To calculate the number of chlorine atoms in 5.0 g of chloral hydrate (C₂H₃Cl₃O₂), we need to go through the following steps:
Step 1: Calculate the molar mass of chloral hydrate
The chemical formula of chloral hydrate is C₂H₃Cl₃O₂. To calculate the molar mass, we sum 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 moles of chloral hydrate in 5.0 g
Using the formula: moles of chloral hydrate=mass of chloral hydratemolar mass of chloral hydrate\text{moles of chloral hydrate} = \frac{\text{mass of chloral hydrate}}{\text{molar mass of chloral hydrate}} moles of chloral hydrate=5.0 g165.394 g/mol≈0.0302 mol\text{moles of chloral hydrate} = \frac{5.0 \, \text{g}}{165.394 \, \text{g/mol}} \approx 0.0302 \, \text{mol}
Step 3: Calculate the number of chlorine atoms
Since each molecule of chloral hydrate contains 3 chlorine (Cl) atoms, the total number of chlorine atoms in 0.0302 mol of chloral hydrate can be calculated by multiplying the moles of chloral hydrate by 3 chlorine atoms per molecule and Avogadro’s number (6.022 × 10²³ atoms/mol): number of chlorine atoms=0.0302 mol×3×(6.022×1023 atoms/mol)\text{number of chlorine atoms} = 0.0302 \, \text{mol} \times 3 \times (6.022 \times 10^{23} \, \text{atoms/mol}) number of chlorine atoms≈5.45×1022 atoms\text{number of chlorine atoms} \approx 5.45 \times 10^{22} \, \text{atoms}
Final Answer:
The number of chlorine atoms in 5.0 g of chloral hydrate is approximately 5.45 × 10²² atoms.