Question

A method used by the U.S. Environmental Protection Agency (EPA) for determining the concentration of ozone in air is to pass the air sample through a "bubbler" containing sodium iodide, which removes the ozone according to the following equation: \(\mathrm{O}_{3}(g)+2 \mathrm{NaI}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow\) $$ \mathrm{O}_{2}(g)+\mathrm{I}_{2}(s)+2 \mathrm{NaOH}(a q) $$ (a) How many moles of sodium iodide are needed to remove \(5.95 \times 10^{-6} \mathrm{~mol}\) of \(\mathrm{O}_{3} ?(\mathbf{b})\) How many grams of sodium iodide are needed to remove \(1.3 \mathrm{mg}\) of \(\mathrm{O}_{3}\) ?

Short answer

(a) 11.9 × 10⁻⁶ mol of sodium iodide are needed to remove 5.95 × 10⁻⁶ mol of ozone. (b) 0.00813 g of sodium iodide are needed to remove 1.3 mg of ozone.

Step-by-step solution

Part (a): Find the moles of sodium iodide necessary to remove the given moles of ozone

The balanced chemical equation is: \[ O_3(g) + 2 NaI (aq) + H_2O(l) \rightarrow O_2(g) + I_2(s) + 2 NaOH(aq) \] From the equation, we can see that: 1 mol of O₃ reacts with 2 mol of NaI. Now, we will determine the number of moles of sodium iodide needed to remove 5.95 × 10⁻⁶ mol of O₃ using mole ratio calculations. Let x be the moles of NaI: \( \frac{5.95 \times 10^{-6} mol~ O_3}{1 mol~ O_3} = \frac{x~ moles~ NaI}{2 mol~ NaI} \) Now, solve for x: \( x = 2 \times (5.95 \times 10^{-6} mol~ O_3) = 11.9 \times 10^{-6} mol~ NaI \) So, 11.9 × 10⁻⁶ mol of sodium iodide are needed to remove 5.95 × 10⁻⁶ mol of ozone.

Part (b): Find the mass of sodium iodide required to remove 1.3 mg of ozone

First, we need to convert the mass of ozone to moles, knowing that the molar mass of O₃ is 48 g/mol. \( \text{moles of }O_3 = \frac{1.3 mg}{1000} \times \frac{1 mol}{48 g} = 2.708 \times 10^{-5} mol \) Now, we can determine the number of moles of sodium iodide needed to remove 2.708 × 10⁻⁵ mol of O₃ using mole ratio calculations: \( \frac{2.708 \times 10^{-5} mol~ O_3}{1 mol~ O_3} = \frac{x~ moles~ NaI}{2 mol~ NaI} \) Now, solve for x: \( x = 2 \times (2.708 \times 10^{-5} mol~ O_3) = 5.416 \times 10^{-5} mol~ NaI \) Now convert the moles of sodium iodide to mass by multiplying by the molar mass of NaI (149.89 g/mol): \( mass~ NaI = 5.416 \times 10^{-5} mol~ NaI \times \frac{149.89 g~ NaI}{1 mol~ NaI} = 0.00813 g \) So, 0.00813 g of sodium iodide are needed to remove 1.3 mg of ozone.

Key concepts

Chemical Reactions

A chemical reaction is a process where substances, known as reactants, transform into new substances, known as products. In the chemical reaction used by the U.S. Environmental Protection Agency to measure ozone concentration, ozone (\( \mathrm{O}_3 \)), sodium iodide (\( \mathrm{NaI} \)), and water (\( \mathrm{H}_2\mathrm{O} \)) react to form oxygen (\( \mathrm{O}_2 \)), iodine (\( \mathrm{I}_2 \)), and sodium hydroxide (\( \mathrm{NaOH} \)).

In chemical equations, the reactants are on the left side and the products on the right, separated by an arrow indicating the direction of the reaction. The number of atoms for each element must be equal on both sides to satisfy the law of conservation of mass.

• The balanced equation for the reaction is: \( \mathrm{O}_3(g) + 2 \mathrm{NaI}(aq) + \mathrm{H}_2\mathrm{O}(l) \rightarrow \mathrm{O}_2(g) + \mathrm{I}_2(s) + 2 \mathrm{NaOH}(aq) \)
• This equation tells us that for every mole of ozone, two moles of sodium iodide are needed to complete the reaction.

Understanding chemical reactions is essential in explaining how substances interact and change during chemical processes.

Mole Calculations

Mole calculations are a fundamental concept in chemistry, providing a bridge between the atomic world and the measurable world. A mole is defined as \( 6.022 \times 10^{23} \) particles of a substance, a number known as Avogadro's number.

In the context of the EPA's method for determining ozone concentration, mole calculations are essential:

• We begin by identifying that one mole of ozone reacts with two moles of sodium iodide.
• If given \( 5.95 \times 10^{-6} \) moles of ozone, you can calculate the moles of sodium iodide required using the mole ratio from the balanced equation: \( 2 \times 5.95 \times 10^{-6} = 11.9 \times 10^{-6} \) moles of sodium iodide.

Mole calculations also involve converting mass to moles using the molar mass of substances. For example, in the exercise, \( 1.3 \) mg of ozone is first converted to grams, then moles using its molar mass (48 g/mol), resulting in \( 2.708 \times 10^{-5} \) moles of ozone. This is subsequently used to find the necessary moles of sodium iodide, helping us calculate the exact amount needed for the reaction.

Environmental Science

Environmental science is the study of how natural and human-made phenomena affect the environment. Measuring the concentration of pollutants like ozone is crucial for understanding and mitigating environmental impacts.

Ozone, while beneficial in the upper atmosphere where it blocks harmful ultraviolet rays, can be harmful at ground level as it contributes to smog and respiratory problems.

• The EPA uses methods, including chemical analysis, to monitor ozone levels in the air, ensuring that air quality standards are met.
• The reaction involving sodium iodide for ozone measurement is an essential tool, allowing scientists to quantify and manage ozone concentrations effectively.

Integrating chemical reactions and mole calculations into environmental science enables better measurement and control of pollutants, fostering a healthier environment and society.