Question

Number of atoms in \(4.25 \mathrm{~g}\) of \(\mathrm{NH}_{3}\) is approximately: (a) \(6 \times 10^{23}\) (b) \(15 \times 10^{23}\) (c) \(1.5 \times 10^{23}\) (d) \(2.5 \times 10^{23}\)

Short answer

(a) \(6 \times 10^{23}\)

Step-by-step solution

Calculate Molar Mass of NH₃

To find the molar mass of NH₃, sum up the atomic masses of nitrogen (N) and hydrogen (H). The atomic mass of nitrogen is approximately 14 g/mol and hydrogen is approximately 1 g/mol. Thus, the molar mass of NH₃ is:\[14 + 3 imes 1 = 17 \text{ g/mol}\]

Calculate Moles of NH₃

We need to calculate how many moles are in 4.25 g of NH₃ by using the formula:\[\text{moles} = \frac{\text{mass}}{\text{molar mass}}\]Plug in the known values:\[\text{moles} = \frac{4.25 \text{ g}}{17 \text{ g/mol}} \approx 0.25 \text{ moles}\]

Calculate Number of Molecules

To find the number of molecules, multiply the number of moles by Avogadro's number, which is \(6.022 \times 10^{23}\) molecules per mole:\[\text{number of molecules} = 0.25 \times 6.022 \times 10^{23} \approx 1.5055 \times 10^{23}\]

Calculate Number of Atoms

Since each NH₃ molecule consists of 4 atoms (1 nitrogen and 3 hydrogen atoms), multiply the number of molecules by 4:\[\text{number of atoms} = 1.5055 \times 10^{23} \times 4 \approx 6.022 \times 10^{23}\]

Choose the Closest Option

From the calculations in the previous steps, the total number of atoms in 4.25 g of NH₃ is approximately \(6.022 \times 10^{23}\). This is closest to option (a).

Key concepts

Molar Mass

The concept of molar mass is fundamental in chemistry when dealing with chemical reactions and conversions. Molar mass, often expressed in grams per mole (g/mol), is the mass of one mole of a given substance. It is calculated by summing up the atomic masses of all atoms in a molecule.
For example, to determine the molar mass of ammonia (\(\text{{NH}}_3\)), you need to consider both nitrogen and hydrogen. The atomic mass of nitrogen (N) is approximately 14 g/mol, and hydrogen (H) is about 1 g/mol. Therefore, the molar mass of NH₃ is:

• 14 g/mol for nitrogen
• 3 times 1 g/mol for each hydrogen atom

All these summed up together gives you 17 g/mol for NH₃. This value is crucial for converting mass to moles, which we will discuss next.

Moles Calculation

Moles provide a bridge between the atomic world and the macroscopic world we interact with. Calculating moles involves determining how many sets of Avogadro's number of molecules you have, based on the mass and molar mass.
To calculate moles, use the formula: \ \[ \text{{moles}} = \frac{{\text{{mass}}}}{{\text{{molar mass}}}} \] Here, you're essentially playing with ratios. For the provided exercise, you have 4.25 grams of NH₃. By dividing this mass by the molar mass of NH₃ (which is 17 g/mol), you get approximately 0.25 moles.

• This conversion is crucial because it allows you to translate the tangible mass of a chemical to a countable number of molecules.

Moles calculation helps you find out how much of a substance is involved in a reaction or contained within a given mass.

Atomic Structure

Understanding atomic structure allows us to comprehend the composition of molecules and how chemical reactions occur. Atoms are composed of a nucleus with protons and neutrons, surrounded by electrons in various energy levels.
In the case of ammonia, NH₃ is made up of nitrogen and hydrogen atoms. Each NH₃ molecule contains:

• 1 nitrogen atom
• 3 hydrogen atoms

Hence, while calculating the total number of atoms, remember that each NH₃ molecule consists of 4 atoms. Knowing the atomic structure lets you determine the number of individual atoms in a given number of molecules. By calculating direct multiplication (1 molecule = 4 atoms in NH₃), we can have a comprehensive understanding of a molecule's architecture. This insight is pivotal for reactions where molecule and atom counts dictate the direction and outcome of chemical processes.