# Ideal Gas Law Formula

The Ideal Gas Law was created to show the relationship between pressure, volume, number of moles of gas and temperature. It is a combination of Boyle's Law and Charles' Law. It shows the equation of a hypothetical ideal gas. Pressure and volume have an inverse relationship with each other (when 1 goes up the other goes down) but have a direct relationship with Temperature (when they go up, temperature goes up)

The equation for the Ideal Gas Law is:

*PV = nRT *

*P* = Pressure (*atm*)

*V* = Volume (*Liters – L*)

*n* = Number of moles (*mol*)

*R* = The Ideal Gas Constant (*0.08206 L-atm/mol-K*)

*T* = Temperature (*Kelvin*)

Ideal Gas Law Formula Questions:

1.) How many moles of gas are contained in 890.0mL at 21 °C and 750mm Hg?

Answer: The Volume is *V* = 890.0*mL* and the Temperature is *T* = 21*°C* and the Pressure is *P* = 750*mmHg*.

To use the Ideal Gas Law Equation, you must covert Volume to Liters, Temperature to Kelvin and Pressure to Atmosphere.

*V* = 890mL/1000 = 0.89*L*

*T* = 21°C + 273 = 294*K *

*P* = 750mmHg/760 = 0.987*atm *

Plug into the Idea Gas Law Equation

*PV = nRT *

0.987*atm*(0.890*L*) = n(0.08206L-*atm/mol-K*)(294*K*)

*n* = 0.037*moles*

There are 0.037moles of gas contained.

2.) Calculate the volume 3.00 moles of a gas will occupy at 24°Celsius and 762.4 mm Hg.

Answer: The number of moles is *n* = 3.00*moles*, temperature is *T* = 24°*C* and pressure is *P* = 762.4 *mmHg*

To use the Ideal Gas Law Equation, you must convert Temperature to Kelvin and Pressure to Atmospheres.

*T* = 24 + 273 = 297*K*

*P* = 762.4/760 = 1.003*atm*

Plug into the Ideal Gas Law Equation

*PV = nRT *

1.003*atm*(V) = 3.00moles(0.08206*L-atm/mol-K*)(297*K*)

*V* = 72.897*L*

The volume of the gas would be 72.897 *Liters*