SAQ : At STP, n number of N2 molecules occupies a volume of V litre. What volume n/2 number of CO2 molecules will occupy at STP?

Question

At STP, n number of N₂ molecules occupies a volume of V litre. What volume n/2 number of CO₂ molecules will occupy at STP? [Ans. V/2 L]

Answer

At STP (Standard Temperature and Pressure), the temperature is 273 K and the pressure is 1 atm. One mole of any gas at STP occupies 22.4 liters of volume.

Therefore, n number of N₂ molecules will occupy a volume of V litres at STP.

n(N₂) = N/N_A, where N is the number of N₂ molecules and N_A is Avogadro’s number

The number of moles of N₂ will be equal to the number of moles of CO₂, assuming both gases are at STP. We can calculate the number of CO2 molecules using the following equation:

n(CO₂) = (n/2)(N_A)

The volume occupied by n/2 number of CO₂ molecules can be calculated using the volume of one mole of CO2 at STP:

V(CO₂) = n(CO₂) × 22.4 L/mol

Substituting the values we get:

n(N₂) = N/NA n(CO2) = (n/2)(NA)

V(CO2) = n(CO2) × 22.4 L/mol

We can simplify n(CO2) as follows:

n(CO2) = (n/2)(NA)

n(CO2) = n(N2)/2

Substituting this in the equation for V(CO2), we get:

V(CO2) = (n(N2)/2) x 22.4 L/mol V(CO2) = (n(N2) x 22.4 L/mol)/2 V(CO2) = V/2