Keith Mack
Gay-Lussac's Law, discovered by French chemist Joseph Gay-Lussac in 1808, describes the relationship between the pressure and temperature of a gas when the volume of gas is held constant. The law states that the pressure of a given mass of gas varies directly with its absolute temperature. To apply Gay-Lussac's law, temperatures must first be converted to Kelvin. This can be done using the formula T(in Kelvin) = T(in Celsius) + 273.15. For example, 20°C = 293.15 K. Once temperatures have been converted to Kelvin, the formula for Gay-Lussac's law can be used to calculate the final pressure. This formula is p₂ = p₁ / T₁ x T₂. So, can you use Celsius in Gay-Lussac's Law? The answer is yes, but temperatures must first be converted to Kelvin before applying the formula.
| Characteristics | Values |
|---|---|
| What is Gay-Lussac's Law? | A mathematical relationship between pressure and temperature when volume and amount are held constant. |
| Who discovered it? | French chemist Joseph Gay-Lussac (1778-1850) |
| When was it discovered? | Around 1808 and published in 1809 |
| What is the formula? | P / T = constant or Pi / Ti = Pf / Tf |
| What is the unit of temperature? | Kelvin |
| Can you use Celsius? | Yes, but it must be converted to Kelvin |
| What is the relationship between pressure and temperature? | Directly proportional |
| What happens when the temperature increases? | Pressure increases |
| What happens when the temperature decreases? | Pressure decreases |
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What You'll Learn
Gay-Lussac's Law and temperature increase
Gay-Lussac's Law states that the pressure exerted by a given mass of gas is directly proportional to its absolute temperature 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 of Gay-Lussac's law can be written as P ∝ T for gases of fixed mass kept at constant volume. This means that the pressure of a gas (kept at constant volume) reduces constantly as it is cooled until the gas eventually undergoes condensation and becomes a liquid. Conversely, increasing the temperature will result in a proportional increase in pressure. This is why pressurised containers, like aerosol cans, have warning labels stating that they must be kept away from fire and stored in a cool environment.
Gay-Lussac's Law can be used to calculate the unknown pressure (P2) of a gas when its temperature is increased. The temperatures must first be converted to Kelvin. The formula for calculating the change in pressure is:
> Final pressure (P2) = (P1T2)/T1
Gay-Lussac's Law is very similar to Charles's Law, with the only difference being the type of container. Charles's Law uses a flexible container, while Gay-Lussac's Law uses a rigid container.
Gay-Lussac's Law is sometimes used to refer to Joseph-Louis Gay-Lussac's law of combining volumes of gases, which was discovered in 1808 and published in 1809. However, in this context, we are referring to the proportionality of the volume of a gas to its absolute temperature at constant pressure, which was published in 1802.
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Gay-Lussac's Law and pressure increase
Gay-Lussac's Law gives the relationship between pressure and temperature when volume and amount are held constant. It states that the pressure exerted by a given mass of gas is directly proportional to its absolute temperature when the volume is kept constant. This means that an increase in temperature will lead to an increase in pressure, and a decrease in temperature will lead to a decrease in pressure.
Gay-Lussac's Law is often used to calculate the unknown pressure of a gas when its temperature is changed. The mathematical expression for Gay-Lussac's Law is:
> \\( \frac{P}{T} \: \: \: \text{and} \: \: \: \frac{P_1}{T_1} = \frac{P_2}{T_2} \\)
Where P is pressure and T is temperature. For example, if the absolute temperature of a fixed amount of gas is doubled at a constant volume, the pressure will also double. This relationship between pressure and temperature can be observed when a car tire is heated during driving, leading to an increase in tire pressure.
Gay-Lussac's Law is similar to Charles's Law, with the primary difference being the type of container used. Gay-Lussac's Law is typically applied to a rigid container, while Charles's Law involves a flexible container. Additionally, Gay-Lussac's Law focuses on the relationship between pressure and temperature, whereas Charles's Law relates volume and temperature.
While Gay-Lussac's Law is typically associated with the Kelvin temperature scale, it can also be applied using Celsius temperatures. For example, when calculating the rate of expansion of gases, Gay-Lussac used the formula:
> \\( \Delta V/V = \alpha \Delta T \\)
Where \\( \Delta V/V \\) represents the relative expansion and \\( \alpha \\) is the rate of expansion. For air, he found a relative expansion of 37.50% and a value of \\( \alpha = 37.50%/100 °C\), indicating that absolute zero was approximately 266.66 °C below 0 °C.
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Gay-Lussac's Law and Charles' Law
Gay-Lussac's Law and Charles's Law are two of the four gas laws, along with Boyle's Law and Avogadro's Law, that describe how gases behave. Gay-Lussac's Law, discovered by French chemist and physicist Joseph-Louis Gay-Lussac, states the relationship between the pressure of a gas and its absolute temperature when volume is kept constant. It is a direct mathematical relationship, meaning that when one variable between pressure and temperature increases, the other variable also increases, while the constant K remains the same.
