Question

How many molecules are present in $22400\ \mathrm{cm^3}$ of a gas at STP?

• A. $22.4 \times 10^{20}$
• B. $6.022 \times 10^{23}$
• C. $6.022 \times 10^{20}$
• D. $22.4 \times 10^{23}$

Hint:

Keep unit equivalences in mind: $22.4\ \text{liters} = 22.4\ \mathrm{dm^3} = 22400\ \mathrm{cm^3} = 22400\ \mathrm{mL}$. Any gas with this volume at STP represents exactly one mole.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We need to find the total number of gas molecules present in a given volume of $22400\ \mathrm{cm^3}$ measured at Standard Temperature and Pressure (STP).

Step 2: Key Formula or Approach:
According to Avogadro's law, $1\ \text{mole}$ of any ideal gas at STP occupies a molar volume of $22.4\ \mathrm{L}$, which is equivalent to $22400\ \mathrm{cm^3}$ ($1\ \mathrm{L} = 1000\ \mathrm{cm^3}$). One mole of any substance contains exactly Avogadro's number ($N_A$) of particles: $$N_A = 6.022 \times 10^{23}\ \text{molecules}$$

Step 3: Detailed Explanation:
Convert the given volume into moles: $$\text{Number of moles } (n) = \frac{\text{Given Volume at STP}}{\text{Molar Volume}} = \frac{22400\ \mathrm{cm^3}}{22400\ \mathrm{cm^3\ mol^{-1}}} = 1\ \text{mol}$$ Since the quantity is precisely $1\ \text{mole}$, the total number of molecules present is equal to Avogadro's constant: $$\text{Number of molecules} = 1 \times 6.022 \times 10^{23} = 6.022 \times 10^{23}$$

Step 4: Final Answer:
The total number of molecules is $6.022 \times 10^{23}$, matching option (B).