Final answer:
Boyle's Law is P1V1 = P2V2, Charles's Law is V1/T1 = V2/T2, the pressure-temperature law by Amontons can be expressed as P1/T1 = P2/T2, and Avogadro's Law is V1/n1 = V2/n2.
Step-by-step explanation:
The scientists mentioned in the question discovered important laws that describe how gases behave under different conditions. The laws are mathematical relationships between variables like pressure, volume, temperature, and the amount of gas.
Robert Boyle
Boyle's Law states that the pressure of a gas is inversely proportional to its volume when the temperature is held constant. This is expressed algebraically as P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
Jacques Charles
Charles's Law indicates the direct proportionality between the volume of a gas and its temperature when the pressure is held constant. The algebraic expression for Charles's Law is V1/T1 = V2/T2, where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature, respectively.
Guillaume Amontons
The relationship discovered by Guillaume Amontons is known as the pressure-temperature law, which states that the pressure of a gas is directly proportional to its temperature when the volume is held constant. This can be represented as P1/T1 = P2/T2.
Amedeo Avogadro
Avogadro's Law posits that equal volumes of all gases, at the same temperature and pressure, contain the same number of molecules. The algebraic form of Avogadro's Law is V1/n1 = V2/n2, where V represents the volume and n is the number of moles of the gas.