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Gay Lussac’s Law claims that, while mass and volume are held constant, the pressure of gas directly varies with temperature. Gay Lussac’s law shows how the increase in a gas's temperature results in the rise of its pressure (considering that the volume does not vary).
- The pressure, in this case, rises along with the temperature.
- The kinetic energy of the gas molecules increases with the temperature, thus causing the phenomena.
- Higher pressure results in the molecules colliding with the container walls with more force due to the increased energy.
- Amonton's Law is another name for Gay Lussac's Law. By creating a thermometer that used measured pressure as a readout for the current temperature, Amonton demonstrated the same rule.
- Since Gay Lussac’s Law more thoroughly demonstrated the law, it is more frequently referred to by his name.
Read Also: Combined Gas Law
Key Terms: Gay Lussac’s Law, Volume, Temperature, Pressure, Gas, Mass, Constant
What is Gay Lussac's Law?
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Gay Lussac’s law asserts that a gas' pressure (when held at a fixed volume and mass) changes directly with its absolute temperature.
- In other words, while the mass is fixed and the volume is constant, the pressure a gas exerts is proportional to the temperature of the gas.
- The temperature and pressure, herein, follow a direct relationship.
- Thus, assuming that the pressure increases and the temperature goes down, then the pressure goes down as well and vice versa.
Gay Lussac's Law
Read More:
| Topic Related Concepts | ||
|---|---|---|
| Partial Pressure | Boiling Point Elevation | Elimination Reaction |
| Pressure of an Ideal Gas | Charles law | Avogadro’s law |
Gay Lussac's Law Formula
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The formula of Gay Lussac’s Law is:
⇒ \(\frac{P_1}{T_1} = \frac{P_2}{T_2}\)
Where:
- P1 = The initial pressure
- T1 = The initial temperature
- P2 = The final pressure
- T2 = The final temperature
Gay Lussac's Law Derivation
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The relationship between pressure and temperature for gas may be used to generate this formula. Due to the fact that P T for gases with fixed mass and constant volume:
Initial pressure/temperature are both constant at P1/T1 = k
Final pressure/final temperature = constant; P2/T2 = k
Thus,
Therefore, \(\frac{P_1}{T_1} = \frac{P_2}{T_2}\) = k
Or, P1T2 = P2T1
Gay Lussac’s Law Examples
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Some examples of Gay Lussac’s law are:
- Due to Gay Lussac's-rule, when a pressurised aerosol can—like a deodorant or spray paint can—is heated, the increased pressure that the gases exert on the container, as a result, might cause an explosion. Because of this, many pressurized containers include warning signs that urge users to store them in cool environments and keep them away from fires.
- Above is an instance of the rise in pressure that follows an increase in the absolute temperature of a gas maintained at a constant volume. Pressure cookers are one of the major examples of Gay Lussac's law. The pressure that the steam within the container exerts grows as the cooker heats up. The food cooks more quickly due to the high pressure and warmth inside the container.
Gay Lussac's Law of Combining Volumes
Gay Lussac’s law claims that when gases react together in order to yield other gases, all volumes are measured at the same temperature and pressure.
In fact, the ratio between the volumes of the reactant gases and the product gas can be expressed in simple whole numbers.
Solved Examples of Gay Lussac’s LawQues. What is Charles's law? Ans. According to Charles' law, with constant pressure, the volume of an ideal gas increases in direct proportion to the absolute temperature. Ques. What is the Gay Lussac law equation? Ans. When the gas volume is maintained constant, the law of Gay-Lussac is a subset of the ideal gas law. While maintaining constant volume, a gas's pressure is exactly proportional to its temperature. The formulas for Gay Lussac's law are P / T = constant or Pi / Ti = Pf / Tf. Ques. What significance does Gay Lussac's law have? Ans. This gas law's significance is that it shows how an increase in a gas's temperature causes a corresponding rise in its pressure (assuming that the volume does not change). In a similar vein, dropping the temperature permits a proportionate drop in strain. |
Things to Remember
- Gay Lussac’s law states that while mass and volume are held constant, the pressure of gas directly varies with temperature.
- Gay Lussac’s law formula is \(\frac{P_1}{T_1} = \frac{P_2}{T_2}\)
- Gay Lussac's Law is also often called Amonton's Law. By creating a thermometer used to measure pressure as a readout for the current temperature, Amonton exhibited the same rule.
- The temperature and pressure, in Gay Lussac’s Law, follow a direct relationship.
Previous Years’ Questions
- According to Boyle's law, the product of pressure and volume…(KCET 2010)
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Sample Questions
Ques. 600 cc of ethane and 3000 cc of oxygen were burned (C2H6). Measure the amount of oxygen that isn't being used. [1 mark]
Ans. The volume of unused oxygen
= 3000 − [7 × 300] 2100
= 900.
Ques. The combination ignited when 60 cc of oxygen was added to 24 cc of carbon monoxide. Determine the amount of oxygen used and the amount of carbon dioxide produced. [1 mark]
Ans. The volume of oxygen used up is 12 cc.
The volume of carbon dioxide formed is 24 cc.
Ques. At room temperature, 200cm3 of carbon monoxide and 200cm3 of oxygen are combined and ignited. Determine the volume of CO2 created after cooling to room temperature. What more gasses, if any, could be present? [1 mark]
Ans. A 200 cm3 of carbon dioxide is produced
While 100 cm3 of oxygen is also present.
