# Combined Gas Law formula

## What is Combined Gas Law?

The combined gas law is the law which combines Charles’s law, Gay-Lussac’s law and Boyle’s law. It’s an amalgamation of the three previously discovered laws. These laws relate one thermodynamic variable to another holding everything else constant.The interdependence of these variables represents combined gas law which states that the ratio between the product of pressure-volume and temperature of a system remains constant.

Combined gas law can be mathematically expressed as

### $$\frac{PV}{T}=K$$ Where,

P = pressure

T = temperature in kelvins

V = volume

K is constant (units of energy divided by temperature)

When two substances are compared in two different conditions, the law can be stated as,

$\frac{P_{i}V_{i}}{T_{i}}=\frac{P_{f}V_{f}}{T_{f}}$

Where,

Pi = initial pressure

Vi = initial volume

Ti = initial temperature

Pf = final pressure

Vf = final volume

Tf = final temperature

Example 1

The initial volume of the gas is 5L and final volume is 3L Calculate the final pressure of gas, given that the initial temperature is 273 K, final temperature is 200k, and initial pressure is 25K Pa

Solution

According to the given parameters,

Pi = 25 kPa

Vi = 5L

Vf = 3L

Ti = 273K

Tf = 200K

According to combined gas law,

$\frac{P_{i}V_{i}}{T_{i}}=\frac{P_{f}V_{f}}{T_{f}}$

Substituting in the formula, we get

25 x 5 / 273 =  Pf x 3 / 200

Therefore, Pf = 30.525 kPa

Example 2

Determine the volume of a gas given Vi = 3L, Ti = 300K, Tf = 250K, Pi = 35 KPa and Pf = 50 kPa

Solution

Given Parameters are

Pi = 35 kPa

Vi = 3L

Ti = 300K

Pf = 50 kPa

Tf = 250K

According to given parameters, we have an equation

$\frac{P_{i}V_{i}}{T_{i}}=\frac{P_{f}V_{f}}{T_{f}}$

Substituting in the above equation, we get

35 x 3 / 300 = 50 x Vf / 250

Therefore, Vf = 1.75 L