Cecily Zamora
Gas laws describe the physical properties and behaviour of gases under various conditions of temperature, pressure, and volume. Gay-Lussac's Law, for example, states that the pressure exerted by a given amount of gas held at a constant volume is directly proportional to its Kelvin temperature. Similarly, Charles' Law, which describes the relationship between volume and temperature when pressure and the amount of gas are held constant, also uses Kelvin temperature. The use of Kelvin in gas laws is attributed to its simplicity and consistency, as it avoids negative numbers and arbitrary zero points seen in other temperature scales.
| Characteristics | Values |
|---|---|
| Gas Laws that use Kelvin | Charles' Law, Gay-Lussac's Law, Combined Gas Law, Ideal Gas Law |
| Kelvin's role in Charles' Law | States that the volume of an ideal gas is directly proportional to its Kelvin temperature |
| Kelvin's role in Gay-Lussac's Law | The pressure of a gas held at a constant volume is directly proportional to the Kelvin temperature |
| Reason for using Kelvin | Simplifies calculations by avoiding negative numbers and keeping the scale neat and simple |
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What You'll Learn
Charles' Law
Charles's law, also known as the law of volumes, describes the relationship between the temperature and volume of a gas. It states that the volume of a given mass of gas varies directly with its absolute temperature when the pressure is kept constant. This means that as the temperature of a gas increases, its volume will also increase proportionally, and conversely, a decrease in temperature will lead to a decrease in volume.
The law was formulated by French physicist Jacques Charles in the 1780s and later confirmed by Joseph-Louis Gay-Lussac in 1802. Charles's law can be expressed mathematically as a relationship between the initial and final volume and temperature of a gas. This equation can be used to calculate any one of the four quantities if the other three are known. It is important to note that the temperatures must be expressed in Kelvin for the direct relationship to hold. The Kelvin scale is used because zero on this scale corresponds to a complete stoppage of molecular motion, which is known as absolute zero.
Charles's law is a special case of the general gas law and can be derived from the kinetic theory of gases. The kinetic theory relates the macroscopic properties of gases, such as pressure and volume, to the microscopic properties of the molecules, such as mass and speed. To derive Charles's law from kinetic theory, a microscopic definition of temperature is necessary, which can be taken as the temperature being proportional to the average kinetic energy of the gas molecules.
Charles's law has implications for the behaviour of gases at extremely low temperatures. According to Gay-Lussac's figures, the volume of a gas will descend to zero at a temperature of −266.66 °C or −273.15 °C. However, Gay-Lussac clarified that this conclusion only holds true if the compressed vapours remain in an elastic state, which requires a sufficiently elevated temperature to resist the pressure that tends to make them assume a liquid state. At absolute zero, the gas possesses zero energy, and the molecules restrict motion.
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Gay-Lussac's Law
Gay-Lussac's work covered some comparison between pressure and temperature, as well as volume and temperature. Gay-Lussac's investigations into the relationship between volume and temperature were published in 1802, and he attributed his findings to Jacques Charles, as he used much of Charles's unpublished data from 1787. Gay-Lussac also discovered the law of combining volumes of gases, which was published in 1809.
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Celsius vs Kelvin
The Kelvin and Celsius scales are two systems used to measure temperature. They follow the same unit difference between each scale but with different starting points. The Kelvin scale is defined in terms of energy, with every 1 Kelvin (K) change in temperature corresponding to a thermal energy change of 1.380649 x10^-23 joules. The Celsius scale, on the other hand, was previously defined by two points: the melting point of ice at 0 °C and the boiling point of water at 100 °C. However, since 1954, the Celsius scale has been defined by absolute zero (-273.15 °C) and the triple point of specially prepared water (0.01 °C).
The key distinction between the Celsius and Kelvin scales lies in their zero points. Absolute zero, the temperature at which no heat energy remains in a substance, is defined as 0 Kelvin and -273.15 degrees Celsius. This means that to convert from Kelvin to Celsius, you subtract 273.15 from the Kelvin temperature. For example, 295 K is equal to 21.85 °C. Conversely, to convert from Celsius to Kelvin, you add 273.15 to the Celsius temperature. For instance, 25 °C is equivalent to 298.15 K.
The Celsius scale is named after the Swedish astronomer Anders Celsius (1701-1744), who devised a similar temperature scale. Initially, the Celsius scale was known as the centigrade scale. The Kelvin scale, on the other hand, is named after the physicist William Thomson, also known as Lord Kelvin. In the early 20th century, the Kelvin scale was sometimes referred to as the "absolute Celsius" scale, reflecting the fact that it counts from absolute zero rather than the freezing point of water.
