# what is an ideal gas equation? express it mathematically.

SAGAR SINGH - IIT DELHI
879 Points
13 years ago

Dear prince,

By combining Boyle's and Charles' laws, an equation can be derived that gives the simultaneous effect of the changes of pressure and temperature on the volume of the gas. This is known as combined Ideal Gas Equation. A simple and direct method of deriving this equation is as follows:

According to Boyle's law, for a given mass of a gas at constant temperature

According to Charles' law,

Combining (i) and (ii)

or

or

Now, if V1 is the volume of a gas at temperature T1 and pressure P1. V2 is the volume of same amount of gas at temperature T2 and pressure P2, then

The above relationship is very useful for converting the volume of a gas from one set of conditions to another.

The numerical value of the constant of proportionality (K) depends upon the quantity of gas. The volume of a gas is directly proportional to the number of moles of gas at constant temperature and pressure (Avogadro's law). This means that 'K' is directly proportional to the number of moles, 'n', i.e.,

K n

or K = nR,

where 'R' is the universal gas constant of proportionality. The value of 'R' is same for all gases.

However, the numerical value of 'R' varies with the units in which pressure and volume are expressed. Therefore the Ideal gas Equation is derived as:

For one mole (n = 1),

PV = RT (Ideal Gas Equation)

The Ideal Gas Equation is also known as the equation of state for gases as it expresses the quantitative relation ship between the four variables that describe the state of the gas. The word 'ideal' is used here because in reality no gas obeys the above condition and the gases, which deviate from ideality are called as real gases.

All the best.

Sagar Singh

B.Tech IIT Delhi

OCEAN GODRE
40 Points
13 years ago

pv=nrt