#### Grahams Law

p
```"""
Title: Graham's Law of Effusion

Description: Graham's law of effusion states that the rate of effusion of a gas is
inversely proportional to the square root of the molar mass of its particles:

r1/r2 = sqrt(m2/m1)

r1 = Rate of effusion for the first gas.
r2 = Rate of effusion for the second gas.
m1 = Molar mass of the first gas.
m2 = Molar mass of the second gas.

"""

from math import pow, sqrt

def validate(*values: float) -> bool:
"""
Input Parameters:
-----------------
effusion_rate_1: Effustion rate of first gas (m^2/s, mm^2/s, etc.)
effusion_rate_2: Effustion rate of second gas (m^2/s, mm^2/s, etc.)
molar_mass_1: Molar mass of the first gas (g/mol, kg/kmol, etc.)
molar_mass_2: Molar mass of the second gas (g/mol, kg/kmol, etc.)

Returns:
--------
>>> validate(2.016, 4.002)
True
>>> validate(-2.016, 4.002)
False
>>> validate()
False
"""
result = len(values) > 0 and all(value > 0.0 for value in values)
return result

def effusion_ratio(molar_mass_1: float, molar_mass_2: float) -> float | ValueError:
"""
Input Parameters:
-----------------
molar_mass_1: Molar mass of the first gas (g/mol, kg/kmol, etc.)
molar_mass_2: Molar mass of the second gas (g/mol, kg/kmol, etc.)

Returns:
--------
>>> effusion_ratio(2.016, 4.002)
1.408943
>>> effusion_ratio(-2.016, 4.002)
ValueError('Input Error: Molar mass values must greater than 0.')
>>> effusion_ratio(2.016)
Traceback (most recent call last):
...
TypeError: effusion_ratio() missing 1 required positional argument: 'molar_mass_2'
"""
return (
round(sqrt(molar_mass_2 / molar_mass_1), 6)
if validate(molar_mass_1, molar_mass_2)
else ValueError("Input Error: Molar mass values must greater than 0.")
)

def first_effusion_rate(
effusion_rate: float, molar_mass_1: float, molar_mass_2: float
) -> float | ValueError:
"""
Input Parameters:
-----------------
effusion_rate: Effustion rate of second gas (m^2/s, mm^2/s, etc.)
molar_mass_1: Molar mass of the first gas (g/mol, kg/kmol, etc.)
molar_mass_2: Molar mass of the second gas (g/mol, kg/kmol, etc.)

Returns:
--------
>>> first_effusion_rate(1, 2.016, 4.002)
1.408943
>>> first_effusion_rate(-1, 2.016, 4.002)
ValueError('Input Error: Molar mass and effusion rate values must greater than 0.')
>>> first_effusion_rate(1)
Traceback (most recent call last):
...
TypeError: first_effusion_rate() missing 2 required positional arguments: \
'molar_mass_1' and 'molar_mass_2'
>>> first_effusion_rate(1, 2.016)
Traceback (most recent call last):
...
TypeError: first_effusion_rate() missing 1 required positional argument: \
'molar_mass_2'
"""
return (
round(effusion_rate * sqrt(molar_mass_2 / molar_mass_1), 6)
if validate(effusion_rate, molar_mass_1, molar_mass_2)
else ValueError(
"Input Error: Molar mass and effusion rate values must greater than 0."
)
)

def second_effusion_rate(
effusion_rate: float, molar_mass_1: float, molar_mass_2: float
) -> float | ValueError:
"""
Input Parameters:
-----------------
effusion_rate: Effustion rate of second gas (m^2/s, mm^2/s, etc.)
molar_mass_1: Molar mass of the first gas (g/mol, kg/kmol, etc.)
molar_mass_2: Molar mass of the second gas (g/mol, kg/kmol, etc.)

Returns:
--------
>>> second_effusion_rate(1, 2.016, 4.002)
0.709752
>>> second_effusion_rate(-1, 2.016, 4.002)
ValueError('Input Error: Molar mass and effusion rate values must greater than 0.')
>>> second_effusion_rate(1)
Traceback (most recent call last):
...
TypeError: second_effusion_rate() missing 2 required positional arguments: \
'molar_mass_1' and 'molar_mass_2'
>>> second_effusion_rate(1, 2.016)
Traceback (most recent call last):
...
TypeError: second_effusion_rate() missing 1 required positional argument: \
'molar_mass_2'
"""
return (
round(effusion_rate / sqrt(molar_mass_2 / molar_mass_1), 6)
if validate(effusion_rate, molar_mass_1, molar_mass_2)
else ValueError(
"Input Error: Molar mass and effusion rate values must greater than 0."
)
)

def first_molar_mass(
molar_mass: float, effusion_rate_1: float, effusion_rate_2: float
) -> float | ValueError:
"""
Input Parameters:
-----------------
molar_mass: Molar mass of the first gas (g/mol, kg/kmol, etc.)
effusion_rate_1: Effustion rate of first gas (m^2/s, mm^2/s, etc.)
effusion_rate_2: Effustion rate of second gas (m^2/s, mm^2/s, etc.)

Returns:
--------
>>> first_molar_mass(2, 1.408943, 0.709752)
0.507524
>>> first_molar_mass(-1, 2.016, 4.002)
ValueError('Input Error: Molar mass and effusion rate values must greater than 0.')
>>> first_molar_mass(1)
Traceback (most recent call last):
...
TypeError: first_molar_mass() missing 2 required positional arguments: \
'effusion_rate_1' and 'effusion_rate_2'
>>> first_molar_mass(1, 2.016)
Traceback (most recent call last):
...
TypeError: first_molar_mass() missing 1 required positional argument: \
'effusion_rate_2'
"""
return (
round(molar_mass / pow(effusion_rate_1 / effusion_rate_2, 2), 6)
if validate(molar_mass, effusion_rate_1, effusion_rate_2)
else ValueError(
"Input Error: Molar mass and effusion rate values must greater than 0."
)
)

def second_molar_mass(
molar_mass: float, effusion_rate_1: float, effusion_rate_2: float
) -> float | ValueError:
"""
Input Parameters:
-----------------
molar_mass: Molar mass of the first gas (g/mol, kg/kmol, etc.)
effusion_rate_1: Effustion rate of first gas (m^2/s, mm^2/s, etc.)
effusion_rate_2: Effustion rate of second gas (m^2/s, mm^2/s, etc.)

Returns:
--------
>>> second_molar_mass(2, 1.408943, 0.709752)
1.970351
>>> second_molar_mass(-2, 1.408943, 0.709752)
ValueError('Input Error: Molar mass and effusion rate values must greater than 0.')
>>> second_molar_mass(1)
Traceback (most recent call last):
...
TypeError: second_molar_mass() missing 2 required positional arguments: \
'effusion_rate_1' and 'effusion_rate_2'
>>> second_molar_mass(1, 2.016)
Traceback (most recent call last):
...
TypeError: second_molar_mass() missing 1 required positional argument: \
'effusion_rate_2'
"""
return (
round(pow(effusion_rate_1 / effusion_rate_2, 2) / molar_mass, 6)
if validate(molar_mass, effusion_rate_1, effusion_rate_2)
else ValueError(
"Input Error: Molar mass and effusion rate values must greater than 0."
)
)
```