Gavin Howe
Gas laws are a set of physical laws that model the behaviour of gases under varying conditions of pressure, volume, temperature, and quantity. The basic gas laws were discovered by the end of the 18th century, with Boyle's Law, Charles' Law, and Gay-Lussac's Law forming the foundation. These laws describe the relationships between pressure, volume, and temperature for a fixed mass of gas. However, the question arises: can these gas laws be violated? The answer lies in the distinction between ideal gases and real gases. While the gas laws are primarily based on ideal gases, real gases may deviate from these laws under certain conditions, such as high pressure and low temperature, where the assumptions of negligible intermolecular interactions and relative size no longer hold.
| Characteristics | Values |
|---|---|
| Ideal gas | A theoretical gas composed of randomly moving particles with no force between them |
| Real gas | Violates the ideal gas law at low temperatures and high pressure due to the force of attraction or repulsion between gas molecules |
| Gas laws | Describe the behaviour of gases under fixed pressure, volume, amount of gas, and absolute temperature conditions |
| Basic gas laws | Discovered by the end of the 18th century, combining several empirical gas laws to form the ideal gas law |
| Combined gas law | Also known as the general gas equation, it combines Boyle's law, Charles's law, and Gay-Lussac's law to show the relationship between pressure, volume, and temperature for a fixed mass of gas |
| Avogadro's law | Provides a relationship between the volume occupied by a gas and the amount of gaseous substance; states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules |
| Boyle's law | Describes the relationship between the pressure and volume of a gas at a constant temperature; the volume of a gas is inversely proportional to its pressure at a constant temperature |
| Charles's law | At constant pressure, the volume of a gas is directly proportional to its absolute temperature for a fixed mass of gas |
| Gay-Lussac's law | Describes the relationship between temperature and pressure at constant volume; the pressure of a gas is directly proportional to its temperature |
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What You'll Learn
Boyle's Law and the relationship between volume and pressure
Gas laws describe the behaviour of gases under fixed pressure, volume, amount of gas, and absolute temperature conditions. The basic gas laws were discovered by the end of the 18th century when scientists found out that relationships between pressure, volume, and temperature of a sample of gas could be obtained, which would hold as an approximation for all gases.
Boyle's law, published in 1662, states that, at a constant temperature, the product of the pressure and volume of a given mass of an ideal gas in a closed system is always constant. In other words, the pressure exerted by a gas (of a given mass, kept at a constant temperature) is inversely proportional to the volume occupied by it. This means that as the volume increases, the pressure decreases, and vice versa, as long as the temperature and the quantity of gas are kept constant.
The relationship between pressure and volume was first noted by Richard Towneley and Henry Power in the 17th century. Robert Boyle confirmed their discovery through experiments and published the results. Boyle's law is based on experiments with air, which he considered to be a fluid of particles at rest between small invisible springs.
Boyle's law can be expressed mathematically as: PV = k, where P is the pressure exerted by the gas, V is the volume occupied by it, and k is a constant value representative of the temperature of the system and the amount of gas. This equation can be used to predict the increase in pressure exerted by a gas on the walls of its container when the volume of its container is decreased, and its quantity and absolute temperature remain unchanged. For example, when a filled balloon is squeezed, the volume occupied by the air inside the balloon decreases, resulting in an increase in the pressure exerted by the air on the balloon, which eventually pops it.
Boyle's law is significant because it explains how gases behave and proves that gas pressure and volume are inversely proportional. This law can be verified experimentally using a pressure gauge and a variable volume container.
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Charles' Law and the relationship between volume and temperature
Gas laws describe the behaviour of gases under fixed pressure, volume, amount of gas, and absolute temperature conditions. The basic gas laws were discovered by the end of the 18th century when scientists found out that relationships between pressure, volume and temperature of a sample of gas could be obtained which would hold to approximation for all gases.
Charles' Law, or the law of volumes, was founded in 1787 by Jacques Charles. It states that, for a given mass of an ideal gas at constant pressure, the volume is directly proportional to its absolute temperature, assuming a closed system. The absolute temperature is the temperature measured with the Kelvin scale. The Kelvin scale must be used because zero on the Kelvin scale corresponds to a complete stop of molecular motion.
Charles' Law can be used to determine the current volume of a gas if its pressure and temperature are known. It can also be used to compare changing conditions for a gas. For example, if the initial volume and temperature of a gas are known, the law can be used to calculate the final volume and temperature after the gas has been heated.
The mathematical relationship of Charles' Law can be represented by the following equation:
> $\frac{V_1}{T_1} = \frac{V_2}{T_2}$
Where $V_1$ and $T_1$ are the initial volume and temperature of a gas, and $V_2$ and $T_2$ are the final volume and temperature. This equation can be used to calculate any one of the four variables if the other three are known.
