Question

When the pressure is changed from $1\ atm$ to $0.5\ atm$, the number of molecules in $1$ mole of ammonia changes to:
(A) $75\%$ of its initial volume
(B) $50\%$ of its initial volume
(C) $25\%$ of its initial volume
(D) None

Answer 1

Hint: The number of molecules in a given element or compound depends only upon the number of moles of the element or compound, and remains unaffected by the change in conditions of pressure or volume at a constant temperature.

Complete step by step answer:
The number of molecules in $1$ mole of ammonia is equal to the Avogadro’s number, which is $6.023\times 10^{23}$ molecules. This can be explained based on Avogadro’s law, which states that the number of molecules in one mole of a substance at a constant temperature is always equal to $6.023\times 10^{23}$.
The initial pressure of ammonia is given as $1\ atm$, and the final pressure is given as $0.5\ atm$. As the pressure changes, the volume of the gas also changes. But, the number of moles in both conditions remains the same, i.e., $1$ mole.
Now, the number of molecules in a substance is given by the general formula:
$Number\; of \;molecules = Number\ of\ moles\times 6.023\times 10^{23}$
Since the number of moles of ammonia in both the conditions is $1$, the number of molecules in ammonia also remains the same as follows:
Number of molecules in $1$ mole of ammonia $= 1\times 6.023\times 10^{23} = 6.023\times 10^{23}$
Therefore, the number of molecules in $1$ mole of ammonia remains unchanged on changing the pressure from $1\ atm$ to $0.5\ atm$.

So, the correct answer is Option D .

Note: one must take note of the fact that the number of moles of ammonia has been said to remain unchanged. So, our calculation of the number of molecules will depend only on it, and not on the changing conditions as the number of molecules in a substance depends only upon the number of moles, and not the changing conditions. The number of moles does change with the changing conditions of pressure and volume, but here, since the number of moles remains the same, we need not get into the calculations of moles, and can simply state the number of molecules in ammonia from its number of moles.