Question

Which of the following contain the same number of atoms? (Given : Molar mass in g mol\(^{-1}\) of H, He, O and S are \(1,4,16\) and \(32\) respectively)}

• [A.] \(2\,\text{g}\) of \(O_2\) gas
• [B.] \(4\,\text{g}\) of \(SO_2\) gas
• [C.] \(1400\,\text{mL}\) of \(O_2\) at STP
• [D.] \(0.05\,\text{L}\) of He at STP
• [E.] \(0.0625\,\text{mol}\) of \(H_2\) gas

Choose the correct answer from the options given below:

• A. A and B only
• B. B and C only
• C. C and D only
• D. A, C and E only

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We need to calculate the total number of atoms (in moles) for each given sample and find which ones are identical.
Step 2: Key Formula or Approach:
Number of atoms = (Number of moles of molecule) \(\times\) (Atomicity).
Number of moles (\(n\)) = mass/molar mass OR Volume at STP / 22.4 L.
Step 3: Detailed Explanation:
A. 2 g \(\text{O}_2\): \(n = 2/32 = 1/16 \text{ mol}\). Atoms = \(2 \times 1/16 = 1/8 = 0.125 \text{ mol}\).
B. 4 g \(\text{SO}_2\): \(n = 4/64 = 1/16 \text{ mol}\). Atoms = \(3 \times 1/16 = 3/16 = 0.1875 \text{ mol}\).
C. 1400 mL \(\text{O}_2\): \(n = 1.4/22.4 = 1/16 \text{ mol}\). Atoms = \(2 \times 1/16 = 1/8 = 0.125 \text{ mol}\).
D. 0.05 L He: \(n = 0.05/22.4\) mol. Atoms = \(1 \times 0.05/22.4 \approx 0.002 \text{ mol}\).
E. 0.0625 mol \(\text{H}_2\): Atoms = \(2 \times 0.0625 = 0.125 \text{ mol} = 1/8 \text{ mol}\).
Samples A, C, and E all have 0.125 moles of atoms.
Step 4: Final Answer:
Samples A, C, and E contain the same number of atoms.