widely used in environmental sciences.

Mole Calculations

Mole calculations are a fundamental part of stoichiometry in chemistry, relating masses, numbers of particles, and volumes of gases. The mole is defined as the amount of substance that contains as many entities (like atoms or molecules) as there are atoms in 12 grams of carbon-12.
When you need to calculate the mass of a substance in a chemical solution:

• First, determine the number of moles of the substance using its given quantity or concentration.
• Use the substance's molecular weight to convert the moles to grams, multiplying them together.

These steps are foundational for further calculations such as computing mass percentages and concentrations, essential in academic and practical laboratory settings.