Question

Calculate the kinetic energy of 10 gram of Argon molecules at 127℃.[Universal gas constant R=8320J/mol K. Atomic weight of Argon=40kg/mol].

Answer 1

Hint: The average kinetic energy is given by $\dfrac{3}{2}$nRT. Where n is the number of moles of argon, R is the gas constant and T is the temperature in kelvin. We can find the number of moles by dividing the given weight of argon by the atomic weight of argon.

Complete step by step answer:
Given, weight of argon molecules, wt. =10 g
Atomic weight of argon, at.wt. =40kg/mol.
Temperature=127℃
  =127+273K
 =400 K
Since 1kg =1000g
Therefore, given weight of argon=$\dfrac{{10}}{{1000}} = 0.01$kg
Number of moles of argon,
 n=$\dfrac{{wt.}}{{at.wt.}}$
 =$\dfrac{{0.01}}{{40}} = 0.00025$
The average kinetic energy, K.E=$\dfrac{3}{2}$nRT
 Where n is the number of moles of argon, R is the gas constant and T is the temperature in kelvin.
Substituting the values given in the question,
K.E=$\dfrac{3}{2}$×0.00025×8320×400
 =1248J

Therefore the kinetic energy of 10 grams of Argon molecules at 127℃ is 1248J.

Additional Information:
Gas particles are in constant motion, and any object in motion has kinetic energy. Kinetic energy, for an individual atom, can be calculated by the following equation where m is the mass, and u is the speed. K.E=$\dfrac{1}{2}m{u^2}$. Overall the molecules in a sample of a gas share an average kinetic energy; however, individual molecules exhibit a distribution of kinetic energies because of having distribution of speeds.

Note:
Units should be kept in mind to avoid any mistake.
Only standard units should be used.
Simple stoichiometric formulae should be known to find the number of moles if other data is provided.