Answer:
The value of of the Boltzmann constant is [tex]3.14\times 10^{-23} J/K[/tex].
Explanation:
Generally the formula for average kinetic energy of a molecule :
[tex]K.E=\frac{3}{2}kT[/tex]
where,
k = Boltzmann’s constant
T = temperature = 290 K
Given:
Number of molecules in 1.7 moles:
[tex]1.7\times 6.022\times 10^{23} molecules=1.0237\times 10^{24} molecules[/tex]
Average kinetic energy of 1.7 moles = 1.4 MJ =[tex]1.4\times 10^6 J[/tex]
Average kinetic energy of 1 molecule = [tex]\frac{1.4\times 10^6 J}{1.023\times 10^{24}} =1.3675\times 10^{-18} J[/tex]
[tex]1.3675\times 10^{-18} J=\frac{3}{2}\times k\times (290K)[/tex]
[tex]k=3.14\times 10^{-23} J/K[/tex]