Gay-Lussac's Law can be used to solve for the unknown pressure of a gas when its temperature is changed. The formula for this law is ΔV/V = αΔT, where ΔV/V is the rate of expansion and αΔT is the rate of expansion per degree Celsius. This formula can be used to calculate the unknown pressure by rearranging the equation algebraically and substituting the known quantities. The temperature must first be converted to Kelvin.
Charles's Law, discovered by French physicist Jacques Charles in the 1780s, describes the relationship between the volume and temperature of a gas when pressure and the amount of gas are held constant. It states that if the Kelvin temperature of a gas is increased, the volume of the gas increases, and if the temperature is decreased, the volume decreases. Charles's Law can be observed in everyday life, such as in the use of a turkey thermometer, where the air inside the thermometer expands as the temperature rises, causing the top to pop up when the meat is cooked.
Gay-Lussac's Law and Charles's Law are similar, with the primary difference being the type of container used in experiments. Charles's Law uses a flexible container, while Gay-Lussac's Law uses a rigid container. Gay-Lussac's work built upon that of Jacques Charles, as he utilised Charles's unpublished data from 1787.
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Gay-Lussac's Law and Avogadro's Law
$$
\frac{P_1}{T_1} = \frac{P_2}{T_2} \text{ at constant } V \text{ and } n
$$
Where $P_1$ and $T_1$ are initial pressure and temperature, and $P_2$ and $T_2$ are final pressure and temperature. This law is applicable when the volume and amount of gas are held constant. In other words, if the temperature of a container increases, the pressure increases, and vice versa.
Gay-Lussac's Law can be used in conjunction with other gas laws, such as Boyle's Law, to solve for unknown pressures or temperatures. For example, if you have a car tyre with a certain pressure and temperature, and the tyre heats up during driving, you can use Gay-Lussac's Law to calculate the new pressure. This law also has practical applications, such as explaining why pressurised containers have warning labels to keep them away from fire.
Avogadro's Law, on the other hand, was proposed by Amedeo Avogadro in 1811. It states that at the same temperature and pressure, equal volumes of different gases contain the same number of gas particles or moles. This law introduces the variable for the amount of gas, which is related to the number of moles (1 mole = 6.022 x 10^23 particles). Avogadro's Law can be expressed mathematically as:
$$
\text{Volume} \propto \text{Number of moles}
$$
Avogadro's Law is significant because it was the first time that the amount of gas, in terms of moles, was introduced as a variable in a gas law. It also helped to name the number of things in a mole as "Avogadro's number".
In summary, Gay-Lussac's Law establishes the relationship between pressure and temperature for a fixed mass of gas at a constant volume, while Avogadro's Law focuses on the relationship between volume and the number of moles of gas at constant temperature and pressure. Both laws contribute to our understanding of gas behaviour and have practical applications in various fields, including chemistry and physics.
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Gay-Lussac's Law and calculations
Gay-Lussac's Law gives the relationship between pressure and temperature when volume and amount are held constant. In simple words, if the temperature of a container is increased, the pressure increases, and if the temperature is decreased, the pressure decreases.
Gay-Lussac's Law is a direct mathematical relationship. This means that there are two connected values, and when one (either pressure or temperature) goes up, the other also increases. The constant K remains the same value. The mathematical expression of Gay-Lussac's law can be written as P1/T1 = k (initial pressure/ initial temperature = constant) and P2/T2 = k (final pressure/ final temperature = constant).
Gay-Lussac's Law is very similar to Charles's Law, with the only difference being the type of container. The container in a Charles's Law experiment is flexible, while it is rigid in a Gay-Lussac's Law experiment. Gay-Lussac's Law can be used to solve for the unknown pressure (P2). The temperatures must first be converted to Kelvin. The equation is then rearranged algebraically to solve for P2. The known quantities are then substituted into the equation and solved.
Gay-Lussac's Law can be used with temperatures in degrees Celsius. For example, if the temperature of a gas in a container is increased to 127.0 °C, Gay-Lussac's Law can be used to determine the new pressure.
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Frequently asked questions
Yes, but the temperatures must first be converted to the absolute scale, Kelvin.
The formula to convert Celsius to Kelvin is: Kelvin = Celsius + 273.15.
Sure, here's an example: If 10.0 L of oxygen exerts 97.0 kPa at 25 degrees Celsius, what temperature (in Celsius) is needed to change its pressure to standard pressure? First, you need to know standard pressure, which is 101.325 kPa. Then, use the formula to convert Celsius to Kelvin: T₁ = 25°C = 298.15 K. Finally, rearrange Gay-Lussac's law formula to estimate the final temperature: T₂ = T₁ × p₂ / p₁ = 298.15 K × 101.325 kPa / 97.0 kPa = 308.4 K. Using the correct number of significant figures, the temperature is 38.3 degrees Celsius.
