Question

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 $- {73^\circ }C$ ?
A. 480 J
B. 4980 J
C. 2490 J
D. 100 J

Answer 1

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.
$\Rightarrow KE = \dfrac{3}{2}nRT$ , 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 $T = - {73^\circ }C = - 73 + 273K = 200K$ [We convert the Celsius scale into Kelvin]
We are also aware that a single atom of oxygen with atomic number 8 has Atomic mass
$\Rightarrow M = 16$
So, we find the number of moles of oxygen in the given amount as:
Number of moles $n = \dfrac{m}{M}$
Putting the values of $m$ and $M$ , we get:
$\Rightarrow n = \dfrac{{32}}{{16}} = 2$
To find the mean kinetic energy, we know that:
$\Rightarrow KE = \dfrac{3}{2}nRT$
Substituting the values with correct units:
$\Rightarrow KE = \dfrac{3}{2} \times 2 \times 8.3 \times 200$
$\Rightarrow KE = 3 \times 8.3 \times 200 = 4980J$ .
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.