Problem 137 - Introductory Chemistry Atoms First

Question

If you have \(200.0 \mathrm{~g}\) of dinitrogen pentoxide, how many atoms of nitrogen do you have? How many atoms of oxygen do you have?

Step-by-Step Solution

Answer

In 200g of dinitrogen pentoxide (N2O5), there are approximately \(2.23 \times 10^{24}\) atoms of nitrogen and \(5.57 \times 10^{24}\) atoms of oxygen.

Step 1: Calculate the number of moles of dinitrogen pentoxide (N2O5)

The first step is to calculate the number of moles of N2O5 in 200g by using the formula: moles = mass (g) / molar mass (g/mol) The molar mass of N2O5 = (2 * molar mass of N) + (5 * molar mass of O) = (2 * 14.007) + (5 * 15.999) = 108.01 g/mol. Now we can find the moles of N2O5: moles of N2O5 = 200g / 108.01 g/mol ≈ 1.85 moles

Step 2: Use stoichiometry to find the moles of nitrogen and oxygen atoms

We know that 1 mole of N2O5 contains 2 moles of N atoms and 5 moles of O atoms. So, from the moles of N2O5 calculated in step 1, we can find the moles of nitrogen and oxygen atoms using stoichiometry: moles of N atoms = (2 moles of N / 1 mole of N2O5) * 1.85 moles of N2O5 ≈ 3.70 moles of N moles of O atoms = (5 moles of O / 1 mole of N2O5) * 1.85 moles of N2O5 ≈ 9.25 moles of O

Step 3: Convert moles of nitrogen and oxygen atoms to the number of atoms using Avogadro's number

Now, we can convert the moles of N and O atoms to the number of atoms using Avogadro's number (6.022 x 10^23 atoms/mol): Number of N atoms = 3.70 moles * 6.022 x 10^23 atoms/mol ≈ 2.23 x 10^24 N atoms Number of O atoms = 9.25 moles * 6.022 x 10^23 atoms/mol ≈ 5.57 x 10^24 O atoms In conclusion, there are approximately \(2.23 \times 10^{24}\) atoms of nitrogen and \(5.57 \times 10^{24}\) atoms of oxygen in 200g of dinitrogen pentoxide (N2O5).

Key Concepts

Molar Mass Calculation

Understanding molar mass calculation is crucial for anyone looking to delve into the world of chemistry. Simply put, the molar mass of a substance is the mass of one mole of that substance. It is typically expressed in grams per mole (g/mol) and can be considered as the 'gram formula mass' when dealing with ionic compounds.

Let's break it down with an example. In the exercise, we calculate the molar mass of dinitrogen pentoxide (N2O5). To do this, we sum the masses of each atom present in the compound, multiplied by their respective quantities. With nitrogen (N) having an atomic mass of approximately 14.007 g/mol and oxygen (O) having a mass of about 15.999 g/mol, the molar mass of N2O5 can be calculated as follows:

• (2 atoms of N) * (14.007 g/mol for N) = 28.014 g/mol for N
• (5 atoms of O) * (15.999 g/mol for O) = 79.995 g/mol for O

The sum, 28.014 g/mol for N plus 79.995 g/mol for O, gives us the molar mass of N2O5, which is 108.01 g/mol. By understanding this step, you can calculate the molar mass of any compound.

Avogadro's Number

Getting to grips with Avogadro's number is a bit like unlocking a secret door to the molecular world. Often symbolized as 6.022 x 10^23, Avogadro's number represents the quantity of particles found in one mole of a substance. These particles could be atoms, molecules, ions, or electrons, depending on the context.

Let's place this into the context of our exercise. Once the number of moles of nitrogen and oxygen atoms in our N2O5 are calculated, we can use Avogadro's number to convert these moles into actual atoms--which is pretty mind-blowing if you think about it! This constant allows us to take what we know at the macroscopic level (like grams of a compound) and translate that into microscopic insights, giving us the number of atoms or molecules involved. It encompasses the bridge between the observable world and the atomic or molecular scale.

Moles to Atoms Conversion

The moles to atoms conversion is a straightforward yet indispensable tool in chemistry. It relies fundamentally on understanding Avogadro's number. To convert moles to atoms, you simply multiply the number of moles you have by Avogadro's constant, 6.022 x 10^23 atoms/mol.

In the exercise, we performed two separate conversions—first for nitrogen atoms, then for oxygen atoms. Here’s how it looks in a nutshell:

• For nitrogen: 3.70 moles of N * 6.022 x 10^23 atoms/mol = 2.23 x 10^24 atoms of N.
• For oxygen: 9.25 moles of O * 6.022 x 10^23 atoms/mol = 5.57 x 10^24 atoms of O.

By understanding this conversion process, estimating atomic quantities in large chemical samples becomes a manageable task. Whether it’s for laboratory experiments, industrial chemical processes, or even understanding the composition of a substance at the molecular level, converting moles to atoms is a fundamental skill that bridges our macro reality to the atomic world.