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/NA, where N is the number of N2 molecules and NA 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)(NA)
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