The Ideal Gas Law represents a formula that relates the behavior of gases under varying conditions of concentration, volume, pressure and temperature.

**The Ideal Gas Law**

Within a closed container, gas molecules behave ideally when the temperature and volume are high while the pressure is low. The Ideal Gas Law equation is represented as:

**R Constant (R)**

The variable of R represents the universal gas constant of the gas. When atmospheres (atm) are incorporated into its units the traditional R value of 0.08206 is used, but changing atmospheres (atm) will change the numerical value of R.

**Pressure (P)**

The variable of P represents the pressure of the gas. Although the SI unit for pressure is pascals, it is customary to use the units of atmospheres (atm).

1.0 atmosphere (atm) is equal to each of the given pressure units based on the given value. For example, 1.0 atm = 760 torrs or 1.0 atm = 101.325 kPa.

**Volume (V) **

The variable of V represents the volume of the gas. The units are in Liters.

**Temperature (T)**

The variable of T represents the absolute temperature of the gas. The units are in Kelvin. Let’s say you are given 90^{o}F and asked to convert it into Kelvin.

Conversion from Fahrenheit to Celsius:

Conversion from Celsius to Kelvin:

**Moles (n) **

The variable of n represents the moles of the gas.

**PRACTICE: **

How many grams of neon gas are present in a 5.0 L container at pressure of 1.35 atm at 35^{o}C?

**STEP 1:** Identify the variables given.

**STEP 2:** Isolate the missing variable of moles (n).

**STEP 3:** Convert the moles (n) into grams.

**Further Applications of the Ideal Gas Law**

The Ideal Gas Law can be rearranged in order to create new equations that determine either the density or molar mass of a gas molecule.

When dealing with the density of a gas molecule we can utilize the following equation:

**Pressure, R constant and Temperature**

The variables of P, R and T still represent pressure, the gas constant, and temperature in Kelvin.

**Molar Mass (M) **

The variable of M represents the molar mass of a gas molecule. The units of molar mass are grams per mole (g/mol).

**Density (d) **

The variable of d represents the density of a gas molecule. As a result of being less dense than solids or liquids, gas molecules have their density in units of grams per liter (g/L).

**PRACTICE: **Determine the density of NH_{3} gas at 435 K and 1.00 atm.

**STEP 1:** Identify the variables given.

**STEP 2:** Solve for the missing variable of density (d).

When dealing with the mass and molar mass of a gas molecule we can utilize the following equation:

**Pressure, Volume, R constant, Molar Mass and Temperature**

The variables of P,V, M, R and T are the same ones used from the previous equations.

**Mass (m)**

The variable of m represents the mass of a gas molecule. The units of mass are grams (g).

**PRACTICE: **An unknown gas contained in a 1.85 L flask is weighed and found to have a mass of 15.87 g at a pressure of 2.45 atm and a temperature of 18.6°C. What is the molecular weight of the gas?

**STEP 1:** Identify the variables given.

**STEP 2:** Isolate the missing variable of molar mass (M).

**Beyond Ideal Gases **

To better understand the reactive nature of gases you can utilize the Kinetic-Molecular Theory and the Van der Waals equation. They help to explain concepts such as effusion rates of gases, Dalton’s Law, Root Mean Square Speed, and the Simple Gas Laws.

A sample of an ideal gas has a volume of 2.30 L at 287 K and 1.03 atm. Calculate the pressure when the volume is 1.08 L and the temperature is 303 K.

A 8.30-L container holds a mixture of two gases at 49°C. The partial pressures of gas A and gas B. respectively, are 0.173 atm and 0.873 atm. If 0.130 mol of a third gas is added with no change in volume or temperature, what will the total pressure become?