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A closed vessel contains a mixture of two diatomic gases A and B. Molar mass of A is 16 times that of B and mass of gas A, contained in the vessel is 2 times that of B. :
- a)Average kinetic energy per molecule of gas A is equal to that of gas B.
- b)Root mean square value of translational velocity of gas B is four times that of A.
- c)Pressure exerted by gas B is eight times of that exerted by gas A.
- d)Number of molecules of gas B in the cylinder is eight times that of gas A.
Correct answer is option 'A,B,C,D'. Can you explain this answer?
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A closed vessel contains a mixture of two diatomic gases A and B. Mola...
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Solution:
Given,
Molar mass of A = 16 × Molar mass of B
Mass of A = 2 × Mass of B
Let's assume the molar mass of B to be 'm'. Then, the molar mass of A will be 16m.
a) Average kinetic energy per molecule of gas A is equal to that of gas B.
The average kinetic energy per molecule of a gas is given by the formula:
KEavg = (3/2)kT
where k is Boltzmann constant and T is the temperature.
Now, the kinetic energy of a gas is directly proportional to its temperature. Since both gases are in the same closed vessel at the same temperature, their average kinetic energy per molecule will be the same.
Therefore, the given statement is true.
b) Root mean square value of translational velocity of gas B is four times that of A.
The root mean square value of translational velocity of a gas is given by the formula:
vrms = √(3kT/m)
Substituting the values of molar mass and mass of A and B in the above formula, we get:
v(rms)A = √(3kT/16m)
v(rms)B = √(3kT/m)
Taking the ratio of the two equations, we get:
v(rms)B/v(rms)A = √(m/16m) = 1/4
Therefore, the given statement is true.
c) Pressure exerted by gas B is eight times of that exerted by gas A.
Assuming that both gases have the same volume and temperature, their pressure can be calculated using the ideal gas equation:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant, and T is the temperature.
Since the number of moles of A is twice that of B, and the molar mass of A is 16 times that of B, the mass of A is also 16 times that of B. Therefore, the number of molecules of A is 8 times that of B.
Now, since both gases are in the same closed vessel at the same temperature, their pressure will be directly proportional to the number of molecules. Hence, the pressure exerted by gas B will be 8 times that of gas A.
Therefore, the given statement is true.
d) Number of molecules of gas B in the cylinder is eight times that of gas A.
As already calculated in point c), the number of molecules of A is 8 times that of B. Therefore, the given statement is false.
Hence, the correct options are A, B, and C.
Given,
Molar mass of A = 16 × Molar mass of B
Mass of A = 2 × Mass of B
Let's assume the molar mass of B to be 'm'. Then, the molar mass of A will be 16m.
a) Average kinetic energy per molecule of gas A is equal to that of gas B.
The average kinetic energy per molecule of a gas is given by the formula:
KEavg = (3/2)kT
where k is Boltzmann constant and T is the temperature.
Now, the kinetic energy of a gas is directly proportional to its temperature. Since both gases are in the same closed vessel at the same temperature, their average kinetic energy per molecule will be the same.
Therefore, the given statement is true.
b) Root mean square value of translational velocity of gas B is four times that of A.
The root mean square value of translational velocity of a gas is given by the formula:
vrms = √(3kT/m)
Substituting the values of molar mass and mass of A and B in the above formula, we get:
v(rms)A = √(3kT/16m)
v(rms)B = √(3kT/m)
Taking the ratio of the two equations, we get:
v(rms)B/v(rms)A = √(m/16m) = 1/4
Therefore, the given statement is true.
c) Pressure exerted by gas B is eight times of that exerted by gas A.
Assuming that both gases have the same volume and temperature, their pressure can be calculated using the ideal gas equation:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant, and T is the temperature.
Since the number of moles of A is twice that of B, and the molar mass of A is 16 times that of B, the mass of A is also 16 times that of B. Therefore, the number of molecules of A is 8 times that of B.
Now, since both gases are in the same closed vessel at the same temperature, their pressure will be directly proportional to the number of molecules. Hence, the pressure exerted by gas B will be 8 times that of gas A.
Therefore, the given statement is true.
d) Number of molecules of gas B in the cylinder is eight times that of gas A.
As already calculated in point c), the number of molecules of A is 8 times that of B. Therefore, the given statement is false.
Hence, the correct options are A, B, and C.
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A closed vessel contains a mixture of two diatomic gases A and B. Molar mass of A is 16 times that of B and mass of gas A, contained in the vessel is 2 times that of B. : a)Average kinetic energy per molecule of gas A is equal to that of gas B.b)Root mean square value of translational velocity of gas B is four times that of A.c)Pressure exerted by gas B is eight times of that exerted by gas A.d)Number of molecules of gas B in the cylinder is eight times that of gas A. Correct answer is option 'A,B,C,D'. Can you explain this answer?