Charles' Law demonstrates the relationship between volume and temperature if the pressure and the amount of gas are held constant. If the Kelvin temperature of a gas is increased, the volume of the gas increases. Conversely, if the Kelvin temperature of a gas is decreased, the volume of the gas decreases. This means that the volume of a gas is directly proportional to its Kelvin temperature.
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Avogadro's Law and the relationship between volume and the amount of gas
Gas laws describe the behaviour of gases under fixed pressure, volume, amount of gas, and absolute temperature conditions. The basic gas laws were discovered by the end of the 18th century when scientists found out that relationships between pressure, volume, and temperature of a sample of gas could be obtained, which would hold as an approximation for all gases.
Avogadro's law, or Avogadro's hypothesis, is an experimental gas law that relates the volume of a gas to the amount of substance of gas present. It is a specific case of the ideal gas law. Avogadro's law states that "equal volumes of all gases, at the same temperature and pressure, have the same number of molecules". This means that for a given mass of an ideal gas, the volume and amount (in moles) of the gas are directly proportional when the temperature and pressure are constant.
Avogadro's law can be used to calculate the quantity of gas in a container. It gives the relationship between volume and the amount of gas in moles when pressure and temperature are held constant. If the amount of gas in a container is increased, the volume increases, and if the amount of gas is decreased, the volume decreases. This relationship is directly proportional, and the equation for calculations is:
> V∝n
Where V is the volume and n is the number of moles.
Avogadro's law is a direct mathematical relationship. If one gas variable (V or n) changes in value (either up or down), the other variable will also change in the same direction. For example, if 0.00810 mol of neon gas at a particular temperature and pressure occupies a volume of 214 mL, Avogadro's law can be used to calculate what volume 0.00684 mol of neon gas would occupy under the same conditions.
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Ideal Gas Law and its assumptions
The ideal gas law is a mathematical equation that combines several different laws to describe the behaviour of gases. It was first proposed by Emile Clapeyron in 1834. The law accounts for pressure (P), volume (V), the number of moles of gas (n), and temperature (T), with an added proportionality constant, the ideal gas constant (R). The ideal gas law assumes that gases behave ideally, adhering to the following characteristics:
- The collisions occurring between molecules are elastic and their motion is frictionless, meaning that the molecules do not lose energy.
- The total volume of the individual molecules is significantly smaller than the volume occupied by the gas.
- There are no intermolecular forces acting between the molecules or their surroundings.
- The molecules are constantly in motion, and the distance between two molecules is significantly larger than the size of an individual molecule.
As a result of these assumptions, an ideal gas would not form a liquid at room temperature. However, many gases deviate from ideal behaviour by becoming liquids at room temperature. The ideal gas law is a good approximation for most gases under moderate pressure and temperature, but it does not account for various intermolecular effects.
The ideal gas law was derived from the work of several scientists, including Evangelista Torricelli, Robert Boyle, Jacques Charles, Joseph Gay-Lussac, and Amedeo Avogadro. These scientists discovered relationships between the pressure, volume, and temperature of a sample of gas, which led to the development of the ideal gas law.
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Gay-Lussac's Law and the relationship between temperature and pressure
Gay-Lussac's Law, also known as the pressure law, describes the relationship between the pressure and temperature of a gas when there is a constant volume of gas in a closed and rigid container. It is one of the four general gas laws, along with Charles's, Boyle's, and Avogadro's Laws, that relate the four basic characteristic properties of gases to each other. Gay-Lussac's Law states that the pressure of a given mass of gas varies directly with the absolute temperature of the gas when the volume is kept constant.
The French chemist Joseph Gay-Lussac (1778-1850) discovered the relationship between the pressure of a gas and its absolute temperature. The mathematical expression for Gay-Lussac's Law is similar to that of Charles's Law:
\[ \frac{P}{T} \: \: \: \text{and} \: \: \: \frac{P_1}{T_1} = \frac{P_2}{T_2}\]
Where P is the pressure, and T is the absolute temperature. The equation shows that the pressure of a gas is directly proportional to its temperature when the volume is held constant. In other words, as the temperature of a gas in a rigid container increases, the pressure of the gas also increases due to the increase in kinetic energy, resulting in the molecules of gas striking the walls of the container with more force.
Gay-Lussac's Law can be used to calculate changes in pressure or temperature. For example, it can explain why a gas cylinder's pressure gauge registers a higher pressure on a hot day than on a cold day. It is important to note that Gay-Lussac's Law, like other gas laws, assumes ideal gas behaviour, neglecting various intermolecular effects. However, it is a good approximation for most gases under moderate pressure and temperature.
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