Question

If a sample of nitrogen gas contains 6.0 x10^24 atoms of nitrogen then about how many moles of nitrogen gas are in the sample

Answer 1

Answer: 5 moles

Explanation: According to Avogadro's law, 1 mole of every substance contains
`6.023* 10^(23)` particles.

1 mole of nitrogen gas
`N_2` contains=
`2* 6.023* 10^(23)=12.046* 10^(23)atoms` of nitrogen.

Thus if
`12.046* 10^(23)atoms` of nitrogen = 1mole

`6.0* 10^(24)atoms` of nitrogen =
`(1)/(12.046* 10^(23))* 6.0* 10^(24)=5moles`

Answer 2

A mole consists of 6.022 x 10²³ units, these units could be atoms making up an element or molecules making up a compound.

Nitrogen gas is a compound - N₂ gas and its made of N₂ gas molecules.

1 mol of N₂ is made of 6.022 x 10²³ nitrogen molecules.

The sample contains 6.0 x 10²⁴ atoms of N, however nitrogen gas is made of N₂ molecules, 2 N atoms make up one nitrogen gas molecule. Therefore the number of nitrogen molecules are half the number of N atoms in the sample

Number of nitrogen molecules - N₂ - 6.0 x 10²⁴ / 2 = 3.0 x 10²⁴ N₂ molecules

6.022 x 10²³ molecules of N₂ make up 1 mol

then 3.0 x 10²⁴ molecules of N₂ make up -( 1 / 6.022 x 10²³ ) x 3.0 x 10²⁴

number of N₂ moles - 5.0 mol

there are 5.0 moles of N₂ in the sample