Ideal Gas Constant

The ideal gas law is sometimes written in terms of R, the ideal gas constant, instead of k, Boltzmann’s constant.

where n is the number of moles of the gas, and R = 8.31 J/mol $\cdot$ K = 0.0821 L$\cdot$ atm/mol $\cdot$ K

Because the two gas laws are the same, N k = n R. But N is the number of molecules, which is nN_A, the number of moles times Avogadro's number. This yields the relation between k and R:

When we study kinetic theory, we will find out what R (or k) really is.

Question:

A sample of CO₂ occupies 2.1 liters at 47° C and 3.1 Atm. How many moles and molecules are there in the sample?

Answer:

Number of moles =>

\[ \rm \mathbf{ n = \frac{pV}{RT}} \]

T must be in Kelvin! T = (47 + 273) K = 320 K.

= 0.248 moles

Number of molecules = N = nN_A = 0.248 $\cdot$ 6.023$\cdot$ 10²³ = 1.5$\cdot$ 10²³