Question

A sample of ammonia, \(\mathrm{NH}_{3}\), weighs \(30.0 \mathrm{~g}\). Calculate the following quantities. (a) moles of \(\mathrm{NH}_{3}\) (c) number of \(\mathrm{N}\) atoms (b) number of \(\mathrm{NH}_{3}\) (d) moles of \(\mathrm{H}\) atoms molecules

Short answer

The solution to the exercise is: (a) 1.76 moles of NH3, (b) \(1.06 \times 10^{24}\) molecules of NH3, (c) \(1.06 \times 10^{24}\) nitrogen atoms in the sample, and (d) 5.28 moles of hydrogen atoms.

Step-by-step solution

Calculate the moles of ammonia (NH3)

The moles of a substance can be calculated from its mass and molecular weight. The molecular weight of NH3 is 17.03 g/mol, so \( moles = \frac{mass}{molecular~ weight} = \frac{30.0 g}{17.03 g/mol} = 1.76 \, moles. \)

Calculate the number of NH3 molecules

The number of molecules can be found by multiplying the number of moles by Avogadro's number (\(6.022 x 10^{23}\)). So \( number ~of~ molecules = moles \times Avogadro's ~number = 1.76 \, moles \times 6.022 \times 10^{23} = 1.06 \times 10^{24} \, molecules. \)

Calculate the number of Nitrogen (N) atoms

1 molecule of NH3 contains 1 atom of nitrogen. Therefore, the number of nitrogen atoms is equal to the number of NH3 molecules. So, \( number ~of~ N ~atoms = 1.06 \times 10^{24} \, atoms. \)

Calculate the moles of Hydrogen (H) atoms

1 molecule of NH3 contains 3 atoms of hydrogen. Therefore, the moles of hydrogen atoms is 3 times the moles of NH3, which is \(3 \times 1.76 \, moles = 5.28 \, moles.\)

Key concepts

Moles Calculation

Understanding moles calculation is fundamental in chemistry, as it links the mass of a substance with the number of particles, such as atoms or molecules, it contains. A mole is defined as a unit of measure that quantifies the amount of a substance. One mole is equal to Avogadro's number \(6.022 \times 10^{23}\) of entities, which can be atoms, molecules, ions, or other particles.

To calculate the number of moles from a given mass, the following formula is used: \[ \text{moles} = \frac{\text{mass}}{\text{molecular weight}} \]. For example, with a sample of ammonia (NH3) that weighs 30.0 g, and knowing ammonia's molecular weight is 17.03 g/mol, the moles of ammonia are calculated as \( 1.76 \text{ moles} \). This step is crucial because it serves as a bridge to finding out the total number of molecules and atoms in the sample.

Avogadro's Number

Avogadro's number, a fundamental constant in chemistry, is the key to unlocking the connection between moles and particle count. It is defined as \(6.022 \times 10^{23}\) entities per mole and is essential in converting moles to a number of particles and vice versa.

Once the number of moles is known, as in the ammonia example where we found \(1.76 \text{ moles}\), we can calculate the actual number of NH3 molecules. Multiply the moles of NH3 by Avogadro's number to arrive at \(1.06 \times 10^{24}\) molecules. This concept is not limited to whole substances; it applies to the number of specific atoms within a molecule as well. For instance, since each ammonia molecule has one nitrogen atom, the sample contains the same \(1.06 \times 10^{24}\) nitrogen atoms.

Molecular Weight

Molecular weight is another cornerstone of stoichiometry, representing the combined mass of all the atoms in a molecule. It's usually expressed in atomic mass units (amu) per molecule or grams per mole (g/mol) for larger quantities. Calculating the molecular weight involves summing the atomic weights of each atom in the molecule.

For NH3, with nitrogen (N) having an atomic weight of approximately 14.01 amu and hydrogen (H) about 1.008 amu, the molecular weight is calculated by adding one nitrogen atom to three hydrogen atoms \(1 \times 14.01 + 3 \times 1.008 = 17.03 \text{amu}\). Knowing the molecular weight allows us to transition from the mass of a compound to moles, which is a fundamental stepping stone in stoichiometric calculations.