#### Ideal Gas Law

p
```"""
The ideal gas law, also called the general gas equation, is the
equation of state of a hypothetical ideal gas. It is a good approximation
of the behavior of many gases under many conditions, although it has
several limitations. It was first stated by Benoît Paul Émile Clapeyron
in 1834 as a combination of the empirical Boyle's law, Charles's law,
Avogadro's law, and Gay-Lussac's law.[1] The ideal gas law is often written
in an empirical form:
------------
| PV = nRT |
------------
P	=	Pressure (Pa)
V	=	Volume (m^3)
n	=	Amount of substance (mol)
R	=	Universal gas constant
T	=	Absolute temperature (Kelvin)

"""

UNIVERSAL_GAS_CONSTANT = 8.314462  # Unit - J mol-1 K-1

def pressure_of_gas_system(moles: float, kelvin: float, volume: float) -> float:
"""
>>> pressure_of_gas_system(2, 100, 5)
332.57848
>>> pressure_of_gas_system(0.5, 273, 0.004)
283731.01575
>>> pressure_of_gas_system(3, -0.46, 23.5)
Traceback (most recent call last):
...
ValueError: Invalid inputs. Enter positive value.
"""
if moles < 0 or kelvin < 0 or volume < 0:
raise ValueError("Invalid inputs. Enter positive value.")
return moles * kelvin * UNIVERSAL_GAS_CONSTANT / volume

def volume_of_gas_system(moles: float, kelvin: float, pressure: float) -> float:
"""
>>> volume_of_gas_system(2, 100, 5)
332.57848
>>> volume_of_gas_system(0.5, 273, 0.004)
283731.01575
>>> volume_of_gas_system(3, -0.46, 23.5)
Traceback (most recent call last):
...
ValueError: Invalid inputs. Enter positive value.
"""
if moles < 0 or kelvin < 0 or pressure < 0:
raise ValueError("Invalid inputs. Enter positive value.")
return moles * kelvin * UNIVERSAL_GAS_CONSTANT / pressure

def temperature_of_gas_system(moles: float, volume: float, pressure: float) -> float:
"""
>>> temperature_of_gas_system(2, 100, 5)
30.068090996146232
>>> temperature_of_gas_system(11, 5009, 1000)
54767.66101807144
>>> temperature_of_gas_system(3, -0.46, 23.5)
Traceback (most recent call last):
...
ValueError: Invalid inputs. Enter positive value.
"""
if moles < 0 or volume < 0 or pressure < 0:
raise ValueError("Invalid inputs. Enter positive value.")

return pressure * volume / (moles * UNIVERSAL_GAS_CONSTANT)

def moles_of_gas_system(kelvin: float, volume: float, pressure: float) -> float:
"""
>>> moles_of_gas_system(100, 5, 10)
0.06013618199229246
>>> moles_of_gas_system(110, 5009, 1000)
5476.766101807144
>>> moles_of_gas_system(3, -0.46, 23.5)
Traceback (most recent call last):
...
ValueError: Invalid inputs. Enter positive value.
"""
if kelvin < 0 or volume < 0 or pressure < 0:
raise ValueError("Invalid inputs. Enter positive value.")

return pressure * volume / (kelvin * UNIVERSAL_GAS_CONSTANT)

if __name__ == "__main__":
from doctest import testmod

testmod()
```