Gases & Solutions
For two samples of ideal gases A and B curves are plotted n vs V (volume of container ) at 16.42 atm pressure. Then temperature of A and B respectively are:
Collision cross-section is an area of an imaginary sphere of radius σ around the molecule within which the centre of another molecule cannot penetrate.
The volume swept by a single molecule in unit time is
V=(πσ2)u where u is the average speed
If N∗ is the number of molecules per unit volume, then the number of molecules within the volume V is
Hence, the number of collision made by a single molecule in unit time will be
In order to account for the movements of all molecules, we must consider the average velocity along the line of centres of two coliding molecules instead of the average velocity of a single molecule . If it is assumed that, on an average, molecules collide while approaching each other perpendicularly, then the average velocity along their centres is 2u as shown below.
Number of collision made by a single molecule with other molecule per unit time is given by
The→talνmberofbimo≤carcollisionsZ_(1)perunitvolumeperunittimeisgivenbyZ_(1)=(1)/(2)(Z_(1)N^(**))or Z_(11)=(1)/(2)(sqrt(2)pisigma^(2)overline(u)N^(**))N^(**)=(1)/(sqrt(2))pisigma^(2)overline(u)N^(**2)Ifthecollsion∈volvetwounlikemo≤cesthentheνmberofcollisionsZ_(12)perunitvolumeperunittimeisgivenasZ_(12)= pisigma _(12)^(2)(sqrt((8kT)/(pimu)))N_(1)N_(2)whereN_(1)andN_(2)aretheνmberofmo≤cesperunitvolumeofthetwotypesofmo≤ces,sigma_(12)istheavera≥diameterofthetwomo≤cesandmuisthereducedmass.Themeaneepathistheavera≥distancetravel≤dbyamo≤cebetweentwo≻essivecollisions.Wecanexpressitasfollows:lambda=("Average distance travelled per unit time")/("NO. of collisions made by a single molecule per unit time")=(overline(u))/(Z_(1))or" "lambda=(overline(u))/(sqrt(2)pisigma^(2)overline(u)N^(**))implies(1)/(sqrt(2)pisigma^(2)overline(u)N^(**))Threeidealgassamp≤s∈separateequalvolumeconta∈ersaretakenandfollow∈gdataisgiven: Gas AGas BGas CPressure1atm2atm4atmTemperature1600K200K400KMean free paths0.16nm0.16nm0.04nmMol.wt.204080
Calculate number of collision by one molecule per sec (Z1).
Which one of the following relationships when graphed does not give a straight line for helium gas?
I. K.E. and T at constant pressure and volume
II. P v/s V at constant temperature for a constant mass
III. V v/s 1/T at constant pressure for a constant mass
The vapour pressure of water at 80∘C is 355 mm of Hg. 1 L vessel contains O2 at 80∘C, which is saturated with water and the total pressure being 760 mm of Hg. The contents of the vessel were pumped into 0.3 L vessel at the same temperature. What is the partial presure of O2?
7 moles of a tetra-atomic non-linear gas 'A' at 10 atm and T K are mixed with 6 moles of another gas B at 3TK and 5 atm in a closed, rigid vessel without energy transfer with surroundings. If final temperature of mixture was 65TK, then gas B is ? (Assuming all modes of energy are active)
If one mole each of a monoatomic and diatomic gases are mixed at low temperature then Cp/Cv ratio for the mixture is :
A 2.24L cylinder of oxygen at 1 atm and 273 K is found to develop a leakage. When the leakage was plugged the pressure dropped to 570 mm of Hg. The number of moles of gas that escaped will be :