Answer
64.8k+ views
Hint: Here, we need to find the formula for kinetic energy of gases. Apply the given condition in two separate cases for two hydrogen molecules and one oxygen molecule. Find the ratio between the two.
Complete Step By Step Solution
We are given that the total number of \[{H_2}\] is double that of the number of \[{O_2}\]molecules. Which means that\[{n_{{H_2}}} = 2 \times {n_{{O_2}}}\]. We need to obtain its energy relation by using the kinetic theory of gases. According to the equi-partition theorem of gases, in thermal equilibrium, the kinetic energy of the particle is a product of average energy created by movement of a gas particle in each of its degrees of freedom. The average energy per particle is given as \[{k_b}T/2\], where \[{k_b}\]is called as Boltzmann’s constant and T is the temperature of the gas particle.
Now according to kinetic theory of gases and equipartition theorem
\[E = \dfrac{3}{2}{k_b}T\] (Since a gas particle have 3 degrees of freedom)
Now, the energy [produced by 2 molecules of hydrogen is given as
\[{E_{{H_2}}} = 2n \times E\]
Now the energy produced by one molecule of oxygen is given as :
\[{E_{{O_2}}} = E\]
Finding the ratio by dividing the above terms, we get,
\[\dfrac{{{E_{{H_2}}}}}{{{E_{{O_2}}}}} = \dfrac{2}{1}\](Common term E is cancelled out)
Therefore the ratios of the energy produced at 300K is \[2:1\]
Hence, Option(c) is the right answer for the given question.
Note Kinetic theory of gases states that gases molecules do not have any force of attraction between them and volume of the gas molecules are significantly smaller than the space occupied by gases. In order to explain this theory, five postulates were constructed which are
1. The molecules of gas are very far apart.
2. Gas molecules move in constant random motion
3. Molecules can collide with each other when they’re within a specified boundary.
4. Due to collision, no molecules lose kinetic energy and are said to be perfectly elastic.
5. Molecules have no attractive or repulsive force but have intermolecular force.
Complete Step By Step Solution
We are given that the total number of \[{H_2}\] is double that of the number of \[{O_2}\]molecules. Which means that\[{n_{{H_2}}} = 2 \times {n_{{O_2}}}\]. We need to obtain its energy relation by using the kinetic theory of gases. According to the equi-partition theorem of gases, in thermal equilibrium, the kinetic energy of the particle is a product of average energy created by movement of a gas particle in each of its degrees of freedom. The average energy per particle is given as \[{k_b}T/2\], where \[{k_b}\]is called as Boltzmann’s constant and T is the temperature of the gas particle.
Now according to kinetic theory of gases and equipartition theorem
\[E = \dfrac{3}{2}{k_b}T\] (Since a gas particle have 3 degrees of freedom)
Now, the energy [produced by 2 molecules of hydrogen is given as
\[{E_{{H_2}}} = 2n \times E\]
Now the energy produced by one molecule of oxygen is given as :
\[{E_{{O_2}}} = E\]
Finding the ratio by dividing the above terms, we get,
\[\dfrac{{{E_{{H_2}}}}}{{{E_{{O_2}}}}} = \dfrac{2}{1}\](Common term E is cancelled out)
Therefore the ratios of the energy produced at 300K is \[2:1\]
Hence, Option(c) is the right answer for the given question.
Note Kinetic theory of gases states that gases molecules do not have any force of attraction between them and volume of the gas molecules are significantly smaller than the space occupied by gases. In order to explain this theory, five postulates were constructed which are
1. The molecules of gas are very far apart.
2. Gas molecules move in constant random motion
3. Molecules can collide with each other when they’re within a specified boundary.
4. Due to collision, no molecules lose kinetic energy and are said to be perfectly elastic.
5. Molecules have no attractive or repulsive force but have intermolecular force.
Recently Updated Pages
Write a composition in approximately 450 500 words class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Arrange the sentences P Q R between S1 and S5 such class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What is the common property of the oxides CONO and class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What happens when dilute hydrochloric acid is added class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
If four points A63B 35C4 2 and Dx3x are given in such class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The area of square inscribed in a circle of diameter class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Other Pages
Excluding stoppages the speed of a bus is 54 kmph and class 11 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
In the ground state an element has 13 electrons in class 11 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Electric field due to uniformly charged sphere class 12 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
A boat takes 2 hours to go 8 km and come back to a class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
According to classical free electron theory A There class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)