Question

6. A sample of nitrogen gas weighs 130 g. Write the chemical formula for nitrogen gas. Howmany molecules of elemental nitrogen is this? How many atoms of nitrogen are in this sample?

Answer 1

The chemical formula for nitrogen gas is N₂. A 130 g sample of nitrogen gas contains 4.64 moles, which equals 2.79 × 10²µ molecules of N₂, and hence 5.58 × 10²µ atoms of nitrogen.

Step-by-step explanation:

The chemical formula for nitrogen gas is N₂. To determine the number of moles of nitrogen gas in a 130 g sample, we use the molar mass of molecular nitrogen, which is 28.01 g/mol. By dividing the mass of the sample by the molar mass, we get:

Number of moles = mass (130 g) / molar mass (28.01 g/mol) = 4.64 moles.

To find the number of molecules of elemental nitrogen in this sample, we multiply the number of moles by Avogadro's number, which is 6.022 × 10²³ molecules/mol:

Number of molecules = 4.64 moles × 6.022 × 10²³ molecules/mol = 2.79 × 10²µ molecules.

Since each molecule of nitrogen gas consists of two nitrogen atoms (N₂), the number of atoms of nitrogen in this sample is:

Number of atoms = 2 × (number of molecules) = 2 × 2.79 × 10²µ = 5.58 × 10²µ atoms.

Answer 2

Chemical formula for nitrogen gas is N₂.

To find the number of molecules in the given sample, we have to convert the mass of the sample to moles by using the molecular mass of elemental nitrogen (N₂).

`130gN_2\cdot(1molN_2)/(28gN_2)=4.64molN_2`

Now, we have to use Avogadro's number (6.022x10^23) that indicates the number of molecules in one mole of substance:

`4.64molN_2\cdot(6.022*10^(23)molecules)/(1molN_2)=2.79*10^(24)molecules`

It means that there are 2.79x10^24 molecules of elemental nitrogen.

To find the number of atoms we just have to multiply the number of molecules by 2, which is the number of atoms of nitrogen per molecule of elemental nitrogen:

`2.79*10^(24)molecules\cdot(2atoms)/(1molecule)=5.59*10^(24)atoms`

There are 5.59x10^24 atoms of nitrogen in the sample.