To calculate the number of molecules of a gas, including oxygen gas, occupying a given volume at a specific temperature and pressure, you can use the ideal gas law equation:
PV = nRT
Where: P = Pressure of the gas (in atmospheres, atm) V = Volume of the gas (in liters, L) n = Number of moles of the gas R = Ideal gas constant (0.0821 L·atm/(mol·K)) T = Temperature (in Kelvin, K)
To solve for the number of moles (n), we rearrange the equation:
n = (PV) / (RT)
Now, let's substitute the given values into the equation and calculate the number of moles of oxygen gas:
P = 3 atm V = 224 ml = 0.224 L (converted to liters) R = 0.0821 L·atm/(mol·K) T = 273 K
n = (3 atm * 0.224 L) / (0.0821 L·atm/(mol·K) * 273 K) n ≈ 0.297 moles
Since 1 mole of a gas contains Avogadro's number (6.022 x 10^23) of molecules, we can calculate the number of molecules by multiplying the number of moles by Avogadro's number:
Number of molecules = (0.297 moles) * (6.022 x 10^23 molecules/mol) Number of molecules ≈ 1.786 x 10^23 molecules
Therefore, approximately 1.786 x 10^23 molecules of oxygen gas would occupy a volume of 224 ml at 273 K and 3 atm pressure.