Question

Two balloons are filled, one with pure He gas and the other by air, respectively. If the pressure and temperature of these balloons are same then the number of molecules per unit volume is:
A. More in the He filled balloon
B. Same in both balloons
C. More in air filled balloons
D. In the ratio of 1:4

Answer 1

Hint: Use the ideal gas equation or Avogadro’s principle to find the answer. According to Avogadro's principle, the volume and moles of the gas are directly proportional if the temperature and pressure are constant.
\[V=kn\], where k is the proportionality constant, n is the number of moles and V is the volume.

Complete step by step answer:
According to Avogadro's law, equal volume of all gases contains equal numbers of molecules at the same temperature and pressure. So, both balloons have the same number of molecules per unit volume.
Ideal gas equation can be written as,
\[pV=nRT\]
Where, n is the number of moles of a gas, p is the pressure of the gas, V is the volume of the gas, R is the universal gas constant and T is the temperature. So, at constant temperature and pressure, both balloons have equal numbers of molecules per unit volume. Therefore, the correct option is B.

Additional information:
Ideal gas is an imaginary gas which contains non-interacting particles and obeys gas law at any conditions. The collisions of ideal gas particles are purely elastic. Hence there is no attraction or repulsion. Volume of these particles are negligible. Ideal gases won’t condensate into liquids at lower temperatures. At low temperature and high pressure, real gases behave like ideal gases and it is known as perfect gases.
Avogadro’s law can be written as,
\[V=kn\], where k is the proportionality constant, n is the number of moles and V is the volume.
For an ideal gas, the volume and moles of the gas are directly proportional if the temperature and pressure are constant.

Note: If either temperature or pressure or both are varying, the number of molecules will not be the same for gases with equal volume. It does not depend upon the properties of the gas. They will behave like the same gases, even if it is helium gas and air, because they are treated in the same conditions i.e. constant pressure, constant volume and constant temperature. So all other options.