Kara Sears
The gas laws are a group of laws that govern the behaviour of gases by providing relationships between the volume occupied by the gas, the pressure exerted by a gas on the walls of its container, the absolute temperature of the gas, and the amount of gaseous substance (or the number of moles of gas). 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. The combination of several empirical gas laws led to the development of the ideal gas law. The ideal gas law was later found to be consistent with atomic and kinetic theory. The ideal gas law gives the relationship between four different variables, namely, pressure, volume, number of moles or molecules, and temperature.
| Characteristics | Values |
|---|---|
| Boyle's Law | The volume of a given amount of gas held at constant temperature varies inversely with the applied pressure when the temperature and mass are constant. |
| Charles' Law | The volume of gas increases as the temperature increases, assuming a constant pressure. |
| Avogadro's Law | The volume of gas increases as the amount of gas increases, assuming constant temperature and pressure. |
| Gay-Lussac's Law | The pressure exerted by a given mass and constant volume of an ideal gas on the walls of its container is directly proportional to its absolute temperature. |
| Henry's Law | For a constant temperature, the amount of dissolved gas in a liquid is directly proportional to the partial pressure of that gas in contact with its surface. |
| Combined Gas Law | Obtained by combining Boyle's Law, Charles' Law, and Gay-Lussac's Law. It shows the relationship between pressure, volume, and temperature for a fixed mass of gas. |
| Ideal Gas Law | The combination of Boyle's Law, Charles' Law, Avogadro's Law, and Gay-Lussac's Law. It relates four variables: pressure, volume, number of moles, and temperature. |
| General Gas Equation | Used when there are multiple sets of conditions (pressure, volume, number of gas, and temperature). |
| Gas Constant (R) | The numerical value of R depends on experimental results and the units used. In some cases, R is given as 8.3145 Joules·mol-1·K-1, and in others as 8.3144598 (kPa∙L)/(mol∙K). |
| Boltzmann Constant (k) | Used in the Ideal Gas Law equation, with a value of 1.381×10−23J·K−1 in SI units. |
| Proportionality Constant (k2) | Used in Charles' Law equation, it is not the same as the proportionality constants in other gas law equations. |
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What You'll Learn
Boyle's Law
Gas laws describe the behaviour of gases under fixed pressure, volume, the 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 approximations for all gases.
The law can be derived from the kinetic theory of gases, assuming a perfect (ideal) gas. It can be experimentally verified using a pressure gauge and a variable volume container. For example, suppose we have a theoretical gas confined in a jar with a piston at the top. The initial state of the gas has a volume of 4.0 cubic meters and a pressure of 1.0 kilopascal. Weights are slowly added to the top of the piston to increase the pressure, and the volume decreases to 3.0 cubic meters when the pressure is 1.33 kilopascals. The product of pressure and volume remains constant (4 x 1.0 = 3 x 1.33).
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Charles' Law
The law states that the volume of a given mass of gas varies directly with the absolute temperature of the gas when pressure is kept constant. In other words, as the temperature of a gas increases, so does its volume, and vice versa. This relationship can be expressed mathematically as:
> V ∝ T
Where V is the volume and T is the absolute temperature. It's important to note that the Kelvin scale must be used for temperature measurements, as zero on the Kelvin scale corresponds to a complete stoppage of molecular motion.
> T2 = (T1 * V2) / V1
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Avogadro's Law
Gas laws describe the behaviour of gases under fixed pressure, volume, amount of gas, and absolute temperature conditions. The three fundamental gas laws—Boyle's Law, Charles' Law, and Avogadro's Law—outline the relationship between pressure, temperature, volume, and amount of gas.
The mathematical expression of Avogadro's Law is:
\[ V = k \times n \: \: \: \text{and} \: \: \: \frac{V_1}{n_1} = \frac{V_2}{n_2}\nonumber \]
Where \(n\) is the number of moles of gas and \(k\) is a constant. This law is evident when blowing up a balloon; as more gas is added, the volume of the balloon increases.
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Gay-Lussac's Law
The mathematical expression of Gay-Lussac's Law can be written as P / T = constant or Pi / Ti = Pf / Tf, where P is pressure and T is absolute temperature. This formula illustrates that as the temperature of a gas increases, its pressure also increases, assuming the volume does not change. Conversely, if the temperature decreases, the pressure decreases proportionally.
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Ideal Gas Law
The ideal gas law, or the general gas equation, is a combination of three fundamental gas laws: Boyle's Law, Charles' Law, and Avogadro's Law. It describes the behaviour of gases under fixed pressure, volume, amount of gas, and absolute temperature conditions.
The ideal gas law equation is as follows:
$$\frac{PV}{nRT} = 1$$
Where:
- P = Pressure
- V = Volume
- N = Number of moles
- R = Universal Gas Constant
- T = Absolute Temperature
The universal gas constant, R, is determined by experimental results and its value changes with units. When using the ideal gas law to calculate any property of a gas, it is important to match the units to the gas constant chosen. The temperature must always be in Kelvin.
The ideal gas law can be used to solve for any variable in the equation. For example, to solve for pressure, the equation can be rearranged as follows:
$$P = \frac{nRT}{V}$$
The ideal gas law is a good approximation for most gases under moderate pressure and temperature, despite having several limitations. It is a useful tool for understanding the relationships between pressure, volume, temperature, and the amount of gas.
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