To calculate the mass of exactly 500 molecules of chloral hydrate, we need to follow these steps:
Step 1: Find the molar mass of chloral hydrate
The chemical formula of chloral hydrate is C₂H₃Cl₃O₂. We calculate the molar mass by summing the atomic masses of all the atoms in the formula:
- Carbon (C): 12.01 g/mol
- Hydrogen (H): 1.008 g/mol
- Chlorine (Cl): 35.45 g/mol
- Oxygen (O): 16.00 g/mol
Molar mass of chloral hydrate=(2×12.01)+(3×1.008)+(3×35.45)+(2×16.00)\text{Molar mass of chloral hydrate} = (2 \times 12.01) + (3 \times 1.008) + (3 \times 35.45) + (2 \times 16.00) Molar mass of chloral hydrate=24.02+3.024+106.35+32.00=165.394 g/mol\text{Molar mass of chloral hydrate} = 24.02 + 3.024 + 106.35 + 32.00 = 165.394 \, \text{g/mol}
Step 2: Calculate the number of moles in 500 molecules
To convert the number of molecules into moles, we use Avogadro’s number (6.022 × 10²³ molecules/mol): moles of chloral hydrate=number of moleculesAvogadro’s number\text{moles of chloral hydrate} = \frac{\text{number of molecules}}{\text{Avogadro’s number}} moles of chloral hydrate=5006.022×1023≈8.30×10−22 mol\text{moles of chloral hydrate} = \frac{500}{6.022 \times 10^{23}} \approx 8.30 \times 10^{-22} \, \text{mol}
Step 3: Calculate the mass of 500 molecules
Now, we can calculate the mass by multiplying the number of moles by the molar mass: mass of 500 molecules=moles of chloral hydrate×molar mass\text{mass of 500 molecules} = \text{moles of chloral hydrate} \times \text{molar mass} mass of 500 molecules=(8.30×10−22 mol)×(165.394 g/mol)≈1.37×10−19 g\text{mass of 500 molecules} = (8.30 \times 10^{-22} \, \text{mol}) \times (165.394 \, \text{g/mol}) \approx 1.37 \times 10^{-19} \, \text{g}
Final Answer:
The mass of exactly 500 molecules of chloral hydrate is approximately 1.37 × 10⁻¹⁹ g.