Chapter 6: Unit 6. Ideal Gas Law

Ideal Gas Law

The ideal gas law holds for all ideal gases at any temperature, pressure, and volume. But the only gases we have around us in the real world are real gases. Real gases behave most like ideal gases at low pressures ( atm or less) and high temperatures ( K or higher). It combines all the gas laws variable into one condition form.

Based on Boyle’s law: P/V = constant

Based on Charles’s law: V/T = constant

Based on Avogadro’s law: V/n= constant

Combining all, PV/n= constant. This constant is symbolized as R and called universal gas constant.

The ideal gas law has the form PV=nRT, where R= Ideal gas Constant (0.08206 L-atm/mol-K). With this equation, any one of the characteristics gas properties (P, V, T or n) can be calculated given the other three.

Ideal gas law follows al the assumptions of kinetic molecular theory. That is why it is called ideal gas law. In real world gas molecules behave differently. Below is the graph that shows how real molecules deviate from ideal gas law. Ideal gas law indicates that plot and PV vs. P should be a constant because PV= constant when temperature is a constant. Real molecules only behave ideally at low pressure and high temperature.

Behavior of Real Gases

Example: How many moles of gas are in a typical human breath that takes in 0.50L of air at 1.0 atm pressure and 35⁰C?

Number of moles n is unknown. T= 35+ 273= 308K

n= PV/RT i.e. 1.0 * 0.50/(0.0821* 308)  n= 0.0198 mol or 0.020 mol

We can determine the mass of a gas from moles if the identity or molar mass of the gas is known. Moles= mass/molar mass.

Here is another video to solve problems using ideal gas laws:

Questions:

1. How many moles of oxygen are contained in a 5.0 L cylinder that has a pressure of 175 atm and temperature 20.0 ⁰C?
2. A person exhales 25.0 g of CO₂ in an hour. What volume does it occur at 1.00 atm and 25.0 ⁰C?

Ans: 1. 36.4 13mol

2.13.9 L