Question

Calculate the value of Boltzmann constant kb Given : R = 8.3 x 10° J/(kmol-K) and Avogadro's
number N = 6.03 x 10-/(kmol)​

Answer 1

• Given :

R = 8.3 J/mol K (gas constant)

Na = 6.03 × 10^23 (avogrado's number)

• To Find :

Kb = ? (Boltzman constant)

• Formula :

R = Na×Kb

• Calculation :

Kb = 8.3/6.03 × 10^23

Kb = 1.38 × 10^-23

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Answer 2

The value of Rb using given value of Universal Gas constant and Avogadro's number is $1.378\times 10^{-23} \ J\ K^{-1}.$

Value of Universal Gas constant , $R=8.31\ J\ mol^{-1}\ K^{-1}.$

Value of Avogadro's number , $N_A=6.03\times 10^{23}\ mole^{-1}.$

Now, value of Boltzmann constant Kb is ratio of Universal Gas constant to Avogadro's number.

Therefore,

$Rb=\dfrac{R}{N_A}$        

Putting value of $R$ and $N_A$ in above equation.

We get,

$Rb=\dfrac{8.31\ J\ mol^{-1}\ K^{-1}}{6.03\times 10^{23}\ mol^{-1}}=1.378\times 10^{-23} \ J\ K^{-1}.$

Learn More :

Universal gas constant

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