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

Concept: Number of atoms: \[ \text{atoms} = (\text{moles}) \times (\text{atoms per molecule}) \times N_A \] At STP: \[ 1\ \text{mol gas} = 22.4\ \text{L} \] Step 1: {Option A} Molar mass of \(O_2 = 32\) \[ \text{moles}=\frac{2}{32}=\frac{1}{16} \] Atoms: \[ 2\times\frac{1}{16}=\frac{1}{8}\ \text{mol atoms} \] Step 2: {Option B} Molar mass \(SO_2=64\) \[ \text{moles}=\frac{4}{64}=\frac{1}{16} \] Atoms per molecule = 3 \[ \text{atoms}=\frac{3}{16}\ \text{mol atoms} \] Not equal to A. Step 3: {Option C} \[ V=1400\,\text{mL}=1.4\,\text{L} \] \[ \text{moles}=\frac{1.4}{22.4}=\frac{1}{16} \] Atoms: \[ 2\times\frac{1}{16}=\frac{1}{8}\ \text{mol atoms} \] Same as A. Step 4: {Option D} \[ 0.05\,\text{L} \] \[ \text{moles}=\frac{0.05}{22.4}\approx0.00223 \] Atoms \(=0.00223\) mol atoms (not equal). Step 5: {Option E} \[ 0.0625\,\text{mol }H_2 \] Atoms: \[ 2\times0.0625=0.125=\frac18 \] Thus A, C and E have the same number of atoms.