Question

How many \(\mathrm{NH}_{3}\) molecules are in \(0.50 \mathrm{~mol}\) of \(\mathrm{NH}_{3}\) ? How many nitrogen atoms and hydrogen atoms are there?

Short answer

There are \(3.01 \times 10^{23}\) NH3 molecules, \(3.01 \times 10^{23}\) nitrogen atoms and \(9.066 \times 10^{23}\) hydrogen atoms.

Step-by-step solution

Calculate the number of \(\mathrm{NH}_{3}\) molecules

First, calculate the number of \(\mathrm{NH}_{3}\) ammonia molecules. We know that one mole of anything contains \(6.022 \times 10^{23}\) of that thing (Avogadro's number). Hence, to find out number of \(\mathrm{NH}_{3}\) molecules in 0.5 mol we simply multiply the number of moles by Avogadro's number. Hence, number of \(\mathrm{NH}_{3}\) molecules = number of moles of \(\mathrm{NH}_{3}\) * Avogadro's number = \(0.5 \times (6.022 \times 10^{23})\)

Calculate the number of nitrogen atoms

Now, to determine the number of nitrogen atoms, observe the composition of an \(\mathrm{NH}_{3}\) molecule - it contains one nitrogen atom. This indicates the number of nitrogen atoms will be equal to the number of \(\mathrm{NH}_{3}\) molecules. Therefore, number of Nitrogen atoms = number of \(\mathrm{NH}_{3}\) molecules = \(0.5 \times (6.022 \times 10^{23})\)

Calculate the number of hydrogen atoms

Lastly, to determine the number of hydrogen atoms, one must consider that an \(\mathrm{NH}_{3}\) molecule contains three hydrogen atoms. Hence, the number of hydrogen atoms will be thrice the number of \(\mathrm{NH}_{3}\) molecules. Therefore, number of Hydrogen atoms = 3 * number of \(\mathrm{NH}_{3}\) molecules = \(3 \times 0.5 \times (6.022 \times 10^{23})\)

Key concepts

Avogadro's Number

Understanding Avogadro's number is crucial for studying chemistry, especially when dealing with mole to molecule conversions. Some students might wonder what this huge number, exactly 6.022 x 10²³, represents. This value, known as Avogadro's number, is defined as the number of atoms, ions, or molecules contained in one mole of a substance. It essentially functions as a bridge between the microscopic world of atoms and molecules and the macroscopic world we can measure in the laboratory.

For instance, when the exercise asks how many molecules are there in 0.50 mol of ammonia (NH₃), the process involves simply multiplying Avogadro's number by the amount of moles: 0.50 mol times 6.022 x 10²³, resulting in approximately 3.011 x 10²³ molecules of ammonia. This fundamental constant helps chemists and students translate measurements in the lab to the reality of atoms and molecules.

Chemical Composition Calculations

Chemical composition calculations allow us to understand the make-up and proportions of different elements within a compound. It becomes particularly useful when you want to know the individual atoms that make up a certain number of molecules of a substance, just like we see in our ammonia example from the exercise.

Breaking Down a Molecule

Let's think about ammonia, NH₃. Its chemical formula tells us that each molecule consists of one nitrogen (N) atom and three hydrogen (H) atoms. By knowing the total number of molecules, we can calculate the number of nitrogen and hydrogen atoms present. With Avogadro's number giving us the corresponding amount per mole, we can use simple multiplication to get our answer. Here, each 0.50 mol of NH₃ has the same number of nitrogen atoms, but three times as many hydrogen atoms due to their ratio within the chemical formula.

Stoichiometry

Stoichiometry is the method used to calculate the relative quantities of reactants and products in chemical reactions. In practice, it is used for more than chemical reactions; it is also used for the kind of mole to molecule calculations we see in the given exercise.

In stoichiometry, the coefficients in a balanced chemical equation provide the ratio of moles of each substance involved. When translating moles to molecules, the same ratios help to determine the number of atoms or molecules.

The Mole Ratio

If a certain number of moles of a compound is given, like in our problem statement (0.50 mol of NH₃), stoichiometry assists in understanding the quantitative relationships within the compound (1 nitrogen atom to 3 hydrogen atoms in ammonia). It is this ratio that guides us to establish that if we have 0.50 mol of NH₃, we have 0.50 mol of nitrogen atoms (since each molecule of NH₃ has one nitrogen atom) and 1.50 mol of hydrogen atoms (each NH₃ molecule has three hydrogen atoms).