THD - Ideal Gas Law

Ideal Gas Law

Introduction

Remember from chemistry that it is known through the work of Robert Boyle, Jacques Charles, and Joseph Gay-Lussac that for any confined gas there is a relationship between the pressure (P), volume (V), and temperature (T) of the gas. By combining Boyle's Law, Charles' Law, and Gay-Lussac's Law and adding consideration for the effect of the amount of gas present we arrive at the Ideal Gas Law,

where n = number of moles of gas and R = universal gas constant = 8.314 J/(mol•K) (J stands for energy units of joules, where 1 J = 1 N•m)

Note 1: Document with more information Links to an external site. about the laws mentioned above.

Note 2: When solving equations using the ideal gas law, remember that temperature must be in kelvins and pressure must be the absolute pressure, not the gauge pressure. Problems involving the ideal gas law will often be solved under the conditions of standard temperature and pressure (STP) where T = 273 K (0 °C) and P = 1.00 atm = 1.013 x 10⁵ Pa.

Ideal Gas Law Practice

1. Determine the volume of 1.00 mol of any ideal gas at STP. 

2. A spherical, helium party balloon has a radius of 18.0 cm. At room temperature (20 °C), its internal pressure is 1.05 atm. A) How many moles of helium are present in the balloon to provide the necessary pressure? B) What mass of helium is present? 

Click here for solutions to problems above. Links to an external site.

If we work with a situation where the amount of gas stays constant and only consider a change in volume, pressure, or temperature, we don't need to use R. Instead we look at differences between the first and second state of the gas. Mathematically, .

In chemistry, you often did calculations in terms of the number of moles of the gas. In physics you may do calculations using moles or you may be given (or asked to calculate) the number of molecules in the gas. The number of molecules in a gas is related to the number of moles in the gas by Avogadro's number. Remember there are Avogadro's number of molecules in one mole of a substance. So, the number of molecules N equals the number of moles n times Avogadro's number N_A. Plugging this into the ideal gas law equation gives:

The ratio of R to N_A is known as Boltzmann's constant, k. We can plug this into the ideal gas law equation to get an equation that is devoid of moles and calculated in terms of number of molecules.

where N_A = Avogadro's number = 6.02 x 10²³ and k = Boltzmann's constant = 1.38 x 10^-23 J/K

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