The choice between using Celsius or Kelvin depends on the context and the specific requirements of the situation. The Celsius scale is commonly used in everyday life and in fields such as weather forecasting, as it aligns with the freezing and boiling points of water under standard atmospheric pressure. The Kelvin scale, being the SI base unit of temperature, is often used in scientific contexts, particularly in thermodynamics and physics, where absolute zero and the concept of thermal energy are important.
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Combined Gas Law
The combined gas law combines Boyle's Law, Charles' Law, and Gay-Lussac's Law. It states that the ratio of the product of pressure and volume to the absolute temperature of a gas is equal to a constant. The law is expressed as follows:
> $\frac{P \times V}{T} = k$
Here, $P$ is pressure, $V$ is volume, $T$ is absolute temperature, and $k$ is a constant. The combined gas law is derived from the fact that only the amount of gas is held constant, while pressure, volume, and temperature can change. This is unlike the individual gas laws, where only one of these variables can change at a time.
The combined gas law has practical applications when dealing with gases at ordinary temperatures and pressures. It is used in thermodynamics and fluid mechanics, such as in the modern refrigerator, where the gas laws are used to remove heat from a system. However, like other gas laws based on ideal behaviour, the accuracy of the combined gas law decreases at high temperatures and pressures.
The combined gas law can be used to solve problems involving the "before and after" conditions of a gas. For example, consider the following problem:
> $2.00 \: \text{L}$ of a gas at $35^\text{o} \text{C}$ and $0.833 \: \text{atm}$ is brought to standard temperature and pressure (STP). What will be the new gas volume?
To solve this problem, we can use the combined gas law equation:
> $V_2 = \frac{P_1 \times V_1 \times T_2}{P_2 \times T_1}$
Substituting the given values and STP values ($273 \: \text{K} and $1 \: \text{atm}$) into the equation, we get:
> $V_2 = \frac{0.833 \: \text{atm} \times 2.00 \: \text{L} \times 273 \: \text{K}}{1.00 \: \text{atm} \times 308 \: \text{K}} = 1.48 \: \text{L}$
Therefore, the new gas volume at STP is $1.48 \: \text{L}$.
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Gas Molecules and Pressure
The behaviour of gases and their response to changes in pressure, temperature, volume, and quantity are described by gas laws. These laws are named after their discoverers and are essential in understanding the characteristics of gases.
The pressure of a gas is influenced by four factors: the quantity of gas, its volume, temperature, and the number of gas particles. The pressure inside a container is directly proportional to the number of gas particles inside. For instance, if the amount of gas in a rigid container is increased, the pressure rises as the gas particles strike the container walls more frequently. Conversely, reducing the quantity of gas in a container leads to a decrease in pressure.
The volume of a container also affects the pressure of a gas. When the volume of a container is decreased, the gas molecules have less space to move, causing them to collide with the container walls more often, which increases pressure. Conversely, increasing the volume of a container leads to a decrease in pressure as the gas molecules have more space to move and strike the walls less frequently.
Gay-Lussac's Law states that the pressure of a fixed volume of gas is directly proportional to its temperature in Kelvin. When gas is heated, its molecules gain energy and move faster, resulting in more collisions with the container walls and increased pressure. Conversely, cooling the gas molecules causes them to slow down, reducing the frequency of collisions and decreasing the pressure.
Boyle's Law describes the inverse relationship between the volume of a gas and its pressure when the temperature and mass are held constant. As the volume of a gas decreases, its molecules strike the container walls more often, increasing the pressure. Conversely, increasing the volume of a gas results in decreased pressure as the molecules have to travel a greater distance to strike the walls, causing them to hit the walls less frequently.
Understanding these gas laws and their relationships is crucial in various applications, from adjusting basketball pressure to ensuring the safe heating of canned food.
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Frequently asked questions
Kelvin keeps things simpler and neater. For example, Gay-Lussac's Law, which states that the pressure of a given amount of gas held at a constant volume is directly proportional to the Kelvin temperature, would result in negative numbers if other temperature scales were used.
Gay-Lussac's Law states that the pressure of a given amount of gas held at a constant volume is directly proportional to the Kelvin temperature. In other words, if you heat a gas, you give the molecules more energy, so they move faster and impact the walls of their container more, increasing the pressure.
Charles' Law gives 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, and if the Kelvin temperature is decreased, the volume of the gas decreases.
The formula for Charles' Law is: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$.
The units of the gas constant are given using atmospheres, moles, and Kelvin. Therefore, it is important to convert values given in other temperature or pressure scales to Kelvin to ensure accurate calculations.
