Question

The temperature of a gas filled in a vessel filled in a vessel is $ 273K $ and the pressure is $ 1.60 \times {10^{ - 3}}N{m^{ - 2}} $ Determine.
(A) Number of molecules in unit volume of the vessel
(B) Average distance between the molecules

Answer 1

Hint :In the above question, we are provided with a gas filled in a vessel with certain temperature and pressure and we have to find the number of particles at unit volume of the vessel. Then we can use the ideal gas equation which is $ PV = nRT $

Complete Step By Step Answer:
Firstly, writing the given quantities
Temperature of the gas filled is $ T = 273K $
Pressure of the gas is $ P = 1.60 \times {10^{ - 3}}N{m^{ - 2}} $
We have to find the number of molecules in the unit volume of the vessel. So, $ V = 1L $
Now using ideal gas equation
 $ PV = nRT $ where P is the pressure of the gas, V is the volume of the gas, n is the number of particles of the gas, R is the universal gas constant whose value is $ 8.314kJ/mol.K $ and T is the temperature of the gas.
Substituting all the values to find the n.
 $ 1.60 \times {10^{ - 3}} \times 1 = n \times 8.314 \times 273 $
 $ n = 0.071 \times {10^{ - 3}}mol $
Finding the number of particles in terms of atoms. As we all know $ 1 $ mole of substance contains $ 6.02 \times {10^{23}} $ moles of atoms. So, multiplying the $ 6.02 \times {10^{23}} $ to the calculated particles,
Number of the particles is $ n = 0.071 \times {10^{ - 3}} \times 6.02 \times {10^{23}} = 0.427 \times {10^{20}}atoms $
The proper information is not given to solve the next part which is to find the average distance between the molecules.

Note :
Here we have used ideal gas law, had there been mentioned in the question that the gas is real we would then have not been able to use the ideal gas equation. Also, while putting the values, we have to be careful that all the temperature values are to be used in Kelvin and R is a gas constant and it has different values in different units.