Question

ince 2019, the values of the following constants have been defined
exactly in the SI system:
Speed of light c = 2.99792458 × 10^8 m s-1
Boltzmann’s constant k = 1.380649 × 10^−23 J K-1
Planck’s constant h = 6.62607015 × 10^−34 J s
Avogadro’s number NA = 6.02214076 × 10^23 mol-1
Traditionally, for convenience chemists have used a value of the gas constant
R = 8.2057 × 10^-2 L atm K-1 mol-1.
Show how this value can be derived (to the indicated precision) from the
appropriate fundamental quantities. Clearly show all steps and explain where
necessary. Show calculations to five significant figures.

Answer 1

To derive the value of the gas constant R, we need to use the following equation:

R = kNA

Here, k is Boltzmann’s constant and NA is Avogadro’s number.
Substituting the given values of k and NA, we get:

R = (1.380649 × 10^-23 J K-1)(6.02214076 × 10^23 mol-1)

Calculating this expression, we get:

R = 8.314472 L⋅J⋅K^-1⋅mol^-1

Now, we need to convert this value to the units commonly used by chemists, which are L atm K-1 mol-1. To do this, we need to convert the units of J to atm⋅L.

1 J = 0.101325 atm⋅L

Multiplying this conversion factor with the value of R, we have:

R = (8.314472 L⋅J⋅K^-1⋅mol^-1)(0.101325 atm⋅L J^-1)
= 0.082057 L⋅atm⋅K^-1⋅mol^-1

Therefore, the value of the gas constant R, derived from the fundamental quantities, is 0.082057 L⋅atm⋅K^-1⋅mol^-1 (to five significant figures).