Question

In which case is the number of molecules of water maximum ?

• A. 18 mL of water
• B. 0·00224 L of water vapours at 1 atm and 273 K
• C. 0·18 g of water
• D. 10^–3 mol of water

Answer 1

The Correct Option is A

To determine in which case the number of water molecules is maximum, we need to calculate the number of moles of water present in each option, because the number of molecules is directly proportional to the number of moles.

1. Understanding the relevant concept: The number of molecules can be calculated using Avogadro's number, which is \(6.022 \times 10^{23}\) molecules per mole. Hence, more moles mean more molecules.
2. Option 1: 18 mL of water
   • The density of water is \(1 \, \text{g/mL}\). Therefore, 18 mL of water has a mass of 18 g.
   • Molecular weight of water (H₂O) = 18 g/mol.
   • Number of moles of water = \(\frac{\text{mass}}{\text{molar mass}} = \frac{18}{18} = 1 \, \text{mol}\).
   • Number of molecules = \(1 \, \text{mol} \times 6.022 \times 10^{23}\, \text{molecules/mol} = 6.022 \times 10^{23} \text{ molecules}\).
3. Option 2: 0.00224 L of water vapours at 1 atm and 273 K
   • At STP (Standard Temperature and Pressure), 1 mole of any gas occupies 22.4 L.
   • Moles of water vapor = \(\frac{0.00224}{22.4} \, \text{mol} = 0.0001 \, \text{mol}\).
   • Number of molecules = \(0.0001 \, \text{mol} \times 6.022 \times 10^{23}\, \text{molecules/mol} = 6.022 \times 10^{19} \text{ molecules}\).
4. Option 3: 0.18 g of water
   • Molecular weight of water = 18 g/mol.
   • Number of moles = \(\frac{0.18}{18} = 0.01 \, \text{mol}\).
   • Number of molecules = \(0.01 \, \text{mol} \times 6.022 \times 10^{23}\, \text{molecules/mol} = 6.022 \times 10^{21} \text{ molecules}\).
5. Option 4: \(10^{-3}\) mol of water
   • Number of molecules = \(10^{-3} \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} = 6.022 \times 10^{20} \text{ molecules}\).
6. Conclusion: The option with the maximum number of molecules is determined by the calculation results. Option 1 gives the largest number of molecules.

Hence, the number of molecules of water is maximum in 18 mL of water.