Ideal Gas Equation and Absolute Temperature

Real gas and ideal gas are the two categories of gases. All gases in the universe are actual gases, and we interact with them daily. Oxygen, hydrogen, carbon dioxide, helium, and other real gases are among them.

This article will explore ideal gas, the ideal gas equation, and more.

What are Ideal gases?

• In everyday life, ideal gases don't exist. However, under some circumstances, some gases behave like ideal gases. For instance, oxygen and nitrogen behave as ideal gases in some situations.
• No real gas is ideal, but some real gas behaves similarly to an ideal gas.
• The most crucial point in this situation is that ideal gases don't exist. They serve as a model for scientists to forecast how real gases behave.
• We can simplify real gas concepts by using ideal gases.
• In reality, gas molecules are comprised of atoms that do occupy some space. However, molecules in an ideal gas have no volume. Chemist disregards this volume when working with ideal gases because it is so little.
• In an ideal gas, the molecules do not interact. Since atoms in gases in the real world are composed of electrons, they have a charge. These molecules may somewhat alter the velocity of the particles by attracting or repelling other molecules. Molecules in ideal gases are thought to travel randomly in straight lines and without interaction.
• The sole factor affecting particle speed in an ideal gas collision is temperature because all ideal gas collisions are elastic. When two molecules collide in the actual world, they come to a complete stop. However, elastic collisions occur in ideal gases, meaning the molecules do not slow down after colliding. If two molecules of an ideal gas collided head-on, they would go in the opposite direction at their pre-collision speed.

Why are the characteristics of ideal gas so important?

Because ideal gases have specific properties, scientists can predict the pressure, volume, temperature, and number of moles of the gas based on changes in any of these parameters.

Ideal gas equation

Boyle's Law

Robert Boyle, an Anglo-Irish physicist, proposed Boyle's law in 1662. The tests carried out to comprehend the fluctuation in volume with respect to pressure for a certain volume of gas at a constant temperature led to the formulation of this law.

Experiment to understand Boyle's Law

Imagine that we can modify (by either compression or expansion) the volume of an air column that contains gas molecules. The particles inside the container are spaced at greater distances and hit the walls less frequently in this situation.

Let's exert the right amount of pressure on this container to reduce its volume. Since there is less room between the particles due to the bundling effect of compression, they start to collide with the container walls more frequently. It appears that there is a linear relationship between the rate of collision and the gas pressure. Therefore, there is no doubt that the container considered in this case is under more pressure compared to the container considered earlier.

This is the main idea behind Boyle's law which dictates that pressure and volume are inversely linked. The pressure will rise if we reduce the volume. Likewise, pressure will decrease if we increase volume. Given that the temperature is constant, the volume determines the pressure of the gas inside the container.

Robert Boyle proclaimed the inverse relationship between pressure and volume as a gas law.

Definition of Boyle's law

According to Boyle's Law, the volume of a fixed quantity of gas is inversely proportional to the pressure applied to it at a constant temperature. The product of the pressure and volume of a particular quantity of gas is constant at a constant temperature.

P=k/V, where P is pressure, V is volume, and k is a proportionality constant, is a mathematical formula that can be used to express this.

Rearrange this equation to get PV=k, which stands for the constant k representing the product of pressure and volume.

The equation that is associated with Boyle's law

Practice problems

1. A 5L air column has a gas pressure of 10atm. If the volume of the column is reduced to 3L, calculate the new pressure in the air column.

Solution:

Given: V₁= 5L and the pressure corresponding to this, P₁= 10atm. When the volume is decreased, the new volume becomes V₂= 3L.

We know that, according to Boyle's law: P₁V₁=P₂V₂

(10atm) *(5L) =P₂*(3L)

P₂= (10*5)/3

P₂= 16.666atm

Note: As the volume decreases, the pressure increases (from 10atm to 16.66atm)

2. A flexible air container has a volume of 12L with a pressure of 50torr. If the pressure is reduced to 25 torrs, how much quantity should the volume be increased?

