Step 1: Understanding the Question:
Match the given mass of various substances to the number of molecules (or formula units) in terms of Avogadro's number ($N_A$). Step 2: Key Formula or Approach:
Number of molecules = $\frac{\text{Mass}}{\text{Molar Mass}} \times N_A$
Note: 1 mg = $10^{-3}$ g. Step 3: Detailed Explanation:
(P) 3.6 mg of $H_2O$ (Molar mass = 18 g/mol):
Number of molecules = $\frac{3.6 \times 10^{-3}}{18} \times N_A = 0.2 \times 10^{-3} N_A = 2 \times 10^{-4} N_A$. (Matches II)
(Q) 1.8 mg of Carbon (Molar mass = 12 g/mol):
Number of atoms = $\frac{1.8 \times 10^{-3}}{12} \times N_A = 0.15 \times 10^{-3} N_A = 1.5 \times 10^{-4} N_A$. (Matches IV)
(R) 4.9 mg of $H_2SO_4$ (Molar mass = 98 g/mol):
Number of molecules = $\frac{4.9 \times 10^{-3}}{98} \times N_A = 0.05 \times 10^{-3} N_A = 0.5 \times 10^{-4} N_A$. (Matches I)
(S) 5.85 mg of $NaCl$ (Molar mass = 58.5 g/mol):
Number of formula units = $\frac{5.85 \times 10^{-3}}{58.5} \times N_A = 0.1 \times 10^{-3} N_A = 1 \times 10^{-4} N_A$. (Matches III) Step 4: Final Answer:
The correct match is P-II, Q-IV, R-I, S-III, which corresponds to option (2).
