1. Convert Units
* Mass to moles: We need to convert the mass of helium (1.00 kg) to moles. The molar mass of helium (He) is 4.003 g/mol.
* 1.00 kg = 1000 g
* moles of He = (1000 g) / (4.003 g/mol) = 249.87 mol
* Temperature to Kelvin: The Ideal Gas Law uses Kelvin.
* 5.00 °C + 273.15 = 278.15 K
* Pressure to atmospheres:
* 735 torr * (1 atm / 760 torr) = 0.967 atm
2. Ideal Gas Law
The Ideal Gas Law is: PV = nRT
Where:
* P = pressure (in atm)
* V = volume (in liters)
* n = number of moles
* R = Ideal Gas Constant (0.0821 L·atm/mol·K)
* T = temperature (in Kelvin)
3. Solve for Volume (V)
Rearrange the Ideal Gas Law to solve for V:
V = (nRT) / P
* V = (249.87 mol * 0.0821 L·atm/mol·K * 278.15 K) / 0.967 atm
* V ≈ 5680 liters
Therefore, 1.00 kg of helium at 5.00 °C and 735 torr occupies approximately 5680 liters.