Solution:

Given: P₁ = 50torr, V₁=12L, and P₂= 25torr

Let us calculate V₂ using Boyle's law: P₁V₁=P₂V₂

V₂= (50*12)/25

V₂= 24L

It has to be noted that, as the pressure reduces, the volume increases (from 12L to 24L).

Charles' Law

Charles' law describes the link between volume and temperature.

Experiment to understand Charles' Law

• Let's see how changing the temperature affects the volume of the gas. To further understand this, let's look at an example. Consider a balloon with a volume of 2L and a temperature of 300K. Now imagine raising the balloon's temperature from 300 K to 600 K, or in other words, doubling the temperature.
• When a gas is heated while maintaining a constant pressure, its volume grows. As a result, in this scenario, the balloon will grow twice as big as before. It will be 2L*2, which is 4L.
• Gases expand when they are heated, and the gas particles travel more quickly and they occupy more space.
• In the balloon example from above, the balloon expands as a result of the gas particles colliding with the sides. Expanding maintains the pressure's stability. The sides of the balloon will be pushed against more forcefully as the gas particles move more quickly, expanding the balloon. On the other hand, cooling the balloon causes the gas particle to slow down. The balloon will shrink as a result.

This is the fundamental idea behind Charles' law. It demonstrates the clear connection between volume and temperature. The volume also increases as the temperature does. The volume will also drop if we lower the temperature. These two have a direct correlation to one another.

Definition of Charles' law

Charles' law asserts that volume and temperature are related to a given amount of gas at a fixed pressure.

Mathematically, this can be expressed as V= kT, where V is the volume, the temperature is denoted by T, and the proportionality constant is K.

This equation can be rearranged to read: V/T=k, or the relationship between volume and temperature is a constant.

The equation that is associated with Charles' Law

Graphical representation of Charles' Law

Consider volume on the x-axis and temperature on the y-axis if we were to graphically represent Charles' law. The temperature rises at the same pace as the volume does. Given that there is a linear relationship between temperature and volume, the graph would appear to be a straight line.

Practice problems

1. A 15L flexible air column has gas at a temperature of 200K. If the temperature increases to 500K, find the new volume in the air column.

Solution:

Given: V₁=15L, T₁=200K, T₂=500K

According to Charles' Law: V₁/T₁=V₂/T₂

V₂=(V₁/T₁) *T₂

V₂= (15L/200K) *500K

V₂= 37.5L

2. A 50ml helium balloon is filled with a helium ga at the temperature of 50C. Find the new volume in the helium balloon if the temperature changes to 25C.

Solution:

Given: V₁=50ml, T₁=50C, T₂=25C

According to Charles' Law: V₁/T₁=V₂/T₂

V₂=(V₁/T₁) *T₂

V₂= (50ml/50C) * 25C

V₂= 25ml

Absolute Temperature

The property of temperature is present in all systems and bodies. A body's temperature is most frequently used to gauge how hot or cold it is. The average kinetic energy of the particles in a system is what scientists use to define temperature.

Suppose we visualise a system and add individual particles to it. Every one of these particles is travelling in some manner at the microscopic level. The movement can be either in rotation, a straight line, or a curve. Kinetic energy is the term for this motion's energy. Thus, we may say that all those motion particles possess kinetic energy. The amount of kinetic energy increases with particle speed. The system has total energy and can be said to have a higher temperature because its average temperature measures the kinetic energy of the particles.

Temperature is often measured on an absolute scale in science. The scale of absolute temperature is Kelvin. The absolute zero point, or -273 degrees Celsius, is the lowest temperature.

Let's examine a few further Kelvin temperature numbers. At 273 Kelvin, water freezes, while at 373 Kelvin, it boils. We'll take the temperature in degree-Celsius and add 273 to get the equivalent temperature in Kelvin. We will receive the temperature in Kelvin as a result.

For instance, we must add 15 to the constant 273 to convert 15^OC to Kelvin. Thus, 273 plus 15 equals 288 Kelvin, or 15 degrees Celsius.