Calculate the pressures, P, in atmospheres at which the mean free path, l, of a hydrogen molecule will be 5.00 μm, 5.00 mm, and 5.00 m at 20.0 °C. The diameter of a H2 molecule is 270 pm.
I= 5.00μm 5.00mm 5.00m
P= ? atm ? atm ? atm
To calculate the pressures at which the mean free path of a hydrogen molecule will be 5.00 μm, 5.00 mm, and 5.00 m at 20.0 °C, we need to use the following formula:
P = (n * k * T) / (π * d²)
Where:
- P is the pressure in atmospheres (atm)
- n is the number density of molecules per unit volume (1/m³)
- k is the Boltzmann constant (1.381 x 10⁻²³ J/K)
- T is the temperature in Kelvin (K)
- d is the diameter of the H2 molecule (m)
First, let's convert the given mean free path and diameter units to meters:
- 5.00 μm = 5.00 x 10⁻⁶ m
- 5.00 mm = 5.00 x 10⁻³ m
- 5.00 m = 5.00 m
Now, we can calculate the pressures using the formula:
For 5.00 μm:
- Convert μm to meters: 5.00 x 10⁻⁶ m
- Calculate the diameter: d = 2 * 270 pm = 2 * 270 x 10⁻¹² m = 540 x 10⁻¹² m
- Plug in the values into the formula: P = (n * k * T) / (π * (540 x 10⁻¹²)²)
For 5.00 mm:
- Convert mm to meters: 5.00 x 10⁻³ m
- Calculate the diameter: d = 2 * 270 pm = 2 * 270 x 10⁻¹² m = 540 x 10⁻¹² m
- Plug in the values into the formula: P = (n * k * T) / (π * (540 x 10⁻¹²)²)
For 5.00 m:
- Convert the diameter to meters: d = 270 pm = 270 x 10⁻¹² m
- Plug in the values into the formula: P = (n * k * T) / (π * (270 x 10⁻¹²)²)
To find the values of n and T, we need additional information or assumptions about the system.