Question

The value of universal gs
constant is 8.3J/mole-K, the
mean kinetic energy of 32gm
of oxygen at -73°C will be​

Answer 1

Answer:

Mean Kinetic Energy of a molecule is the energy calculated with the RMS velocity.

The formula to calculate Root Mean Square (RMS) velocity is given as:

$\implies \boxed{ \bf{V_{rms} = \sqrt{ \dfrac{3RT}{m} }}}$

Hence substituting the value of 'v' in the formula of Kinetic Energy we get:

$\implies K.E. = \dfrac{1}{2}\times m \times V_{rms}^2\\\\\\\implies K.E. = \dfrac{1}{2} \times m \times \sqrt{\dfrac{3RT}{m}} \times \sqrt{\dfrac{3RT}{m}}\\\\\\\implies K.E. = \dfrac{1}{2} \times m \times \dfrac{3RT}{m}\\\\\\\implies K.E. = \dfrac{1}{2} \times 3RT\\\\\\\implies \boxed{ \bf{ K.E. = \dfrac{3RT}{2}}}$

According to the question,

R = 8.3 J/mol.K

T = -73 °C

Converting T from °C to °K, we get:

⇒ T = -73 + 273

⇒T = 200 K

Therefore substituting the values in the formula, we get:

$\implies K.E. = \dfrac{3 \times 8.3 \times 200}{2}\\\\\\\implies K.E. = 3 \times 8.3 \times 100\\\\\\\implies \boxed{ \bf{K.E. = 2490\:\:J}}$

This is the required answer.