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A container has 3 gases whose mass ratio is 1:3:5. What is the ratio of mean square speed of the molecules of two gases? Their atomic masses are 20u, 30u & 40u corresponding to the order in which the ratios are given.
  • a)
    2:3:4
  • b)
    4:3:2
  • c)
    2:√3:√2
  • d)
    √2:√3:2
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A container has 3 gases whose mass ratio is 1:3:5. What is the ratio o...


Given information:
- Mass ratio of gases in the container: 1:3:5
- Atomic masses of the gases: 20u, 30u, 40u

Calculating the mean square speed ratio:
- The mean square speed of gas molecules is directly proportional to the square root of the temperature and inversely proportional to the square root of the molar mass.
- The mean square speed ratio is inversely proportional to the square root of the molar mass ratio.

Calculating the molar mass ratio:
- Given molar masses of gases: 20u, 30u, 40u
- The molar mass ratio is 20:30:40, which simplifies to 2:3:4

Calculating the mean square speed ratio:
- Inverse of the molar mass ratio is 1/2:1/3:1/4, which simplifies to 3:2:1
- Therefore, the mean square speed ratio of the gases is 3:2:1

Comparing the mean square speed ratio with the given options:
- The options provided are in the form of square roots, so we need to square them to compare.
- Squaring the options:
- Option a) (2:3:4) squared gives 4:9:16
- Option b) (4:3:2) squared gives 16:9:4
- Option c) (2:√3:√2) squared gives 4:3:2
- Option d) (√2:√3:2) squared gives 2:3:4
- Comparing the squared values with the calculated mean square speed ratio, we find that option b) (4:3:2) matches the result.

Therefore, the correct answer is option b) 4:3:2.
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Community Answer
A container has 3 gases whose mass ratio is 1:3:5. What is the ratio o...
Their average kinetic energies will be the same. Thus, 1/2mv2will be the same.
v12:v22:v32 =m3:m2:m1
= 40:30:20
= 4:3:2.
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A container has 3 gases whose mass ratio is 1:3:5. What is the ratio of mean square speed of the molecules of two gases? Their atomic masses are 20u, 30u & 40u corresponding to the order in which the ratios are given.a)2:3:4b)4:3:2c)2:√3:√2d)√2:√3:2Correct answer is option 'B'. Can you explain this answer?
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