which one of the following pairs of gases contains the same no. of molecules:

To determine which pair of gases contain the same number of molecules, we need to compare the number of moles of each gas. The number of moles can be calculated using the ideal gas law equation:

n = PV / RT

where:
n = number of moles
P = pressure (in atm)
V = volume (in liters)
R = gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)

By rearranging the equation, we can calculate the number of molecules (N) using Avogadro's number (6.022 x 10^23 molecules/mole):

N = n * (6.022 x 10^23)

Let's consider the pairs of gases and calculate the number of molecules for each pair:

1. Oxygen (O2) and Hydrogen (H2):
Assuming the pressure, volume, and temperature are the same for both gases, we can compare the number of moles:
n(O2) = PV / RT
n(H2) = PV / RT
Since the pressure, volume, and temperature for both gases are the same,
n(O2) = n(H2)
Therefore, the pair Oxygen (O2) and Hydrogen (H2) contains the same number of molecules.

2. Oxygen (O2) and Carbon Dioxide (CO2):
Similarly, assuming the pressure, volume, and temperature are the same for both gases, we compare the number of moles:
n(O2) = PV / RT
n(CO2) = PV / RT
Since the pressure, volume, and temperature for both gases are the same,
n(O2) = n(CO2)
Therefore, the pair Oxygen (O2) and Carbon Dioxide (CO2) contains the same number of molecules.

3. Nitrogen (N2) and Carbon Monoxide (CO):
Again, assuming the pressure, volume, and temperature are the same for both gases, we compare the number of moles:
n(N2) = PV / RT
n(CO) = PV / RT
Since the pressure, volume, and temperature for both gases are the same,
n(N2) = n(CO)
Therefore, the pair Nitrogen (N2) and Carbon Monoxide (CO) contains the same number of molecules.

So, the pairs Oxygen (O2) and Hydrogen (H2), Oxygen (O2) and Carbon Dioxide (CO2), Nitrogen (N2) and Carbon Monoxide (CO) all contain the same number of molecules.