derive the general gas equation and ideal gas equation

Answer 1

The general gas equation is derived by combining Boyle's law, Charles' law, and Avogadro's law.

Boyle's law states that the volume of a gas is inversely proportional to its pressure, assuming constant temperature and amount of gas. It can be written mathematically as:
PV = constant

Charles' law states that the volume of a gas is directly proportional to its temperature, assuming constant pressure and amount of gas. It can be written mathematically as:
V/T = constant

Avogadro's law states that the volume of a gas is directly proportional to the number of moles of gas, assuming constant pressure and temperature. It can be written mathematically as:
V/n = constant

Combining these three laws, we can write the general gas equation as:
PV = nRT

Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of gas
R = ideal gas constant
T = temperature of the gas

The ideal gas equation is a special case of the general gas equation, where the gas behaves ideally. It assumes that the gas particles have no volume and do not interact with each other. The equation is written as:
PV = NRT

Where:
N = number of gas particles (also known as the number of molecules)

In both equations, R is the ideal gas constant, which is 0.0821 L·atm/(mol·K) or 8.314 J/(mol·K). The units used depend on the units of pressure, volume, and temperature being used in the equation.