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A closed vessel contains a mixture of two diatomic gases A and B. Molar mass of A is 16 times that of B and mass of gas A, contained in the vessel is 2 times that of B. : a)Average kinetic energy per molecule of gas A is equal to that of gas B.b)Root mean square value of translational velocity of gas B is four times that of A.c)Pressure exerted by gas B is eight times of that exerted by gas A.d)Number of molecules of gas B in the cylinder is eight times that of gas A. Correct answer is option 'A,B,C,D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A closed vessel contains a mixture of two diatomic gases A and B. Molar mass of A is 16 times that of B and mass of gas A, contained in the vessel is 2 times that of B. : a)Average kinetic energy per molecule of gas A is equal to that of gas B.b)Root mean square value of translational velocity of gas B is four times that of A.c)Pressure exerted by gas B is eight times of that exerted by gas A.d)Number of molecules of gas B in the cylinder is eight times that of gas A. Correct answer is option 'A,B,C,D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A closed vessel contains a mixture of two diatomic gases A and B. Molar mass of A is 16 times that of B and mass of gas A, contained in the vessel is 2 times that of B. : a)Average kinetic energy per molecule of gas A is equal to that of gas B.b)Root mean square value of translational velocity of gas B is four times that of A.c)Pressure exerted by gas B is eight times of that exerted by gas A.d)Number of molecules of gas B in the cylinder is eight times that of gas A. Correct answer is option 'A,B,C,D'. Can you explain this answer?.
A closed vessel contains a mixture of two diatomic gases A and B. Molar mass of A is 16 times that of B and mass of gas A, contained in the vessel is 2 times that of B. : a)Average kinetic energy per molecule of gas A is equal to that of gas B.b)Root mean square value of translational velocity of gas B is four times that of A.c)Pressure exerted by gas B is eight times of that exerted by gas A.d)Number of molecules of gas B in the cylinder is eight times that of gas A. Correct answer is option 'A,B,C,D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A closed vessel contains a mixture of two diatomic gases A and B. Molar mass of A is 16 times that of B and mass of gas A, contained in the vessel is 2 times that of B. : a)Average kinetic energy per molecule of gas A is equal to that of gas B.b)Root mean square value of translational velocity of gas B is four times that of A.c)Pressure exerted by gas B is eight times of that exerted by gas A.d)Number of molecules of gas B in the cylinder is eight times that of gas A. Correct answer is option 'A,B,C,D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A closed vessel contains a mixture of two diatomic gases A and B. Molar mass of A is 16 times that of B and mass of gas A, contained in the vessel is 2 times that of B. : a)Average kinetic energy per molecule of gas A is equal to that of gas B.b)Root mean square value of translational velocity of gas B is four times that of A.c)Pressure exerted by gas B is eight times of that exerted by gas A.d)Number of molecules of gas B in the cylinder is eight times that of gas A. Correct answer is option 'A,B,C,D'. Can you explain this answer?.
Solutions for A closed vessel contains a mixture of two diatomic gases A and B. Molar mass of A is 16 times that of B and mass of gas A, contained in the vessel is 2 times that of B. : a)Average kinetic energy per molecule of gas A is equal to that of gas B.b)Root mean square value of translational velocity of gas B is four times that of A.c)Pressure exerted by gas B is eight times of that exerted by gas A.d)Number of molecules of gas B in the cylinder is eight times that of gas A. Correct answer is option 'A,B,C,D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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A closed vessel contains a mixture of two diatomic gases A and B. Molar mass of A is 16 times that of B and mass of gas A, contained in the vessel is 2 times that of B. : a)Average kinetic energy per molecule of gas A is equal to that of gas B.b)Root mean square value of translational velocity of gas B is four times that of A.c)Pressure exerted by gas B is eight times of that exerted by gas A.d)Number of molecules of gas B in the cylinder is eight times that of gas A. Correct answer is option 'A,B,C,D'. Can you explain this answer?, a detailed solution for A closed vessel contains a mixture of two diatomic gases A and B. Molar mass of A is 16 times that of B and mass of gas A, contained in the vessel is 2 times that of B. : a)Average kinetic energy per molecule of gas A is equal to that of gas B.b)Root mean square value of translational velocity of gas B is four times that of A.c)Pressure exerted by gas B is eight times of that exerted by gas A.d)Number of molecules of gas B in the cylinder is eight times that of gas A. Correct answer is option 'A,B,C,D'. Can you explain this answer? has been provided alongside types of A closed vessel contains a mixture of two diatomic gases A and B. Molar mass of A is 16 times that of B and mass of gas A, contained in the vessel is 2 times that of B. : a)Average kinetic energy per molecule of gas A is equal to that of gas B.b)Root mean square value of translational velocity of gas B is four times that of A.c)Pressure exerted by gas B is eight times of that exerted by gas A.d)Number of molecules of gas B in the cylinder is eight times that of gas A. Correct answer is option 'A,B,C,D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A closed vessel contains a mixture of two diatomic gases A and B. Molar mass of A is 16 times that of B and mass of gas A, contained in the vessel is 2 times that of B. : a)Average kinetic energy per molecule of gas A is equal to that of gas B.b)Root mean square value of translational velocity of gas B is four times that of A.c)Pressure exerted by gas B is eight times of that exerted by gas A.d)Number of molecules of gas B in the cylinder is eight times that of gas A. Correct answer is option 'A,B,C,D'. Can you explain this answer? tests, examples and also practice JEE tests.
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