# Molecular Speed Formula

## Molecular Speed Formula

The average speed of a group of molecules is called Molecular Speed. It holds true in an ideal gas, where molecules do not interact among themselves. Small molecules diffuse more quickly than larger molecules. This characteristic is explained by the idea of Molecular Speed Formula. A gas molecule’s Molecular Speed Formula is determined by its temperature and molar mass. A gas’s molecular speed is inversely proportional to its molar mass and directly proportional to its speed. As a result, a gas’s Molecular Speed Formula will increase as its temperature rises. For instance, helium has the highest Molecular Speed Formula because it has the lowest molecular mass. Despite that, the lowest Molecular Speed Formula is found in xenon, which has the highest molar mass. If we examine the gas molecules of two gases at the same temperature, it can be observed that a gas with a heavier mass is slower than a gas with a lighter mass. The molecules of a gas move continuously and in a straight line until they clash with another molecule, according to the kinetic theory of gases. In an ideal gas, every molecule collides with every other molecule.

### Types of Molecular Speed

There are three different types of Molecular Speed Formula. These are the root mean square speed, average molecular speed, and most probable speed.

### Average Molecular Speed

The average speed of a set of molecules in a gas is known as average Molecular Speed Formula. It is denoted by vav.

### Root Mean Square Speed

The speed of the particles in a given gas is calculated using the root mean square speed. It is denoted by vrms.

### Most Probable Speed

The speed that the majority of the molecules in a gas acquire is known as the most probable speed. It is denoted by vmp

## Relation between Molecular Speeds

The relationship between root mean square speed, most probable speed, and average molecular speed is vrms> vav > vmp, where vav stands for average molecular speed, vrms for root mean square speed, and vmp for most probable speed. When it comes to the molecular speeds of a particle, the volume of a gas molecule is smaller than the total volume of the container. The gas atoms are completely mobile and move around freely. As a result, there is no force of attraction between the gaseous molecules. The ratio of average molecular speed, root mean square speed, and most probable speed is 1:1.128:1.224.

## Maxwell Distribution of Molecular Speeds

For the purpose of determining the distribution of different molecular speeds in a gas, Maxwell and Boltzmann developed an equation. With the aid of this equation, the Maxwell distribution of speeds can be graphically illustrated. The y-axis of the Maxwell-Boltzmann distribution graph represents the number of molecules per unit speed. The total area under the entire curve represents the number of molecules in the gas. If we heat the gas to a higher temperature, the peak of the graph will shift to the right. Similar to how the graph shortens and expands as the gas heats up, the graph increases in height and narrowness as the gas cools. The shape of the speed distribution curve can reveal a lot about the gas on being carefully examined. The molar mass and temperature of the gas will affect the shape of the Maxwell distribution of speed curve. Maxwell and Boltzmann were able to demonstrate through experimentation and deduction that the molecular mass and gas temperature affect the distribution of molecular speeds.

### Inferences from the Graph

The most probable speed is the one that corresponds to the peak of the curve. The speed that is somewhat greater than the most probable speed is the average molecular speed. And the root mean square speed is the speed that matches the average kinetic energy of molecules. When we monitor the gas at higher temperatures, the Maxwell distribution of the speed curve will widen and flatten. As the temperature rises and the most probable speed rises, we will see the peak shift to the right. Additionally, it has been noticed that gas particle motion is generally faster. When we consider gases with increasing molar mass, the Maxwell distribution of speed curve becomes taller and flatter. In this instance, as the most probable speed drops, the peak moves to the left. In an equilibrium state, the distribution of speeds is constant and fixed.

### Solved Example On Molecular Speed Formula

To thoroughly understand the concept of Molecular Speed Formula, students need to solve examples and exercises based on it. Students also need accurate solutions to check their answers while solving these problems. Various solved examples on Molecular Speed Formula can be found on the Extramarks platform. These examples can help students learn the right way of solving problems based on the Molecular Speed Formula.