Question

Which of the following contains maximum number of molecules

(a) 1g of CO2
(b) 1g of N2
(c) 1g of H2
(d) 1g of CH4

Answer 1

The maximum number of molecules is present in 1g of H2. (Option C).

Step-by-step explanation:

To determine the number of molecules, we can use the formula:

`\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]`

The molar mass of a substance is the mass of one mole of that substance. For
`\(H_2\), \(N_2\), \(O_2\), and \(CH_4\`), the molar masses are approximately 2 g/mol, 28 g/mol, 32 g/mol, and 16 g/mol, respectively.

Now, calculating the number of moles for each option:

(a)
`\( \frac{1\, \text{g}}{44\, \text{g/mol}} = 0.0227\, \text{mol} \) (CO2)`

(b)
`\( \frac{1\, \text{g}}{28\, \text{g/mol}} = 0.0357\, \text{mol} \) (N2)`

(c)
`\( \frac{1\, \text{g}}{2\, \text{g/mol}} = 0.5\, \text{mol} \) (H2)`

(d)
`\( \frac{1\, \text{g}}{16\, \text{g/mol}} = 0.0625\, \text{mol} \) (CH4)`

Now, using Avogadro's number
`(6.022 * 10^(23) \, \text{mol}^(-1))`, we can find the number of molecules:

(a)
`\(0.0227 * 6.022 * 10^(23) = 1.37 * 10^(22)\)` molecules (CO2)

(b)
`\(0.0357 * 6.022 * 10^(23) = 2.15 * 10^(22)\)` molecules (N2)

(c)
`\(0.5 * 6.022 * 10^(23) = 3.01 * 10^(23)\)` molecules (H2)

(d)
`\(0.0625 * 6.022 * 10^(23) = 3.76 * 10^(22)\)` molecules (CH4)

Therefore, 1g of H2 contains the maximum number of molecules among the given options.