Step 1: Understanding the Concept:
We must calculate the total number of atoms in a given mass of several substances. This requires converting the mass to moles of the molecule/formula unit, and then multiplying by the atom count per molecule. Step 2: Key Formula or Approach:
1. Moles $n = \frac{\text{Given Mass}}{\text{Molar Mass}}$.
2. Number of molecules = $n \times N_A$.
3. Total atoms = Number of molecules $\times$ (atoms per molecule). Step 3: Detailed Explanation:
A. 1.8 mg water ($H_2O$):
Molar mass of $H_2O = 18\text{ g/mol}$.
Moles of $H_2O = \frac{1.8 \times 10^{-3}\text{ g}}{18} = 10^{-4}\text{ mol}$.
One molecule of $H_2O$ has 3 atoms (2 Hydrogen, 1 Oxygen).
Total atoms = $3 \times 10^{-4} \times N_A$. (Matches III)
B. 9.8 mg sulphuric acid ($H_2SO_4$):
Molar mass of $H_2SO_4 = 2(1) + 32 + 4(16) = 98\text{ g/mol}$.
Moles of $H_2SO_4 = \frac{9.8 \times 10^{-3}\text{ g}}{98} = 10^{-4}\text{ mol}$.
One molecule of $H_2SO_4$ has 7 atoms (2 Hydrogen, 1 Sulfur, 4 Oxygen).
Total atoms = $7 \times 10^{-4} \times N_A$. (Matches IV)
C. 1.8 mg carbon ($C$):
Molar mass of C = $12\text{ g/mol}$.
Moles of C = $\frac{1.8 \times 10^{-3}\text{ g}}{12} = 0.15 \times 10^{-3}\text{ mol} = 1.5 \times 10^{-4}\text{ mol}$.
Carbon is an elemental atom.
Total atoms = $1.5 \times 10^{-4} \times N_A$. (Matches II)
D. 5.85 mg salt (NaCl):
Molar mass of NaCl = $23 + 35.5 = 58.5\text{ g/mol}$.
Moles of NaCl = $\frac{5.85 \times 10^{-3}\text{ g}}{58.5} = 10^{-4}\text{ mol}$.
One formula unit of NaCl has 2 ions/atoms (1 Na, 1 Cl).
Total atoms = $2 \times 10^{-4} \times N_A$. (Matches I)
Matching summary: A-III, B-IV, C-II, D-I. Step 4: Final Answer:
The correct matching is A-III, B-IV, C-II, D-I.
