Contents

- Introduction to gas laws
- The relationship between pressure and volume
- The relationship between temperature and pressure
- The relationship between temperature and volume
- The ideal gas law
- Real gases and the gas laws
- The effect of a change in pressure on a gas
- The effect of a change in temperature on a gas
- The effect of a change in volume on a gas
- The applications of gas laws

Learn about the gas laws and how they affect the behavior of gases. We’ll cover Boyle’s law, Charles’ law, and the Ideal Gas Law, and explain how each of them works.

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## Introduction to gas laws

In chemistry, the gas laws are a set of intuitively obvious observations about gases, collected by Robert Boyle, Jacques Charles, and John Dalton in the late 17th and early 18th centuries. The modern form of the gas laws can be concisely stated as follows.

Boyle’s law: At constant temperature, the volume of a given amount of gas varies inversely with the applied pressure; i.e., V₁/V₂ = P₂/P₁.

Charles’s law: At constant pressure, the volume of a given amount of gas varies directly with its absolute temperature; i.e., V₁/T₁ = V₂/T₂.

Gay-Lussac’s law: At constant volume, the pressure of a given amount of gas varies directly with its absolute temperature; i.e., P₁/T₁ = P₂/T₂.

Dalton’s law: The pressure exerted by a mixture of gases is equal to the sum of the partial pressures exerted by each constituent gas.

## The relationship between pressure and volume

Gas law is the name given to a set of scientific laws that describe the behavior of gases. The most famous of these laws is the relationship between pressure and volume, which was first described by French physicist and mathematician Blaise Pascal in the 17th century.

The gas law states that, for a given mass of gas, the pressure exerted on the walls of its container is directly proportional to the volume of the container. This relationship is represented by the equation:

PV = k

where P is pressure, V is volume, and k is a constant.

This equation can be used to solve for any one of the three variables if the other two are known. For example, if you know that a gas has a pressure of two atmospheres and a volume of 10 liters, you can use the equation to calculate the value of k:

2 x 10 = k

k = 20

## The relationship between temperature and pressure

In order to understand gas law, one must first understand the relationship between temperature and pressure. Pressure is a measure of the amount of force exerted on a given area, and temperature is a measure of the average kinetic energy of the particles in a substance. The higher the temperature of a gas, the faster the particles are moving, and the more force they exert on the walls of their container. The relationship between these two properties can be represented by an equation known as the Ideal Gas Law.

The Ideal Gas Law states that PV=nRT, where P is pressure, V is volume, n is number of moles, R is the universal gas constant, and T is temperature. This equation shows that there is a direct relationship between pressure and temperature – as one increases, so does the other.

The Ideal Gas Law can be used to solve for any one of these variables when the others are known. For example, if you know that a sample of gas has a volume of 2 liters (V=2L), a pressure of 1 atmosphere (P=1atm), and contains 1 mole of particles (n=1mol), you can use the Ideal Gas Law to calculate its temperature. T=(PV)/(nR)=(1)(2)/(1)(0.08206)=24.4Kelvin.

While the Ideal Gas Law is useful for understanding the relationships between these variables, it does have some limitations. It only applies to gases that are at relatively low densities and pressures, and it does not take into account the attractive forces between molecules. Nevertheless, it provides a good approximation for many situations encountered in everyday life.

## The relationship between temperature and volume

Gas laws deal with the relationship between temperature and volume. The most common gas law is the ideal gas law, which relates these two variables along with the amount of gas present and a constant called the Universal Gas Constant. The ideal gas law is PV = nRT, where P is pressure, V is volume, n is moles of gas, R is the Universal Gas Constant, and T is temperature. This law only applies to ideal gases, which are gases that do not interact with each other. Most real-world gases behave similarly to ideal gases under certain conditions, so the ideal gas law can be used to model their behavior.

The Ideal Gas Law can be used to solve for any of the four variables if the other three are known. For example, if you know the moles of gas, temperature, and pressure, you can use the Ideal Gas Law to solve for volume. This is helpful in many real-world applications, such as designing storage tanks for compressed gases or predicting how much a gas will expand when heated.

## The ideal gas law

The ideal gas law is an equation of state that describes the behavior of a hypothetical ideal gas. It is a combination of the empirical Boyle’s law, Charles’s law, Avogadro’s law, and Gay-Lussac’s law. The ideal gas law was first stated by Émile Clapeyron in 1834 as a generalization of these empirical laws.

