the kinetic gas equation for N number of molecules in volume v having mass m and root mean square velocity u is
Answers
Answer:
On the basis of the postulates of kinetic theory of gases, it is possible to derive the mathematical expression, commonly known as kinetic gas equation. PV = 1/3 m n u^3? <br> where, P= Pressure of the gas, V a volume of the gas, m=Mass of a molecule, n = Number of molecules present in the given amount of a gas and u = root mean square speed <br> For one mole of gas, PV = RT and n=N_A <br> 1/3 m N_a u^2 = RT or 2/3 .1/2m N_A u^2 = N_A <br> [1/2mN_Au^2 = KE "per mole"] ,2/3K.E. = RT implies K.E. 3/2RT <br> Average kinetic energy per mol does not depend on the nature of the gas but depends only on temperature. This, when two gases are mixed at the same temperature, there will be no rise or decrease in temperature unless both react chemically. <br> Average kinetic energy per molecule = ("Average K.E. per mole")/N = 3/2(RT)/(N) implies 3/2kT <br> where k is the Boltzmann constant <br> The average kinetic energy (in joule) of the molecules in 8g methane at 27&@C is.
logo
Solution
8g=12 mole
⇒KE=32×KT=32×8.3146×1023×300=6×10−21