Problem 36 - Chemistry: The Central Science

Question

(a) What is the mass percentage of iodine \(\left(\mathrm{I}_{2}\right)\) in a solution containing \(0.035 \mathrm{~mol} \mathrm{I}_{2}\) in \(115 \mathrm{~g}\) of \(\mathrm{CCl}_{4} ?\) (b) Seawater contains \(0.0079 \mathrm{~g} \mathrm{Sr}^{2+}\) per kilogram of water. What is the concentration of \(\mathrm{Sr}^{2+}\) measured in \(\mathrm{ppm} ?\)

Step-by-Step Solution

Answer

The mass percentage of iodine (I₂) in CCl₄ is approximately 7.37%, and the concentration of Sr²⁺ in seawater is approximately 7.9 ppm.

Step 1: Part (a) - Calculate Total Mass of I₂

Given the number of moles of I₂, which is 0.035 mol and the molar mass of I₂ is approximately 253.81 g/mol, we can calculate the mass: $$ \text{Total mass of I₂} = (\text{number of moles}) \times (\text{molar mass}) $$ $$ \text{Total mass of I₂} = (0.035 \ \text{mol}) \times (253.81 \ \text{g/mol}) $$

Step 2: Part (a) - Calculate Mass Percentage of I₂ in CCl₄

Now that we have the total mass of I₂, we can calculate the mass percentage of I₂ in CCl₄: $$ \text{Mass Percentage} = \frac{\text{Mass of I₂}}{\text{Total Mass of Solution}} \times 100\% $$ We already have the mass of I₂, and the mass of the CCl₄ solution is given as 115 g. So, the total mass of the solution is: $$ \text{Total Mass of Solution} = \text{Mass of I₂} + \text{Mass of CCl₄} $$ Now we can plug in the values and calculate the mass percentage: $$ \text{Mass Percentage} = \frac{\text{Mass of I₂}}{\text{Total Mass of Solution}} \times 100\% $$

Step 3: Part (b) - Calculate Sr²⁺ Concentration in Seawater

We are given that seawater contains 0.0079 g of Sr²⁺ per kilogram (1000 g) of water. To find the concentration in ppm (parts per million), we can use the formula: $$ \text{Concentration (ppm)} = \frac{\text{Mass of Sr²⁺ (g)}}{\text{Mass of Water (g)}} \times 10^6 $$ Plug in the given values: $$ \text{Concentration (ppm)} = \frac{0.0079 \ \text{g}}{1000 \ \text{g}} \times 10^6 $$ Calculate the Sr²⁺ concentration in seawater.

Key Concepts

Concentration in ppm

Understanding concentration in parts per million (ppm) is essential for quantifying very dilute substances. It measures the quantity of a substance in a million parts of a solution. For example, to find the ppm concentration of a solute in a solution, you would use the formula:
\[\text{ppm} = \frac{\text{Mass of Solute (g)}}{\text{Mass of Solution (g)}} \times 10^6\]
This is a simple ratio scaled up to reflect the number of parts per million. When dealing with substances like trace elements in water, this measurement becomes incredibly useful because the amounts are typically minute. Using this approach allows for an easier understanding and comparison of low concentration levels.

Molar Mass

The concept of molar mass is a cornerstone in chemistry, representing the mass of one mole of a substance. It's measured in grams per mole (g/mol) and directly relates to the compound's molecular weight — the sum of the atomic masses of all atoms in a molecule. In practical terms, the molar mass lets you convert between grams and moles for a substance. The formula:
\[\text{Molar Mass} = \frac{\text{Total Mass of Substance (g)}}{\text{Number of Moles (mol)}}\]
facilitates these conversions. It's essential for accurately measuring the amount of substance needed for reactions, illustrating stoichiometric relationships in chemical equations, and calculating solution concentrations.

Solution Concentration

Solution concentration expresses the amount of solute dissolved in a solvent. It can be communicated in several ways, including molarity, molality, and the aforementioned ppm. The mass percentage is one such measure, describing the mass of the solute compared to the total mass of the solution in which it resides.
\[\text{Mass Percentage} = \frac{\text{Mass of Solute}}{\text{Total Mass of Solution}} \times 100\%\]
By understanding how to calculate it, you can determine how concentrated a solution is, which is crucial in fields like medicine, biology, and environmental science.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It's rooted in the balanced chemical equation, from which you can deduce the proportions of chemicals needed or produced. Stoichiometry relies heavily on the mole concept and molar mass, as these allow chemists to calculate quantities involved in chemical reactions. Whether you're gauging how much product a certain amount of reactants will yield or determining the amount needed to completely react with a given quantity of another substance, stoichiometric calculations form the mathematical foundation of these predictions. Mastery of stoichiometry is essential for practical lab work, making it an indispensable tool for chemists and students alike.