Question

Arrange the following in decreasing order of number of molecules contained in:
(A) 16 g of \( O_2 \) 
(B) 16 g of \( CO_2 \) 
(C) 16 g of \( CO \) 
(D) 16 g of \( H_2 \) 

• A. D>B>C>A
• B. D>A>B>C
• C. A>D>C>B
• D. D>A>C>B

Hint:

To determine the number of molecules in a given mass of a substance, use the formula \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \) and multiply by Avogadro's number \( N_A \). The substance with the smallest molar mass will have the largest number of molecules.

Answer 1

The Correct Option is D

To rank the compounds by the number of molecules present in 16 g of each, we first calculate the moles of each compound using the formula:

\[\text{Number of moles} = \frac{\text{Given mass (g)}}{\text{Molar mass (g/mol)}}\]

Compound	Molar Mass (g/mol)	Number of Moles
\(O_2\)	32	\( \frac{16}{32} = 0.5 \)
\(CO_2\)	44	\( \frac{16}{44} \approx 0.364 \)
\(CO\)	28	\( \frac{16}{28} \approx 0.571 \)
\(H_2\)	2	\( \frac{16}{2} = 8 \)

Next, we convert moles to the number of molecules by multiplying with Avogadro's number, \(6.022 \times 10^{23}\).

• \(O_2\): \(0.5 \times 6.022 \times 10^{23} \approx 3.011 \times 10^{23}\) molecules
• \(CO_2\): \(0.364 \times 6.022 \times 10^{23} \approx 2.192 \times 10^{23}\) molecules
• \(CO\): \(0.571 \times 6.022 \times 10^{23} \approx 3.439 \times 10^{23}\) molecules
• \(H_2\): \(8 \times 6.022 \times 10^{23} \approx 48.176 \times 10^{23}\) molecules

Arranging these in decreasing order of molecular count yields: \(H_2 > O_2 > CO > CO_2\).
This corresponds to the order:

D>A>C>B