Question

Identify the pair of gases which have same number of molecules at S.T.P.?

• A. \(11\ \text{g of }CO_2\) and \(14\ \text{g of }N_2\)
• B. \(16\ \text{g of }O_3\) and \(16\ \text{g of }CH_4\)
• C. \(5\ \text{g of }H_2\) and \(40\ \text{g of }CH_4\)
• D. \(28\ \text{g of }N_2\) and \(22\ \text{g of }CO_2\)

Hint:

To compare number of molecules, compare number of moles using \(n=\frac{w}{M}\).

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
According to Avogadro’s Law, equal number of moles of any gas will contain the same number of molecules at STP. Therefore, the task is to find which pair of gases has the same number of moles.
Step 2: Detailed Explanation:

Formula for moles: \(n = \text{Given Mass} / \text{Molar Mass}\).

Evaluate Option (A):
Moles of \(CO_2 = 11 / 44 = 0.25\) moles.
Moles of \(N_2 = 14 / 28 = 0.5\) moles. (Different)

Evaluate Option (B):
Moles of \(O_3 = 16 / 48 = 0.33\) moles.
Moles of \(CH_4 = 16 / 16 = 1.0\) mole. (Different)

Evaluate Option (C):
Moles of \(H_2 = 5 / 2 = 2.5\) moles.
Moles of \(CH_4 = 40 / 16 = 2.5\) moles. (Same)

Evaluate Option (D):
Moles of \(N_2 = 28 / 28 = 1.0\) mole.
Moles of \(CO_2 = 22 / 44 = 0.5\) moles. (Different)

Since Option C results in the exact same number of moles (2.5) for both gases, they will contain an identical number of molecules (\(2.5 \times 6.022 \times 10^{23}\)).

Step 3: Final Answer:
The pair (5 g of \(H_2\) and 40 g of \(CH_4\)) contains the same number of molecules at STP.