Answer:
The volume occupied by 2.36 x 10^24 molecules of tetrahydrofuran (C4H8O) at 20 °C is approximately 87.97 liters
Step-by-step explanation:
To calculate the volume occupied by a given number of molecules of a substance at a certain temperature and using the substance's density, you can use the ideal gas law and the molar mass of the compound. However, it's important to note that tetrahydrofuran (C4H8O) is not a gas at room temperature, so the ideal gas law doesn't apply directly. We can use the density to determine the volume.
Here's the step-by-step calculation:
1. Calculate the molar mass of tetrahydrofuran (C4H8O):
- Carbon (C) has a molar mass of approximately 12.01 g/mol.
- Hydrogen (H) has a molar mass of approximately 1.01 g/mol.
- Oxygen (O) has a molar mass of approximately 16.00 g/mol.
Molar mass of C4H8O = (4 * 12.01 g/mol) + (8 * 1.01 g/mol) + (1 * 16.00 g/mol) = 48.04 g/mol
2. Convert the density to g/L. Since the density is given in g/mL, you can use the fact that 1 mL = 1 cm³ = 0.001 L:
- Density of tetrahydrofuran = 0.881 g/mL = 0.881 g/0.001 L = 881 g/L
3. Calculate the number of moles of tetrahydrofuran using the density and molar mass. The formula to calculate moles (n) is:
n = density / molar mass
n = 881 g/L / 48.04 g/mol = 18.34 mol/L
4. Calculate the number of molecules in 1 mole (Avogadro's number):
1 mole = 6.022 x 10^23 molecules
5. Calculate the number of molecules in the given number of moles:
(2.36 x 10^24 molecules) / (6.022 x 10^23 molecules/mol) = 3.92 moles
6. Finally, calculate the volume occupied by 2.36 x 10^24 molecules at 20 °C using the number of moles and molar volume at standard temperature and pressure (STP), which is 22.4 L/mol:
Volume = (3.92 moles) * (22.4 L/mol) = 87.97 L