Ques. At 40.0°C, a gas has a pressure of 699.0 mmHg. At normal pressure, what is the temperature? [2 Marks]
Ans. Solution:P1/T1 = P2/T2
699.0 / 313 = 760 / x
x = 340 K
(Note that the conversion factor is canceled from both sides of the equation, which is why pressure is not converted to atm.)
Ques. Nitric oxide is created when one volume of nitrogen and one volume of oxygen mix. Determine how much of each reactant is needed to make 250 ml of nitric oxide. [3 Marks]
Ans. N2(g) + O2(g) → 2NO(g)
i.e. 1vol : 1vol → 2vol
To calculate the amount of N2 required
NO:N2
Thus, 250: X
X = 125ml
Amount of N2 = 12ml
To determine the amount of O2 required.
NO: O2
2:1
Thus, 250 : X
Hence, Amount O2 required = 125ml.
Ques. 200 ml of C2H4 are burned using the formula C2H4 + 3O22CO2 + 2H2O [g] in just enough air (20% oxygen). Determine the composition of the resulting mixture [at 100°C and steady press]. [3 Marks]
Ans. When oxygen is 600 ml. the nitrogen is = 80×600/20 =240 ML
Hence the composition of the resultant mixture is
Carbon Dioxide= 400 ml
Steam= 400 ml [Thus, At 100 degree celsius steam has volume]
Nitrogen= 2400 ml
Hence, Ethylene = (200 - 200) ml = 0 ml
Oxygen =(600 – 600) ml = 0 ml.
Ques. 200cm3 of oxygen and 450cm3 of carbon monoxide are combined, and then ignited. Determine the mixture's composition by calculation. [3 Marks]
Ans. 2CO(g) + O2(g) → 2CO2(g) [By Lussac's Law]
i.e. 2 volt : 1 vol → 2vol
To calculate the amount of unused CO.
CO: O2
2:1
X = 200
X = 400cm
Amount of unused CO = 450 – 400 = 50cm3
Unused CO : 50cm3
To calculate the amount of CO2 formed.
O2 : CO2
1:2
200: X1
X1= 400cm3
Amount of CO2 formed = 400cm3
[Total mixture: 450cm3]
Ques. An example would be to place a 30.0 L sample of nitrogen at 20.0°C within a hard metal container inside a 50.0°C oven. At 20.0°C, the container's internal pressure was 3.00 atm. What pressure does nitrogen have when its temperature reaches 50.0°C? [3 Marks]
Ans. In Gay Lussac’s Law we have knowledge that at constant volume (30 L in this question),
P1/T1 = P2/T2
Converting the given temperature in the degree to Kelvin from Celcius.
T1 = 20 + 273
T1 = 293 K
T2 = 50 + 273
T2 = 323 K
Let, P1 = 3.00 atm and P2 = y;
Then,
3 / 293 = y / 323
Which means ,
y = 3.31 atm
Ques. Identify two uses of Gay Lussac's Law and explain them. [3 Marks]
Ans. Some uses of Gay Lussac’s Law are
- The use of pressure cookers for preparing food is governed by Gay Lussac's Law (the relationship between temperature and pressure). The water in the pressure cooker evaporates and turns into steam when we apply heat to it. The dish may be cooked using the thermal energy in the steam.
- A tyre blowout is a direct outcome of Gay Lussac's Law. On a hot day, as the temperature of the air increases around the tyre, the pressure of the gas within the tyre increases, putting pressure on the tyre walls. As a result, when a certain threshold is achieved, the tyre bursts.
Ques. When a gas is heated to a temperature of 250K, it has a 1.5 atm pressure within a cylinder. If the gas's original pressure was 1 atm, what was its initial temperature? [5 Marks]
Ans. Given,
P1 = the initial pressure in atm
P2 = 1.5 atm as the final pressure
T2 = the final temperature of 250 K.
Gay Lussac's law states that P1T2 = P2T1
T1 = (P1T2)/P2
= (1*250)/(1.5)
= 166.66 Kelvin
The pressure of the gas inside a deodorant container is 3 atm at 300 K. Calculate the gas's pressure at 900 K in temperature.
P1 = the initial pressure of 3 atm
300 K is the initial temperature.
900 K is the final temperature (T2).
Final pressure (P2) is therefore equal to (P1T2/T1) = (3 atm*900K)/(300K/900K) = 9 atm.
Ques. Give an illustration of the Law of Gaseous Volume of Gay Lussac. What is the law of Gay Lussac? Give its formula. [5 Marks]
Ans. The example of hydrogen and chlorine is a straightforward approach to illustrate Gay Lussac's law. When one volume of hydrogen and one volume of chlorine are mixed, hydrochloric acid gas is always produced. The volume ratio of the reactants to the product in this reaction is straightforward, or 1:1:2.
The Gay Lussac’s law is an adaptation of the ideal gas law that maintains a constant gas volume. A gas's pressure increases in direct proportion to its temperature while the volume of the gas stays constant.
Gay Lussac's law are often calculated using the formulas P / T = constant or Pi / Ti = Pf / Tf . This gas law aims to show that raising a gas's temperature results in a proportionate rise in its pressure (assuming that the volume does not change). In a similar manner, decreasing the temperature decreases the strain appropriately.
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