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

The value of of the Boltzmann constant is
`3.14* 10^(-23) J/K`.

Step-by-step explanation:

Generally the formula for average kinetic energy of a molecule :

`K.E=(3)/(2)kT`

where,

k = Boltzmann’s constant

T = temperature = 290 K

Given:

Number of molecules in 1.7 moles:

`1.7* 6.022* 10^(23) molecules=1.0237* 10^(24) molecules`

Average kinetic energy of 1.7 moles = 1.4 MJ =
`1.4* 10^6 J`

Average kinetic energy of 1 molecule =
`(1.4* 10^6 J)/(1.023* 10^(24)) =1.3675* 10^(-18) J`

`1.3675* 10^(-18) J=(3)/(2)* k* (290K)`

`k=3.14* 10^(-23) J/K`