Ideal gas law calculator

What is the ideal gas law?

The ideal gas law, also known as the Mendeleev-Clapeyron equation, plays a fundamental role in thermodynamics and statistical mechanics. It establishes a relationship between pressure ($P$), volume ($V$), the amount of substance ($n$), and temperature ($T$) of a gas, allowing predictions of how the state of the gas changes when one of these parameters is altered.

An ideal gas is a hypothetical model used for a simplified description of the behavior of real gases, assuming that its particles interact solely through elastic collisions and that intermolecular forces are absent. It has been empirically shown that many real gases behave like ideal gases under conditions of high temperatures and low pressures.

Formula

The formula for the ideal gas law:

$$PV = nRT$$

where:

• $P$ is the pressure,
• $V$ is the volume,
• $n$ is the number of moles,
• $R$ is the universal gas constant $(8.314 \, \text{J/(mol\,K)})$,
• $T$ is the temperature in Kelvin.

Historical context: Clapeyron and Mendeleev

Before delving into the equation, it’s worth noting the roles of Clapeyron and Mendeleev in its formulation. Benoît Clapeyron, a French physicist, first proposed this equation in 1834. He demonstrated that for an ideal gas, the product of pressure and volume is directly proportional to the temperature and the amount of substance in moles.

However, the equation gained substantial popularity and broad applicability thanks to the work of Dmitri Mendeleev, who made certain refinements and adapted the formula to the form we use today. Mendeleev added more detailed explanations of chemical processes and reactions, significantly expanding its use across various scientific disciplines.

Exploration of ideal gas laws

Boyle’s law

This law states that at a constant temperature, the product of the volume and pressure of a gas remains constant. In other words, if the gas is compressed, its pressure increases. Mathematically, it is expressed as:

$$P_1V_1 = P_2V_2$$

You can solve calculations related to this with our Boyle’s law calculator, which conveniently and quickly solves tasks based on the dependencies between pressure and volume. Using the calculator allows you to focus on analysis and spend less time on computations.

Charles’s law

Charles’s law describes the volume-temperature relationship at constant pressure. It states that the volume of a gas is proportional to its absolute temperature:

$$\frac{V_1}{T_1} = \frac{V_2}{T_2}$$

Gay-Lussac’s law

This law describes the pressure-temperature relationship at constant volume, stating that the pressure of a gas is proportional to its temperature:

$$\frac{P_1}{T_1} = \frac{P_2}{T_2}$$

Avogadro’s law

States that at identical conditions (pressure and temperature), equal volumes of different gases contain the same number of molecules.

Examples

1. Pressure calculation example: There is $0.5\, \text{mol}$ of an ideal gas at a temperature of $273\, \text{K}$ and a volume of $22.41\, \text{L}$. Find the pressure:

   $P = \frac{nRT}{V} = \frac{0.5 \times 8.314 \times 273}{22.41} \approx 0.5\, \text{atm}$

2. Volume calculation example: Gas at $2\, \text{atm}$, $300\, \text{K}$, and $0.65\, \text{mol}$. What volume will it occupy?

   $V = \frac{nRT}{P} = \frac{0.65 \times 8.314 \times 300}{2} \approx 8\, \text{L}$

Notes

• The universal gas constant $R$ remains unchanged at $8.314\, \text{J/(mol\,K)}$.
• Real gases exhibit behavior that can be described by this equation under low-pressure and high-temperature conditions.

Frequently asked questions

How to find the volume of a gas given the number of moles and temperature?

To calculate the volume, you need to consider the pressure, using the ideal gas equation $PV = nRT$, transforming it to $V = \frac{nRT}{P}$.

Is the ideal gas law applicable to real gases?

The ideal gas law is most suitable for describing dilute gases or gases at high temperatures and low pressures. In other conditions, the Van der Waals equation might be required.

How will pressure change during an isothermal process?

In an isothermal process, as volume increases, pressure decreases, explaining Boyle’s Law.

Why consider temperature in the ideal gas law?

Temperature affects the average kinetic energy and speed of gas particles. Its consideration is essential for an accurate description of the gas’s state.

Why can intermolecular forces be neglected in real gases?

In certain conditions, like high temperatures and low pressures, intermolecular forces become negligible, allowing the use of idealized gas models.