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).
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.
1 answer