From the ideal gas law, calculate the volume per helium atom in a litre of helium gas kept
at room temperature and atmospheric pressure.
Additionally, calculate the length of the side of a cube with this volume.
To calculate the volume per helium atom in a liter of helium gas at room temperature and atmospheric pressure, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature in Kelvin
First, let's convert the given values:
Pressure = atmospheric pressure = 1 atm
Volume = 1 liter
Temperature = room temperature in Kelvin = 298 K
Next, we need to determine the number of moles of helium gas. Helium is a monoatomic gas, so we can assume that each helium atom is one mole of gas. Therefore, the number of moles (n) is equal to Avogadro's number (6.022 x 10^23) or simply 1 mole.
Now, we can rearrange the ideal gas law equation to solve for V:
V = (nRT) / P
Plugging in the values:
V = (1 mol * 0.0821 L·atm/mol·K * 298 K) / 1 atm
V ≈ 24.38 L·atm/mol
So, the volume per helium atom in a liter of helium gas is approximately 24.38 L/mol.
To calculate the length of the side of a cube with this volume, we need to find the cube root of the volume per helium atom:
Side length of cube = (Volume per helium atom)^(1/3)
By substituting the value we found:
Side length of cube = (24.38 L/mol)^(1/3)
Side length of cube ≈ 2.94 L^(1/3)
Thus, the length of the side of a cube with this volume is approximately 2.94 liters raised to the 1/3 power.