Explaining Brownian Motion & Gas Laws: Homework Solutions in 65 chars or less

In summary: Keep up the good work!In summary, the conversation discusses Brownian motion, Boyle's Law, the pressure exerted by gas molecules, and a quantity of mono-atomic gas. Brownian motion is caused by the random movement of air particles, Boyle's Law states that pressure and volume are inversely proportional, and the pressure exerted by gas molecules is calculated using the equation P=1/3nm². The conversation also includes an explanation of the assumptions used to derive this equation. Finally, the last part of the conversation involves calculating the moles, internal energy, and root mean square speed of the mono-atomic gas.
  • #1
BoanviaFx
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Homework Statement


Can someone confirm if I answered correctly? Thanks for support and help!

a) In the Brownian motion experiment, small particles of matter are seen moving randomly. Give an explanation for this motion.

b) Boyle's Law is fundamental when discussing the gas laws.
i) State Boyle's law.
ii) Draw a labelled diagram of the apparatus used in an experiment to verify this law.
iii) Sketch the graph which is obtained from such an experiment

c) The pressure exerted on a surface by gas molecules is given by P=1/3nm² where n is the number of molecules per unit volume, m is the mass of a molecule and c² is the mean square velocity of the molecules.
i) state four assumptions used to derive this equation
ii) Derive the above equation for the pressure exerted by gas molecules

d) A quantity of an ideal mono-atomic gas of density 1.2kg/m3 occupies a volume of 1.2x10-2m-3 at a pressure of 1x105Pa and a temperature of 255K.
i) How many moles of gas are present?
ii) What is the internal energy of this gas?
iii) Calculate the root mean square speed of the molecules.

Homework Equations


Molar gas constant, R=8.31Jmol-1K-1

The Attempt at a Solution



a) The small particles of matter are seen moving randomly due to the bombardment of air particles traveling in random directions.

bi) For a fixed amount of an ideal gas kept at a fixed temperature, pressure and volume are inversely proportional.
ii)
2uppq1v.png
Since pressure and volume are inversely proportional we can notice that the constant C will always remain the same.
iii)
r8w113.png


ci) 1) The molecules are considered as hard, identical spheres undergoing rapid, random motion, their size being much smaller than their separations.
2) Their kinetic energy is assumed constant as all collisions inside the container are taken to be perfectly elastic in nature.
3) Intermolecular forces are assumed negligible except during collisions but then the time of collisions is assumed to be of insignificant magnitude.
4) Newtonian mechanics is perfectly applicable to the motion of the molecules.
ii) P=1/3ρc²

di) PV=nRT
1x105*1.2x10-2=n*8.31Jmol-1K-1*255
n=0.566
ii) E=3/2nRT
E=3/2*0.566*8.31*255 =1800J
iii) Crms = (3RT/M)
ρ=m/v
m= 1.2*0.012 = 0.0144kg
Now to find Molar Mass
M = m/n
M = 0.0144/0.566
M = 0.0254
Crms = (3*8.31*255/0.0254)
Crms = 499m/s
 
Last edited:
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  • #2
(a) be more specific.
(b) how does this diagram differ from that of other thermodynamic processes?
(c) i. OK ii. incomplete.
(d) looks good to me.
 
  • #3
Sorry for late response, but since you pointed out where I had to improve, I manged to get this question right :)
 
  • #4
Well done.
 

Related to Explaining Brownian Motion & Gas Laws: Homework Solutions in 65 chars or less

What is Brownian motion?

Brownian motion is the random movement of particles suspended in a fluid, caused by collisions with other particles.

What are gas laws?

Gas laws describe the behavior of gases, including their volume, pressure, and temperature relationships.

How does Brownian motion relate to gas laws?

Brownian motion is a result of gas molecules colliding, which is a key factor in understanding gas properties and behavior.

What are some real-world applications of Brownian motion and gas laws?

Some examples include diffusion in cells, air pollution control, and the functioning of gas-filled balloons and tires.

How can I solve homework problems related to Brownian motion and gas laws?

You can use the provided solutions, as well as applying mathematical formulas and understanding the basic principles behind these concepts.

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