TBR Chemistry Chapter 6, Passage 2, Q #10

[drechie]

I got this question right, however, I think it was more luck than intuition. Basically, I need help on understanding simple arithmetic. Would someone care to help? Basically, I want to know why mathematically, a gass' mass plays a larger role in determining momentum than does velocity, when all else is equal. Thank you in advance

QUESTION:

Which of the following gases has the GREATEST momentum, if they are all under identical conditions of temperature and pressure?

A. Helium
B. Neon
C. Nitrogen
D. Sulfur dioxide (ANSWER)

Solution:

Choice D is correct. Under identical conditions, the gases are all at the same temperature, so they have the same average kinetic energy. The equation for kinetic energy is K.E. = V2 mv2. This means that if two particles have different masses, they must have different average velocities. Because velocity, v, is squared in the kinetic energy relationship, it varies inversely with the square root of the mass. In other words, if one particle is four times as massive as another, it has half the velocity of the lighter particle. Momentum is the product of mass and velocity, so particles with greater mass have greater momentum. This means that the gas

with the greatest particle momentum is the heaviest gas. Sulfur dioxide is the heaviest gas of the choices, so choice D is the best answer.

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[chemtopper]

I got this question right, however, I think it was more luck than intuition. Basically, I need help on understanding simple arithmetic. Would someone care to help? Basically, I want to know why mathematically, a gass' mass plays a larger role in determining momentum than does velocity, when all else is equal. Thank you in advance

QUESTION:

Which of the following gases has the GREATEST momentum, if they are all under identical conditions of temperature and pressure?

A. Helium
B. Neon
C. Nitrogen
D. Sulfur dioxide (ANSWER)

Solution:

Choice D is correct. Under identical conditions, the gases are all at the same temperature, so they have the same average kinetic energy. The equation for kinetic energy is K.E. = V2 mv2. This means that if two particles have different masses, they must have different average velocities. Because velocity, v, is squared in the kinetic energy relationship, it varies inversely with the square root of the mass. In other words, if one particle is four times as massive as another, it has half the velocity of the lighter particle. Momentum is the product of mass and velocity, so particles with greater mass have greater momentum. This means that the gas

with the greatest particle momentum is the heaviest gas. Sulfur dioxide is the heaviest gas of the choices, so choice D is the best answer.

Since all the gases are at the same temperature so it means they have the same KE
KE= 1/2 mV^2
it means Velocity = Constant / square root of mass
if mass becomes 4times -velocity becomes half or if mass becomes 16times -velocity becomes 1/8th
Momentum is mass times velocity so heavy gases with same KE will show higher momentum.

 

[drechie]

Since all the gases are at the same temperature so it means they have the same KE
KE= 1/2 mV^2
it means Velocity = Constant / square root of mass
if mass becomes 4times -velocity becomes half or if mass becomes 16times -velocity becomes 1/8th
Momentum is mass times velocity so heavy gases with same KE will show higher momentum.

Thank you --- why isnt velocity equal to the square root of (2 * constant / mass?)

 

[chemtopper]

Thank you --- why isnt velocity equal to the square root of (2 * constant / mass?)

It is actually square root(2KE/mass) and I am taking square root2KE as constant because it is going to be same in all gases at the same temperature.