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If the value of the universal gas constant is 8.3J/mole/K , what will be the mean kinetic energy of 32 gm of oxygen at 73C ?
A. 480 J
B. 4980 J
C. 2490 J
D. 100 J

Answer
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Hint
The average kinetic energy of a gas is a measure of its temperature. As the temperature changes, the molecules of the gas start moving at different speeds colliding with one another and adding up to the kinetic energy.
KE=32nRT , where KE is the mean kinetic energy of a substance with n number of moles, R is the universal gas constant and T is the temperature of the gas.

Complete step by step answer
We are provided with a certain amount of oxygen in the question and are asked to find its mean kinetic energy. Let us look at the values that are given to us:
Universal gas constant R=8.3J/mole/K
Mass of oxygen m=32gm
Temperature T=73C=73+273K=200K [We convert the Celsius scale into Kelvin]
We are also aware that a single atom of oxygen with atomic number 8 has Atomic mass
M=16
So, we find the number of moles of oxygen in the given amount as:
Number of moles n=mM
Putting the values of m and M , we get:
 n=3216=2
To find the mean kinetic energy, we know that:
 KE=32nRT
Substituting the values with correct units:
 KE=32×2×8.3×200
 KE=3×8.3×200=4980J .
Hence, the average kinetic energy of 32 gm of oxygen is option (B) i.e. 4980 J.

Note
It is important to note that the question is talking about nascent oxygen (1 atom of oxygen) rather than molecular oxygen which has two atoms. This small detail would change the number of moles. Moles are used as a quantity for measuring the mass of atoms as they are very small in size.
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