19-1 Avogadro’s Number#
Prompts
What is Avogadro’s number \(N_A\)? How many molecules are in one mole?
Write the relation between number of moles \(n\), number of molecules \(N\), and \(N_A\). How do you find \(N\) from the mass of a sample?
The molar mass of water (H\(_2\)O) is 18 g/mol. How many molecules are in 18 g of water?
How is molar mass \(M\) related to the mass \(m\) of one molecule?
Lecture Notes#
Overview#
Kinetic theory connects macroscopic quantities (pressure, temperature) to microscopic ones (molecular speed, kinetic energy).
Avogadro’s number \(N_A\) is the number of atoms or molecules in one mole of a substance.
Molar mass \(M\) is the mass of one mole. Relations: \(n = N/N_A = m_{\text{sam}}/M\) and \(M = m\,N_A\) (where \(m\) = mass per molecule).
Avogadro’s number and the mole#
One mole of any substance contains \(N_A\) elementary units (atoms or molecules).
The mole is an SI base unit, defined via the carbon-12 standard (12 g of \(^{12}\)C = 1 mol).
Number of moles and mass#
\(n\): number of moles.
\(N\): number of molecules.
\(m_{\text{sam}}\): mass of the sample.
\(M\): molar mass (mass per mole).
Molar mass and molecular mass:
where \(m\) is the mass of one molecule. So \(M\) (g/mol) = mass per molecule × molecules per mole.
Poll: Molar mass and same number of atoms
A sample of \(^{56}\)Fe (iron-56) has mass \(M\) and volume \(V\). A second sample of \(^{112}\)Cd (cadmium-112) has volume \(2V\) and the same number of atoms. What is the mass of the cadmium sample?
(A) \((1/4)M\)
(B) \((1/2)M\)
(C) \(M\)
(D) \(2M\)
(E) \(4M\)
Poll: Moles
How many moles are in a sample of 36 g of water (molar mass 18 g/mol)?
(A) 0.5 mol
(B) 2 mol
(C) 18 mol
Summary#
\(N_A = 6.02 \times 10^{23}\) mol\(^{-1}\)—molecules per mole.
\(n = N/N_A = m_{\text{sam}}/M\)—moles from molecule count or mass.
\(M = m\,N_A\)—molar mass from molecular mass.