The question asks for the number of moles of oxygen in one litre of air containing 21% oxygen by volume, in standard conditions. To solve this problem, we need to use the concept of mole fraction.

1. Understanding Mole Fraction:
Mole fraction is a way to express the concentration of a component in a mixture. It is defined as the ratio of the number of moles of a component to the total number of moles in the mixture.

2. Calculation of Mole Fraction of Oxygen:
Given that the air contains 21% oxygen by volume, we can calculate the mole fraction of oxygen as follows:

Mole fraction of oxygen = (Volume of oxygen/Total volume of air) x (Molar volume of air/Molar volume of oxygen)

Since we are given the volume percentage, we can assume a total volume of 100 L for simplicity. Therefore, the volume of oxygen is 21 L.

Molar volume of air is equal to 22.4 L/mol (at standard conditions), and the molar volume of oxygen is also 22.4 L/mol (since oxygen is a diatomic gas).

Mole fraction of oxygen = (21 L/100 L) x (22.4 L/mol / 22.4 L/mol) = 0.21

3. Calculation of Moles of Oxygen:
Now that we have the mole fraction of oxygen, we can calculate the number of moles of oxygen in one litre of air. Since the total volume of air is 1 L, the number of moles of oxygen is equal to the mole fraction of oxygen multiplied by the total number of moles in one litre of air.

Number of moles of oxygen = Mole fraction of oxygen x Total moles in 1 L of air

The total moles in 1 L of air can be calculated using the ideal gas equation:
PV = nRT

At standard conditions (STP), the pressure (P) is 1 atm, the volume (V) is 1 L, the gas constant (R) is 0.0821 L.atm/mol.K, and the temperature (T) is 273 K.

Therefore, n = PV/RT = (1 atm)(1 L) / (0.0821 L.atm/mol.K)(273 K) = 0.0448 mol

Number of moles of oxygen = 0.21 x 0.0448 mol = 0.0093 mol

Therefore, the correct answer is option 'D', which is 0.0093 mol.