Question

One mole of a gas refers to:
  (A) the number of molecules in one litre of gas
  (B) the number of molecules in one gram of gas
  (C) the number of molecules contained in 12 grams of $^{12}C$ isotope
  (D) the number of molecules in 22.4 litres of a gas at S.T.P

Answer 1

Hint: We can define mole as the amount of substance. For converting between grams and moles, we could use the molar mass of the substance and for converting moles and volume of a gas we could use the concept of number of moles present in 22.4 litre of volume of a gas.


Complete step by step solution:
- Let's start with the idea of Avogadro number and concept of moles. Avogadro’s number can be defined as a proportion that relates molar mass on an atomic scale to physical mass on a human scale. It is defined as the number of elementary particles such as molecules, atoms, compounds, etc. per mole of a substance.
- Or in other words, the number of units in one mole of any substance is called Avogadro’s number or Avogadro’s constant. Its value is given as $6.023\times {{10}^{23}}$.
- A major property of Avogadro’s number is that the substance’s molecular weight is equal to the mass of one mole of that substance. Also, the gram atomic mass of an element is the mass of one mole of that element and the gram molecular mass of a compound refers to the mass of a single mole of the compound.
- The concept of moles can also be defined in terms of volume. That is at standard temperature and pressure (STP) conditions, one mole of any gas( $6.023\times {{10}^{23}}$particles) occupies a volume of 22.4 litres. Let's calculate the number of moles in given options from above defined concepts of moles.
From the above descriptions, we can see that option(D) matches exactly with the concept of one mole. That is one mole of a gas is the number of molecules in 22.4 litres of a gas at S.T.P.

Therefore, the answer is option (D).


Note: There will be a confusion on calculating the number of moles in volume. If we are given the volume of gas in litres or $d{{m}^{3}}$, then to calculate number of moles present we should divide the given volume by 22.4 and if we are given number of moles then to calculate the volume multiply the number of moles by 22.4.