Question

Calculate the number of molecules present in 2.24 \(\text{dm}^3\) of carbon dioxide at STP ?

• A. \(2.011\times 10^{22}\)
• B. \(3.011\times 10^{22}\)
• C. \(6.022\times 10^{22}\)
• D. \(0.1\times 10^{23}\)

Hint:

At STP one mole of any gas occupies 22.4 dm\(^3\), so find the moles first and multiply by Avogadro's number.

Answer 1

The Correct Option is C

Step 1: Use the molar volume
22.4 dm$^3$ of gas at STP holds $6.022\times10^{23}$ molecules, so the number of molecules is proportional to volume.

Step 2: Scale by the volume ratio
The given volume is $\dfrac{2.24}{22.4}=\dfrac{1}{10}$ of a molar volume.
\[ N = \frac{1}{10}\times 6.022\times10^{23} = 6.022\times10^{22} \]
So the number is one tenth of Avogadro's number, which is option (C).

Final Answer:
The sample is one tenth of a molar volume, so it has $6.022\times10^{22}$ molecules, option (C). \[ \boxed{6.022\times10^{22}} \]