When pressure molar amount and temperature are known what can the ideal gas law be used to calculate?

The Ideal Gas Law Calculator finds the unknown variable in the equation PV = nRT when three of the variables are known.

Ideal Gas Law Formula

The ideal gas law formula states that pressure multiplied by volume is equal to moles times the universal gas constant times temperature.

Where:

• P = pressure
• V = volume
• n = number of moles
• T = temperature
• R = gas constant

Gas Constant R

The gas constant R is a constant of units of energy per temperature increment per mole. It is also known as the universal gas constant, ideal gas constant and molar gas constant.

The value of gas constant R depends on the units you are using in your calculation. See Wikipedia Gas Constant for a table of R values and their corresponding units.

This calculator uses R = 8.31446261815324 m3·Pa·K-1·mol-1. If necessary, your calculator inputs are converted to these same units to perform the calculation and then converted back into your answer units.

Calculations Using the Ideal Gas Law

The Ideal Gas Law equation can be used to find the pressure of the gas, the volume of the gas, the amount of substance contained in the volume of gas, or the temperature of the gas. We rewrite the equation below to calculate each of the Ideal Gas Law variables.

Calculate pressure:

Calculate volume:

Calculate moles:

Calculate temperature:

There are a number of chemical reactions that require ammonia. In order to carry out the reaction efficiently, we need to know how much ammonia we have for stoichiometric purposes. Using gas laws, we can determine the number of moles present in the tank if we know the volume, temperature, and pressure of the system.

The Combined Gas Law shows that the pressure of a gas is inversely proportional to volume and directly proportional to temperature. Avogadro's Law shows that volume or pressure is directly proportional to the number of moles of gas. Putting these together leaves us with the following equation:

\[\dfrac{P_1 \times V_1}{T_1 \times n_1} = \dfrac{P_2 \times V_2}{T_2 \times n_2} \nonumber \]

As with the other gas laws, we can also say that \(\dfrac{\left( P \times V \right)}{\left( T \times n \right)}\) is equal to a constant. The constant can be evaluated provided that the gas being described is considered to be ideal.

The Ideal Gas Law is a single equation which relates the pressure, volume, temperature, and number of moles of an ideal gas. If we substitute in the variable \(R\) for the constant, the equation becomes:

\[\dfrac{P \times V}{T \times n} = R \nonumber \]

The Ideal Gas Law is conveniently rearranged to look this way, with the multiplication signs omitted:

\[PV = nRT \nonumber \]

The variable \(R\) in the equation is called the ideal gas constant.

The value of \(R\), the ideal gas constant, depends on the units chosen for pressure, temperature, and volume in the ideal gas equation. It is necessary to use Kelvin for the temperature and it is conventional to use the SI unit of liters for the volume. However, pressure is commonly measured in one of three units: \(\text{kPa}\), \(\text{atm}\), or \(\text{mm} \: \ce{Hg}\). Therefore, \(R\) can have three different values.

We will demonstrate how \(R\) is calculated when the pressure is measured in \(\text{kPa}\). The volume of \(1.00 \: \text{mol}\) of any gas at STP (Standard temperature, 273.15 K and pressure, 1 atm) is measured to be \(22.414 \: \text{L}\). We can substitute \(101.325 \: \text{kPa}\) for pressure, \(22.414 \: \text{L}\) for volume, and \(273.15 \: \text{K}\) for temperature into the ideal gas equation and solve for \(R\).

\[\begin{align*} R &= \dfrac{PV}{nT} \\[4pt] &= \dfrac{101.325 \: \text{kPa} \times 22.414 \: \text{L}}{1.000 \: \text{mol} \times 273.15 \: \text{K}} \\[4pt] &= 8.314 \: \text{kPa} \cdot \text{L/K} \cdot \text{mol} \end{align*} \nonumber \]

This is the value of \(R\) that is to be used in the ideal gas equation when the pressure is given in \(\text{kPa}\). The table below shows a summary of this and the other possible values of \(R\). It is important to choose the correct value of \(R\) to use for a given problem.

Notice that the unit for \(R\) when the pressure is in \(\text{kPa}\) has been changed to \(\text{J/K} \cdot \text{mol}\). A kilopascal multiplied by a liter is equal to the SI unit for energy, a joule \(\left( \text{J} \right)\).