Question

What is the value of the boltzmann constant of 1.7 moles of gas at 290 K that has an average kinetic energy of 1.4 MJ? A. 7x10^-24 J/K
B. 1.4x10^-23 J/K
C. 6x10^-3 J/K
D. 7x10^-3 J/K

Answer 1

Answer:

The value of  of the Boltzmann constant is $3.14\times 10^{-23} J/K$.

Explanation:

Generally the formula for average kinetic energy of a molecule :

$K.E=\frac{3}{2}kT$

where,

k = Boltzmann’s constant

T = temperature = 290 K

Given:

Number of molecules in 1.7 moles:

$1.7\times 6.022\times 10^{23} molecules=1.0237\times 10^{24} molecules$

Average kinetic energy of 1.7 moles = 1.4 MJ =$1.4\times 10^6 J$

Average kinetic energy of 1 molecule = $\frac{1.4\times 10^6 J}{1.023\times 10^{24}} =1.3675\times 10^{-18} J$

$1.3675\times 10^{-18} J=\frac{3}{2}\times k\times (290K)$

$k=3.14\times 10^{-23} J/K$