Question

Some of the acid in acid rain is produced by the following reaction: $$ 3 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{HNO}_{3}(a q)+\mathrm{NO}(g) $$ If a falling raindrop weighing \(0.050 \mathrm{~g}\) comes into contact with \(1.0 \mathrm{mg}\) of \(\mathrm{NO}_{2}(g)\), how many milligrams of \(\mathrm{HNO}_{3}\) can be produced?

Short answer

0.063 mg of HNO3 can be produced.

Step-by-step solution

Calculate moles of NO2

Convert the mass of NO2 from milligrams to grams, then calculate the moles of NO2 using its molar mass.

Use stoichiometry to find moles of HNO3

Use the balanced chemical equation to find the ratio of moles of HNO3 produced per mole of NO2 reacted. Then calculate the moles of HNO3 that can be produced from the moles of NO2.

Convert moles of HNO3 to mass

Use the molar mass of HNO3 to convert the moles of HNO3 into grams. Then convert the mass from grams to milligrams.

Key concepts

Stoichiometry

Stoichiometry is at the heart of chemical reactions. It’s the calculation behind how elements and compounds react with each other to form new substances. Imagine you’re following a recipe. Stoichiometry is like the recipe for a chemical reaction, detailing the exact amount of each reactant you need to end up with your desired product, just like a cooking recipe tells you how much of each ingredient to use to get your dish right.

To solve stoichiometry problems, such as calculating how much nitric acid, or \( \mathrm{HNO}_3 \) can be formed from nitrogen dioxide, or \( \mathrm{NO}_2 \) in acid rain, you need to look at the coefficients in the balanced chemical equation. They tell you the ratio of the moles of each reactant needed and the moles of each product formed. You'll use these ratios to relate the moles of one substance to the moles of another. In our example, the equation indicates that three moles of \( \mathrm{NO}_2 \) yield two moles of \( \mathrm{HNO}_3 \), which is a 3:2 ratio.

Mole Concept

The mole concept is a way of expressing amounts of a chemical substance. It connects the microscopic world of atoms and molecules to the macroscopic world we can measure in the laboratory. One mole is defined as exactly 6.02214076×10²³ particles - the same number of atoms in exactly 12 grams of carbon-12.When you measure a substance in moles, you’re counting out a specific number of molecules or atoms. In our exercise about acid rain, we use the mole concept to relate the actual mass of \( \mathrm{NO}_2 \) to the number of moles, because reactions occur on a molecular level, and it's moles that react, not grams. The mass of \(1.0 \text{ mg}\) of \( \mathrm{NO}_2 \) we start with represents a certain number of moles, which we need to know to figure out how much \( \mathrm{HNO}_3 \) is produced.

Molar Mass Calculations

Molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol). It is calculated by adding up the atomic masses of all the atoms in the formula of the compound. You can find the atomic masses on the periodic table. When performing molar mass calculations, carefully sum each element’s mass according to the number of times it appears in the chemical formula.

In the context of the acid rain reaction, the molar mass of \( \mathrm{NO}_2 \) and \( \mathrm{HNO}_3 \) are crucial for converting between moles and grams. Say we're given the mass of \( \mathrm{NO}_2 \) in milligrams; to find out how many moles that is, we divide by its molar mass. Then, we can use stoichiometry to find out how many moles of \( \mathrm{HNO}_3 \) we’d get from that amount, and ultimately, we use the molar mass of \( \mathrm{HNO}_3 \) to convert those moles back to grams or milligrams.