Introduction
We have already talked about ideal gas law in one of our other articles. Ideal gas law is the combination of the following four laws –
Boyle’s Law
Charles's Law
Avogadro’s Law
Gay Lussac’s Law
We have explained Boyle’s Law, Charle’s Law and Avogadro’s law in separate articles. So, in this article, we are going to discuss Gay Lussac’s Law in detail.
We have three variables to study gases which are temperature, volume and pressure. In Boyle’s law, the temperature remained constant while in Charle’s law pressure remained constant. In Gay Lussac’s Law volume is kept constant. It defines the relationship between temperature and pressure for gas when it is kept under fixed volume.
What is Gay Lussac’s Law?
Gay-Lussac's is defined as the pressure of a given mass of gas varies directly with the absolute temperature of the gas when the volume is kept constant. Mathematically, it can be written as P/T=k. It is a special case of the ideal gas law.
Vedantu’s website contains separate articles and pdfs on the other three ideal gas laws that are Boyle’s law, Charles’s law and Avogadro’s law. This article is mainly concerned with the Study of gay lussac’s law.
The three elements that help to study gases are temperature, volume and pressure. While studying gay lussac’s law volume is kept constant, the temperature remains constant in Boyle’s law and pressure remains constant in Charles law. Gay lussac’s law defines the relationship between temperature and pressure of a gas when kept in a fixed volume.
An example of gay lussac’s law can be seen in -The propane tanks that we use for barbeque grills. In order to keep a measure of the amount of gas that is left in the tank, people use gauges that measure the pressure in the tank to keep a check on the amount of gas left. The gauge registers a higher pressure when the air temperature is hot. Therefore the air temperature has to be taken into account before refilling the propane tank.
Gay lussac’s law is named after the French chemist who discovered the relationship between the pressure of a gas and its absolute temperature. His name was Joseph gay lussac (1778-1850).
It can be expressed as follows –
P ∝ T (when V = constant)
On removing proportionality –
P = kT -----------(1)
Where P = pressure exerted by the gas
K = constant
T = absolute temperature of the gas
Ideal Gas Equation –
PV = nRT ----------(2)
On keeping the value of P from equation (1) to (2) –
kTV = nRT
k = nR/V
k ∝ 1/V -------------(3)
From equation (3), it means when volume will increase k will decrease.
Gay Lussac’s Law Graph
Mathematical formula or expression for Gay Lussac’s law can be written as –
P = kT
Now on comparing the above equation with Y = mX, we get Y = P, m = k and X = T so it can be illustrated by a graph as given below – the image will be uploaded soon.
The blue line or slope in the above graph represents k which is inversely proportional to volume (from equation 3). So, if we increase the volume, the slope will decrease. If V4>V3>V2>V1 then for all these volumes graphs between pressure and temperature can be represented as given below – the image will be uploaded soon.
Gay Lussac’s Law of Gaseous Volumes
Law of Gaseous Volumes was proposed by Joseph Louis Gay-Lussac in 1808. According to this law when measured at the same temperature and pressure, the ratio of the volumes of reacting gases are small whole numbers. This can be considered as a different form of the law of definite proportions. This law is with respect to volume while law of definite proportion is with respect to mass.
Example - Images will be uploaded soon.
If 200ml of hydrogen is reacting with 100ml of oxygen then by using Gay Lussac’s law we can calculate how much amount of water(gas) will form. But all should be in gaseous form as Gay lussac’s law is applicable on gases only. If 200ml of hydrogen is reacting with 100ml of oxygen then according to the above equation 200ml of water (gas) will be produced.
This was brief on Gay Lussac’s Law, if you are looking for various numerical questions based on the law then log on to the Vedantu website or download the Vedantu learning app. By doing so you can get access to detailed study notes, revision notes, NCERT Solutions, mock tests and much more.
FAQs on Gay Lussac's Law
1. What does Gay-Lussac's Law state about the relationship between pressure and temperature?
Gay-Lussac's Law states that for a fixed mass of a gas at constant volume, the pressure of the gas is directly proportional to its absolute temperature (measured in Kelvin). This means that if you heat a gas in a rigid container, its pressure will increase, and if you cool it, its pressure will decrease.
2. What is the mathematical formula for Gay-Lussac's Law?
The mathematical representation of Gay-Lussac's Law is P ∝ T, which can be written as P/T = k, where 'k' is a constant. For comparing the same gas under two different conditions, the formula is expressed as:
P₁ / T₁ = P₂ / T₂
Here, P₁ and T₁ are the initial pressure and absolute temperature, and P₂ and T₂ are the final pressure and absolute temperature.
3. How is Gay-Lussac's Law different from Charles's Law and Boyle's Law?
The key difference lies in which property of the gas is held constant:
- In Gay-Lussac's Law, the volume is held constant to study the pressure-temperature relationship.
- In Charles's Law, the pressure is held constant to study the volume-temperature relationship.
- In Boyle's Law, the temperature is held constant to study the pressure-volume relationship.
4. What are some real-world examples that demonstrate Gay-Lussac's Law?
Several everyday phenomena illustrate Gay-Lussac's Law:
- Pressure Cooker: As the cooker is heated, the temperature of the steam inside increases, which in turn significantly increases the pressure inside the sealed pot, cooking food faster.
- Aerosol Cans: Warning labels on deodorant or spray paint cans advise against heating them because increasing the temperature will dangerously increase the internal pressure, potentially causing an explosion.
- Car Tires: The air pressure inside a car tire increases after a long drive because friction with the road heats the air inside the tire. Conversely, tire pressure drops in cold weather.
5. Why is it essential to use the absolute temperature (Kelvin) scale for Gay-Lussac's Law calculations?
It is crucial to use the Kelvin scale because it is an absolute temperature scale, where zero Kelvin (0 K) represents absolute zero—the point at which all molecular motion ceases. The direct proportionality in Gay-Lussac's Law (P ∝ T) only holds true with an absolute scale. If the Celsius or Fahrenheit scale were used, you could get zero or negative temperature values, which would incorrectly imply zero or negative pressure, a physical impossibility.
6. What is Gay-Lussac's Law of Combining Gaseous Volumes?
This is a separate but related law also proposed by Gay-Lussac. It states that when gases react together to form other gases, and all volumes are measured at the same temperature and pressure, the ratio between the volumes of the reacting gases and the products can be expressed in simple whole numbers. For example, in the reaction N₂(g) + 3H₂(g) → 2NH₃(g), one volume of nitrogen reacts with three volumes of hydrogen to produce two volumes of ammonia.
7. How does a graph of Pressure vs. Temperature illustrate Gay-Lussac's Law?
A graph plotting Pressure (P) on the y-axis against Absolute Temperature (T) on the x-axis for an ideal gas results in a straight line passing through the origin. This linear relationship visually confirms that pressure is directly proportional to temperature. The slope of this line (P/T) is the constant 'k'. If you draw multiple lines for different constant volumes, a line for a smaller volume (V₁) will have a steeper slope than a line for a larger volume (V₂).
8. Under what conditions does a real gas deviate from the behavior predicted by Gay-Lussac's Law?
Gay-Lussac's Law is one of the ideal gas laws, which assume that gas particles have no volume and no intermolecular forces. Real gases deviate from this ideal behaviour, particularly under conditions of high pressure and low temperature. At high pressures, the volume of the gas molecules becomes significant compared to the container volume. At low temperatures, intermolecular attractive forces become strong enough to affect the pressure exerted by the gas.
