Problem 62 - Chemistry The Molecular Nature of Matter

Question

What is the total number of \(\mathrm{N}, \mathrm{H},\) and \(\mathrm{O}\) atoms \(\mathrm{in}\) \(0.356 \mathrm{~mol}\) of ammonium nitrate, \(\mathrm{NH}_{4} \mathrm{NO}_{3}\), an important fertilizer?

Step-by-Step Solution

Answer

There are approximately \(4.28 \times 10^{23}\) N atoms, \(8.55 \times 10^{23}\) H atoms, and \(6.42 \times 10^{23}\) O atoms in 0.356 mol of NH_4NO_3.

Step 1: Determine the number of atoms per molecule

Identify the number of nitrogen (N), hydrogen (H), and oxygen (O) atoms in one molecule of ammonium nitrate, (NH_4NO_3). There are 2 nitrogen atoms, 4 hydrogen atoms, and 3 oxygen atoms in each molecule.

Step 2: Calculate the total number of moles of atoms

Since there are 2 mol of N, 4 mol of H, and 3 mol of O per mole of NH_4NO_3, multiply the number of moles of NH_4NO_3 by the number of atoms per mole of compound. For N: \((0.356 \, \mathrm{mol} \, NH_4NO_3) \times (2 \, \mathrm{mol} \, N / 1 \, \mathrm{mol} \, NH_4NO_3)\). For H: \((0.356 \, \mathrm{mol} \, NH_4NO_3) \times (4 \, \mathrm{mol} \, H / 1 \, \mathrm{mol} \, NH_4NO_3)\). For O: \((0.356 \, \mathrm{mol} \, NH_4NO_3) \times (3 \, \mathrm{mol} \, O / 1 \, \mathrm{mol} \, NH_4NO_3)\).

Step 3: Convert moles of atoms to number of atoms

Use Avogadro's number (approximately \(6.022 \times 10^{23}\) atoms per mole) to convert moles of N, H, and O to the number of atoms. For N: \((0.356 \, \mathrm{mol} \, N) \times (6.022 \times 10^{23} \, \mathrm{atoms} / \mathrm{mol})\). For H: \((0.356 \, \mathrm{mol} \, H) \times (6.022 \times 10^{23} \, \mathrm{atoms} / \mathrm{mol})\). For O: \((0.356 \, \mathrm{mol} \, O) \times (6.022 \times 10^{23} \, \mathrm{atoms} / \mathrm{mol})\).

Step 4: Perform the calculations

Complete the calculations to determine the total number of atoms. For N: \(0.356 \times 2 \times 6.022 \times 10^{23}\). For H: \(0.356 \times 4 \times 6.022 \times 10^{23}\). For O: \(0.356 \times 3 \times 6.022 \times 10^{23}\). These calculations will give the total number of each type of atom.

Key Concepts

Understanding the Mole Concept

The mole concept is a fundamental cornerstone in chemistry that relates the microscopic world of atoms and molecules to the macroscopic quantities we measure in the laboratory. Essentially, a mole represents a specific number of particles, just like a dozen represents 12 of any objects. By definition, one mole is the amount of a substance that contains exactly 6.022 x 10^23 elementary entities (this could be atoms, molecules, ions, etc.), a value known as Avogadro's number.

When dealing with chemical substances, the mole allows chemists to count particles by weighing them. For instance, one mole of carbon-12 atoms has a mass of 12 grams and contains 6.022 x 10^23 atoms of carbon. This relationship is crucial for chemical calculations since it links mass, which is easily measurable, to the number of particles, which are not.

Navigating Chemical Calculations

Chemical calculations are essential tools for chemists to predict the outcomes of chemical reactions, determine the purity of substances, and formulate products. These calculations are based on the balanced chemical equation, the mole concept, and Avogadro's number, allowing for precise work with quantities in moles or grams.

For complex compounds like ammonium nitrate (NH4NO3), understanding the formula and the composition of one mole of the compound is the first step. Each mole of NH4NO3 consists of specific moles of nitrogen (N), hydrogen (H), and oxygen (O) atoms. Multiplying the moles of the compound by the ratio of the number of atoms per mole of the compound gives us the total moles of each element. Then, by applying Avogadro's number, we convert moles to actual numbers of atoms, moving from the concept to tangible amounts.

Appreciating Avogadro's Number

Avogadro's number (\(6.022 \times 10^{23}\)) is named after the Italian scientist Amedeo Avogadro, and it provides a bridge between the atom and the macro world. It is the number of particles found in one mole of a substance, providing a scale to measure atoms, much like the dozen scale for eggs. Avogadro's number enables chemists to work out the exact number of atoms or molecules they have in a given mass of a substance, which is why it is such a vital component in chemical calculations.

When multiplied with the number of moles, Avogadro's number transforms an abstract mole quantity into a tangible count of atoms, molecules, or ions. This powerful number is also central to many research areas in chemistry, including stoichiometry, as it relates the macroscopic mass of a substance to its microscopic composition.