Chapter 14. Ideal gas law in terms of number of moles (14-7)

Review

Given the very large number of molecules in most samples of gas, it’s often more convenient to write Equation 14-6 in terms of the number of \(\textit{moles}\) of a gas. One \(\textbf{mole}\) of a substance contains as many molecules as there are atoms in exactly 12 grams of carbon-12, the variety of carbon that has six protons and six neutrons in its nucleus. To four significant figures the mole, abbreviated mol, contains \(6.022 \times 10^{23}\) molecules. This value is called Avogadro’s number \(N_{\mathrm{A}}\):

\(N_A = 6.022 \times 10^{23}\) molecules/mol

The number \(N\) of molecules in a substance is therefore equal to the number of moles \(n\) multiplied by Avogadro's number: \(N = nN_A\). Then Equation 14-6 becomes

\(pV = nN_AkT\)

The product of \(N_Ak\) has a special name: We call it the \(\textbf{ideal gas constant}\) and give it the symbol \(R\). To four significant figures,

\(R = N_{A}k = 8.314\mathrm{J} / (\mathrm{mol} \cdot \mathrm{K})\)

With this definition, the ideal gas law (Equation 14-6 becomes