Anaya Nolan
The ideal gas law, also known as the general gas equation, describes the state of a hypothetical ideal gas. It is a useful approximation of the behaviour of many gases under various conditions, although it has limitations. The ideal gas law was first stated by Benoît Paul Émile Clapeyron in 1834 as a combination of Boyle's Law, Charles's Law, Avogadro's Law, and Gay-Lussac's Law. The ideal gas law can be used to determine how changes in pressure, temperature, volume, and the number of moles of a substance affect a system. While the ideal gas law is a useful tool, it is important to note that it assumes that gas molecules have negligible volume compared to the container they are in, move randomly, and collide in completely elastic collisions.
| Characteristics | Values |
|---|---|
| State of a gas | Determined by its pressure, volume, and temperature |
| Gas constant | R |
| SI units | p is measured in pascals, V in cubic metres, n in moles, and T in kelvins |
| Gas constant R value | 8.314 J/(mol·K) = 1.989 ≈ 2 cal/(mol·K), or 0.0821 L⋅atm/(mol⋅K) |
| Standard condition of temperature and pressure | STP, with a universal value of 1 atm (pressure) and 0°C |
| Volume of a gas at STP | 1 mole of gas will take up 22.4 L of the volume of the container |
| Temperature units | Always in SI units of Kelvin (K) rather than Celsius (C) |
| Amount of gas units | Always measured in moles |
| Gas pressure and volume units | May vary, but must be converted to the appropriate units if necessary |
| Gas constant R | Will change when dealing with different units of pressure and volume |
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What You'll Learn
The ideal gas law
It is important to recognize that the ideal gas law is a simplification and has certain limitations. It neglects molecular size and intermolecular attractions, which become more significant at higher densities and lower temperatures. For gases that deviate from ideal conditions, more complex equations, such as the van der Waals equation, are used to account for these deviations.
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Gas constant, R
The gas constant, also known as the universal gas constant, molar gas constant, or ideal gas constant, is denoted by the symbol R or R. It is a physical constant that features in many fundamental equations in the physical sciences, such as the ideal gas law, the Arrhenius equation, and the Nernst equation. The gas constant is defined as the product of pressure and volume, expressed in units of energy per temperature increment per amount of substance. It is the constant of proportionality that relates the energy scale in physics to the temperature scale and the scale used for the amount of substance.
The value of the gas constant R is given by R = 8.3144598(48) J⋅mol^−1⋅K^−1 or R = 8.314 J / (mol·K) when using SI units. However, the value of the gas constant can be expressed in various units, including:
- R = 0.08205 L·atm/(mol·K)
- R = 8.3145 L·kPa/(mol·K)
- R = 8.3145 J/(mol·K)
- R = 1.987 cal/(mol·K)
- R = 62.364 L·torr/(mol·K)
The specific gas constant of a gas or mixture of gases (Rspecific) is given by the molar gas constant divided by the molar mass (M) of the gas or mixture. The gas constant R is a universal constant for all gases, and its values are typically listed in the "Physical Constants" sections of textbooks and handbooks. It is important to use the proper numerical value for the gas constant R according to the units of the parameters in the equation.
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Graham's law
Mathematically, Graham's law can be stated as:
> Rate1 / Rate2 = √(M2 / M1)
Where:
- Rate1 is the rate of effusion for the first gas (volume or number of moles per unit time)
- Rate2 is the rate of effusion for the second gas
- M1 is the molar mass of gas 1
- M2 is the molar mass of gas 2
For example, consider two gases, gas 1 and gas 2, with the same temperature and pressure. If the molecular weight of gas 1 is four times that of gas 2, then gas 1 will diffuse through a porous plug or escape through a small pinhole in a vessel at half the rate of gas 2. This is because heavier gases diffuse more slowly.
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Dalton's law of partial pressures
Gas laws are often illustrated using pure gases. However, gases are frequently found as mixtures. For instance, the air we breathe is a mixture of 78% nitrogen, 21% oxygen, and 1% other gases such as carbon dioxide, argon, and hydrogen. Chemist John Dalton recognized this issue and formulated Dalton's law of partial pressures, which states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases.
Mathematically, the pressure of a mixture of non-reactive gases can be defined as:
> ! [equation: p_{total} = p_1 + p_2 + p_3 + ... + p_n](https://render.githubusercontent.com/render/math?math=p_%7Btotal%7D%20%3D%20p_1%20%2B%20p_2%20%2B%20p_3%20%2B%20...%20%2B%20p_n)
Where p1, p2, ..., pn represent the partial pressures of each component.
In a gas mixture at the same temperature, all molecules of each gas have the same kinetic energy and collide with the same force. Each gas exerts pressure on the sides of the container, and its contribution to the total pressure represents a partial amount of the total pressure. This pressure exerted by one gas in a mixture of gases is called that gas's partial pressure.
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Charles's law
The law describes how a gas expands as the temperature increases, and conversely, how a decrease in temperature will lead to a decrease in volume. This relationship can be observed when a container of confined gas is heated, and its molecules increase in kinetic energy, pushing outward and resulting in an increase in volume.
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Frequently asked questions
In the SI system, p (pressure) is measured in pascals, V (volume) is measured in cubic metres, n (number density of molecules) is measured in moles, and T (temperature) is measured in kelvins.
The universal value of STP is 1 atm (pressure) and 0°C (273 Kelvin).
R is the ideal gas constant. Its value will change depending on the units of pressure and volume used. For example, if you use the value of R = 0.082057 L atm/mol-1K-1, your units for pressure, volume, and temperature must be atm, liters, and Kelvin, respectively.
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