Question

Consider the following gas samples: 10. g of hydrogen gas, 10. g of helium gas, 2.5 moles of nitrogen gas, 110. g of carbon dioxide gas, and 365 g of sulfur hexafluoride gas. Arrange the gas samples in order of increasing number of total atoms present.

Answer 1

Explanation:

As we know ,

One mole of a gas contains 6.023 * 10 ²³ number of atoms .

Moles is denoted by given mass divided by the molecular mass ,  

Hence ,  

n = w / m

n = moles ,  

w = given mass ,  

m = molecular mass .

( a ) From the question ,

w = 10 g ,

As we know molecular mass of Hydrogen = 2 g/mol

Using the above formula , and putting the respective values ,

Moles = n ,

n = w / m  = 10 / 2 = 5 mol

The number of atoms in one molecule of Hydrogen = 2

Hence ,

The number of atoms = 5 * 2 *  6.023 * 10 ²³ = 60.23 * 10 ²³ atoms .

( b )  From the question ,

w = 10 g

As we know molecular mass of helium gas = 4 g/mol

Using the above formula , and putting the respective values ,

Moles = n ,

n = w / m  = 10 /4 = 2.5 mol

The number of atoms in one molecule of Helium = 1

Hence ,

The number of atoms = 5 * 1 *  6.023 * 10 ²³ = 30.115 * 10 ²³ atoms .

( c ) From the question ,

moles of nitrogen gas = 2.5 mol

The number of atoms in one molecule of  nitrogen gas = 2

Hence ,

The number of atoms = 2.5 * 2 *  6.023 * 10 ²³ = 30.115 * 10 ²³ atoms .

( d ) From the question ,

w = 110 g

As we know molecular mass of carbon dioxide gas = 44 g/mol

Using the above formula , and putting the respective values ,

Moles = n ,

n = w / m  = 110 / 44 = 2.5 mol

The number of atoms in one molecule of  carbon dioxide = 3

Hence ,

The number of atoms = 2.5 * 3 *  6.023 * 10 ²³ = 45.17 * 10 ²³ atoms .

( e )

From the question ,

w = 365 g

As we know molecular mass of  sulfur hexafluoride gas = 146 g/mol

Using the above formula , and putting the respective values ,

Moles = n ,

n = w / m  =  365 / 146 = 2.5 mol .

The number of atoms in one molecule of sulfur hexafluoride gas = 7

Hence ,

The number of atoms = 2.5 * 7 *  6.023 * 10 ²³ = 105.40 * 10 ²³ atoms .

Hence ,

The order is -

sulfur hexafluoride > Hydrogen > carbon dioxide  > nitrogen gas = helium gas