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**Table of Content**

The ideal gas law calculator helps to calculate the unknown measurable properties of the ideal gas law equation (PV=nRT) when three of the variables are known.

An ideal gas does not exist in reality, it is composed of many unsystematically moving particles that interact with each other by means of an elastic collision following a specific law, or an elementary equation and are responsive to examination known as an ideal gas.

It follows an elementary calculation that is recognized as the ideal gas law equation:

**PV = nRT**

It can be used to find the unknown pressure, volume, temperature, or amount of substance. Let’s see how!

**Calculate Pressure:**

**\(\ P = \dfrac{nRT}{V}\)**

**Calculate Volume:**

**\(\ V = \dfrac{nRT}{P}\)**

**Calculate moles:**

**\(\ n=\dfrac{PV}{R}\)**

**Calculate Temperature:**

**\(\ T = \dfrac{PV}{nR}\)**

Where

- n = It represents the number of moles
- R = It is the ideal gas constant and is also known as universal gas constant = 8.3145 J/mol K
- T = Standard temperature in Kelvin
- P = Standard pressure(Pascals)
- V = It signifies the volume

The R is also known as the universal, molar, or ideal gas constant. This R is referred to as a physical constant that is introduced in different fundamental equations in the physical sciences, such as the Arrhenius equation, and the Nernst equation.

The gas constant R is also said to be a combination of the constants from Boyle’s law, Charles’s law, Avogadro’s law, and Gay-Lussac’s law. The value of R is 8.3144626 J K−1 mol−1.

They are:

**Boyle’s Law:** It states that if temperature and gas quantity remain unchanged then the pressure will be multiplied by the volume and remains constant.

\(\ p_{1}.\ V_{1}=\ p_{2}.\ V_{2}\)

**Charles’s Law:** It states that if we keep the pressure and gas quantity constant and divide by its temperature then it will be constant as well.

\(\dfrac{V_{1}}{T_{1}} =\dfrac{V_{2}}{T_{2}}\)

**Gay-Lussac’s Law:** For a constant volume and quantity the pressure divided by its temperature is constant.

\(\ p_{1}.\ T_{1}=\ p_{2}.\ T_{2}\)

**Avogadro’s Law:** It states that if the temperature and pressure are constant and we divide the gas volume by its quantity then it will come out as a constant as well.

\(\dfrac{V_{1}}{n_{1}} =\dfrac{V_{2}}{n_{2}}\)

Follow these steps:

- Determine the known values from pressure (P), volume (V), temperature (T), and number of moles (n).
- Now convert the units if necessary
- Put the known values in the above-mentioned ideal gas formula

**Case 1: **If you are asked to find the volume from the given values that are:

- Pressure = 200 k pascals
- Temperature = 300 Kelvin
- n = 0.250 mol
- T = 300K

**Solution:**

\(\ Volume\ (V) =\dfrac{nRT}{P} =\dfrac{0.250\times\ 8.314\times\ 300}{200}\)

\(\ V =\dfrac{623.55}{200}\)

V = 3.12 L

**Case 2:** If you are asked to calculate the temperature from the given values that are:

- Pressure = 153k pascals
- \(\ V =\ 250\ ml =\dfrac{250}{1000} =\ 0.250\ L\)
- n = 0.50 moles

**Solution:**

\(\ T =\dfrac{PV}{nR} =\dfrac{(153\times0.250)}{(0.50\times8.314)}\)

\(\ T =\dfrac{38.25}{4.16} =\ 9.2\ Kelvin\)

Ideal gas law is applicable in the following situations:

- High Temperature
- Low Pressure
- Sufficient Volume
- Non reacting gases