Question

4.095 into 10 raised to the power 24 nitrogen atoms are filled in an enclosed gas cylinder of 2 litre the number of moles of nitrogen gas in the cylinder is

(a) 14.7
(b) 6.8
(c) 3.4
(d) 2.9​

Answer 1

The number of moles of nitrogen gas in a cylinder with 4.095 × 10¹¹ atoms is found by dividing by Avogadro's number and then by 2, resulting in 6.8 moles of nitrogen gas (option b).

Step-by-step explanation:

To find the number of moles of nitrogen gas in a cylinder when 4.095 × 10²⁴ nitrogen atoms are given, we need to use Avogadro's number, which is 6.022 × 10²³ atoms/mol. To find the number of moles, we divide the number of nitrogen atoms by Avogadro's number since one mole of nitrogen gas, N₂, contains two atoms of nitrogen.

The calculation is as follows:

1. Divide 4.095 × 10²⁴ by 6.022 × 1023 to get the number of moles of nitrogen atoms.
2. Since N₂ has two nitrogen atoms, divide the result from step 1 by 2 to get the number of moles of nitrogen gas.

By performing the calculation we get: (4.095 × 10⁴ atoms) / (6.022 × 10²³ atoms/mol)

= 6.8 mol

Therefore, the number of moles of nitrogen gas in the cylinder is 6.8 moles, which corresponds to option (b).