The ideal gas law describes the relationship between the pressure, volume, temperature, and molarity of an ideal gas. An ideal gas is one that behaves according to the assumptions of the kinetic theory of gases. These assumptions are that the collisions between atoms or molecules in an ideal gas are perfectly elastic (i.e., they do not change the kinetic energy of the particles), and that there are no interactions between particles other than collisions.

## Real gases and the gas laws

In chemistry, a gas is a matter in a state of lower density than liquid or solid. In the physical sciences, a real gas is defined as a gas which obeys the gas laws. A real gas is composed of molecules which interact with each other through van der Waals forces. The ideal gas laws describe how an idealized theoretical gas behaves. This idealization neglects the intermolecular attractive forces and tries to describe the behavior of a hypothetical perfect gas. The laws are stated in terms of an extensive property, volume, and intensive properties, temperature and pressure.

In contrast, the van der Waals equation of state considers the intermolecular attractive forces between molecules. The van der Waals equation correctly describes the behavior of real gases at low densities and near absolute zero temperature. At higher densities or temperatures closer to the critical point, other equations of state such as the virial equation are used to describe the behavior of real gases.

## The effect of a change in pressure on a gas

Gas laws deal with the relationship between pressure, temperature, and volume when it comes to gases. The most famous of these laws is probably the Ideal Gas Law, which states that when pressure and temperature are held constant, the volume of a gas is directly proportional to the amount of gas present. The Ideal Gas Law is a simplification of reality that works well under many circumstances, but doesn’t apply in all cases. In general, though, all gas laws deal with how a change in one variable affects the others.

For example, let’s say you have a sealed container of gas at a certain temperature. If you increase the pressure on that gas (by, for example, tightening the lid), then the gas will take up less space (i.e. its volume will decrease). It’s also worth noting that when you decrease the pressure on a gas, its volume will increase.

The relationship between pressure and volume is defined by Boyle’s Law, which states that when temperature is held constant, the volume of a gas is inversely proportional to its pressure. In other words, as pressure increases, volume decreases; as pressure decreases, volume increases.

This relationship can be expressed mathematically as:

PV = k

where P is pressure, V is volume, and k is a constant.

You can think of Boyle’s Law as saying that “pressure andvolume are inversely related.” This means that if you double thepressure on a fixed amount of gas, thevolume will be cut in half; ifyou halve the pressure on a fixed amountof gas, thevolume will double.

## The effect of a change in temperature on a gas

The effect of a change in temperature on a gas was first studied by Robert Boyle in the seventeenth century. He observed that when the temperature of a sample of gas is increased, the volume of the gas also increases. This relationship between temperature and volume is known as Boyle’s law.

Boyle’s law can be stated as follows: For a given mass of gas at a constant pressure, the volume of the gas is directly proportional to its temperature.

This relationship can be expressed mathematically as:

V ∝ T

or

V = kT

where V is the volume of the gas, T is the absolute temperature of the gas, and k is a proportionality constant.

Boyle’s law only applies to ideal gases, which are hypothetical gases that obey all the assumptions of the kinetic molecular theory. These assumptions include: (1) The molecules of an ideal gas are point particles with no size or mass. (2) The molecules of an ideal gas are in constant, random motion. (3) The collisions between molecules are elastic; that is, they conserve both energy and momentum. (4) There are no attractive or repulsive forces between molecules.

## The effect of a change in volume on a gas

When the volume of a gas is increased, the molecules have more room to move around. This means that they will collide with the walls of the container more often. As a result, the pressure of the gas will increase.

## The applications of gas laws

The gas laws deal with how gases behaves in relation to pressure, temperature, volume, and amount.

Boyle’s Law deals with the relationship between pressure and volume. Charles’s Law deals with the relationship between temperature and volume. The Ideal Gas Law is a combination of all three of these laws and states that PV=nRT, where P is pressure, V is volume, n is moles (amount), R is the universal gas constant, and T is temperature.

The Ideal Gas Law is important because it allows scientists to predict the behavior of gases under a variety of conditions. For example, if you know the molar mass of a gas (n), you can use the Ideal Gas Law to determine how many molecules are in a sample of gas. This is helpful for studying chemical reactions at the atomic level.

The Ideal Gas Law also tells us that increasing the pressure on a gas will decrease its volume. This relationship is helpful for understanding how different atmospheric conditions can affect things like weather patterns or airplane flights. For example, if you know that a storm is coming and will increase the atmospheric pressure, you can expect the weather to be colder than usual because cold air takes up less space than warm air.