Answer:
The length of an edge of each small cube is approximately 2.74 x 10^-8 meters, or 0.0274 nanometers.
Step-by-step explanation:
The length of an edge of each small cube can be calculated using the ideal gas law and the concept of molar volume.
First, we need to calculate the molar volume of the gas, which is the volume occupied by one mole of the gas at a given temperature and pressure. The molar volume can be calculated using the ideal gas law:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles of gas, R is the universal gas constant, and T is the temperature in Kelvin.
Rearranging this equation to solve for V/n, we get:
V/n = RT/P
At 27.0 degrees Celsius, which is 300.15 K, and 2.00 atmospheres of pressure, the molar volume of the gas is:
V/n = (0.0821 L*atm/(mol*K)) * (300.15 K) / (2.00 atm) = 12.3 L/mol
This means that each mole of gas occupies 12.3 liters of volume at these conditions.
Now, we can calculate the volume occupied by a single gas molecule by dividing the molar volume by Avogadro's number (6.022 x 10^23 molecules/mol):
Volume occupied by a single gas molecule = 12.3 L/mol / (6.022 x 10^23 molecules/mol) = 2.04 x 10^-23 L/molecule
The volume of a cube with edge length L is given by V = L^3. Therefore, the length of an edge of each small cube can be calculated by setting the volume occupied by a single gas molecule equal to the volume of a cube:
L^3 = 2.04 x 10^-23 L/molecule
Taking the cube root of both sides, we get:
L = (2.04 x 10^-23 L/molecule)^(1/3) = 2.74 x 10^-8 meters
Therefore, the length of an edge of each small cube is approximately 2.74 x 10^-8 meters, or 0.0274 nanometers.