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: Understanding the Concept
At STP, one mole of an ideal gas occupies 22.4 dm\(^3\). One mole contains \(6.022\times10^{23}\) molecules (Avogadro's number).
So we first convert the given volume into moles, then into molecules.

Step 2: Key Formula or Approach
Moles \(n = \dfrac{V}{22.4\ \text{dm}^3}\) and number of molecules \(N = n \times N_A\).

Step 3: Detailed Explanation
Moles of CO\(_2\):
\[ n = \frac{2.24}{22.4} = 0.1\ \text{mol} \]
Number of molecules:
\[ N = 0.1 \times 6.022\times10^{23} = 6.022\times10^{22} \]
Options (A) and (B) come from slips in the multiplication, and (D) \(0.1\times10^{23}\) equals \(1\times10^{22}\), which is not the product above. Only \(6.022\times10^{22}\) matches the calculation.

Final Answer:
2.24 dm\(^3\) of CO\(_2\) at STP is 0.1 mol, which holds \(6.022\times10^{22}\) molecules. This is option (C). \[ \boxed{6.022\times10^{22}\ \text{(C)}} \]