Solveeit Logo
Login

Question

Question: The kinetic energy of translational of 20 gm of oxygen at \({{47}^{\circ }}C\) is (molecular wt of o...

The kinetic energy of translational of 20 gm of oxygen at 47∘C{{47}^{\circ }}C is (molecular wt of oxygen is 32gm/mol and R=8.3J/mol/K)
a) 2490 joules
b) 2490 ergs
c) 830 joules
d) 124.5 joules

Explanation

Solution

Oxygen is a diatomic gas, hence its kinetic energy for one mole of gas is given by K.E=f2RTK.E=\dfrac{f}{2}RT where f is the degree of freedom of the gas, R is the gas constant and T is the temperature of the gas. In the question it is asked to calculate the translational energy of oxygen hence f=3. Further, we can calculate the total energy of the 20 gm of Oxygen by multiplying the no of moles to the above equation of kinetic energy for one mole of gas.

Complete step-by-step answer:
To begin with let us first define degrees of freedom of a gas. It is defined as the total number of ways a molecule of gas can absorb energy. In diatomic gas there are 3 translational degrees of freedom. Oxygen has 3 translational degrees of freedom, hence the kinetic energy for one mole of a gas is given by,
K.E=32RTK.E=\dfrac{3}{2}RT . It is given that the gas is kept at 40 degree Celsius. We have to convert it into Kelvin as the units of the gas constant R is expressed in terms of Kelvin. Hence 40 degree Celsius is 320 Kelvin. Therefore numerically the value of kinetic energy is,
K.E=32×8.3×320 K.E=3984J \begin{aligned} & K.E=\dfrac{3}{2}\times 8.3\times 320 \\\ & K.E=3984J \\\ \end{aligned}
The above obtained energy is for one mole of oxygen gas. But we are asked to calculate the energy for only 20 gm of oxygen. Hence the number of moles of gas in 20gm of oxygen is,
No of moles=Given massMolar mass=2032=0.625\text{No of moles}=\dfrac{\text{Given mass}}{\text{Molar mass}}=\dfrac{20}{32}=0.625
Hence the kinetic energy of 0,625 moles of oxygen is,
K.E=no of moles !!×!! Energy of 1 mole of gas K.E=0.625×3984J K.E=2490J \begin{aligned} & K.E=\text{no of moles }\\!\\!\times\\!\\!\text{ Energy of 1 mole of gas} \\\ & K.E=0.625\times 3984J \\\ & K.E=2490J \\\ \end{aligned}

So, the correct answer is “Option A”.

Note: The total number of degrees of freedom of oxygen gas is 5. That is 3 translational and two rotational. At higher temperatures it also possesses 2 vibrational degrees of freedom. Hence the total degrees of freedom at higher temperature is 7. In the above question we have assumed that the entire energy of the gas is in the form of kinetic energy.