# Gas Law Problem

1. Apr 16, 2015

### BoanviaFx

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
Molar gas constant, R=8.31Jmol-1K-1

3. The attempt at a solution

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

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

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: Apr 16, 2015
2. Apr 17, 2015

### Simon Bridge

(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. Apr 21, 2015

### BoanviaFx

Sorry for late response, but since you pointed out where I had to improve, I manged to get this question right :)

4. Apr 23, 2015

Well done.