Question

Number of molecules and moles in 2.8375 litre of O₂ at STP.

Answer 1

Step 1: Calculate the Number of Moles of O₂

At STP, 1 mole of a gas occupies 22.7 liters. The given volume of O₂ is 2.8375 liters. The number of moles is calculated as:

\[ n_{\text{O}_2} = \frac{\text{Volume of O}_2}{22.7} \]

Substitute the given values:

\[ n_{\text{O}_2} = \frac{2.8375}{22.7} = 0.125 \, \text{moles} \]

Step 2: Calculate the Number of Molecules of O₂

The number of molecules of O₂ is given by:

\[ \text{Molecules of O}_2 = n_{\text{O}_2} \cdot N_A \]

Where \( N_A = 6.022 \times 10^{23} \, \text{mol}^{-1} \) (Avogadro’s number).

Substitute the values:

\[ \text{Molecules of O}_2 = 0.125 \cdot 6.022 \times 10^{23} = 7.527 \times 10^{22} \, \text{molecules} \]

Final Answer:

• The number of moles of O₂ is 0.125 mol.
• The number of molecules of O₂ is 7.527 × 10²².

Answer 2

At STP, one mole of any gas occupies 22.4 liters. For the given volume of oxygen gas (2.8375 liters):

Step 1: Calculate the Number of Moles of O₂

The number of moles is calculated as:

\[ \text{Number of moles of O}_2 = \frac{2.8375 \, \text{L}}{22.4 \, \text{L/mol}} = 0.125 \, \text{mol} \]

Step 2: Calculate the Number of Molecules of O₂

Using Avogadro’s number (\( 6.022 \times 10^{23} \, \text{molecules/mol} \)):

\[ \text{Number of molecules of O}_2 = 0.125 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} \]

\[ \text{Number of molecules of O}_2 = 7.527 \times 10^{22} \, \text{molecules} \]

Final Answer:

• Number of moles of O₂: 0.125 mol
• Number of molecules of O₂: \( 7.527 \times 10^{22} \, \text{molecules} \)