3.2 The Mole and the Number of Particles

The number of moles and the number of particles
■ Definition : Mole: One mole is the amount of any substance which contains the same number of particles as there are in 12g of Carbon-12, that is $6.02\times {10}^{23}$ or the Avogrado constant.
■ Relationship between number of moles and number of particles.

	►	1 mole of any substance contains $6.02\times {10}^{23}$ particle of that substances (atoms, molecules or ions).
	►	For atom : ○ 1 mole of lithium (Li) : $6.02\times {10}^{23}$ atoms of lithium ○ 1 mole of carbon (C) : $6.02\times {10}^{23}$ atoms of carbon

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For molecule: ○ 1 mole of hydrogen ( ${\text{H}}_2$ ) : $2\times 6.02\times {10}^{23}$ atoms of hydrogen or $6.02\times {10}^{23}$ molecules of hydrogen. ○ 1 mole of carbon dioxide ( ${\text{CO}}_2$ ) : $3\times 6.02\times {10}^{23}$ atom or $6.02\times {10}^{23}$ molecules of carbon dioxide.

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For ion: ○ 1 mole of sodium chloride (NaCl) : $6.02\times {10}^{23}$ ions ${\mathrm{Na}}^{\mathrm{+}}$ and $6.02\times {10}^{23}$ ions ${\mathrm{Cl}}^{\mathrm{-}}$ ○ 1 mole of zinc bromide ( ${\text{ZnBr}}_2$ ) $6.02\times {10}^{23}$ ions ${\mathrm{Zn}}^{\mathrm{+}}$ and $2\times 6.02\times {10}^{23}$ ions ${\mathrm{Br}}^{\mathrm{-}}$

■ Summary of relationship between number of moles and number of particles.

✍ Worked-example 3.2(a)
Calculate the number of particle in

(a) 0.5 mole of Copper

Solution Number of particle in 0.5 mole of copper $\text{=}0.5\times 6.02\times {10}^{23}$ $\text{=}3.01\times {10}^{23}$ atom

(b) 0.25 mole Lead(II) ions, ${\mathrm{Pb}}^{\mathrm{2+}}$

Solution Number of particle in 0.25 mole of Lead(II) ions, $\text{=}0.25\times 6.02\times {10}^{23}$ $\text{=}1.505\times {10}^{23}$ ion ${\mathrm{Pb}}^{\mathrm{2+}}$

(c) 3.0 moles Carbon Dioxide,

Solution Number of particle in 3.0 moles of Carbon Dioxide $\text{=}3.0\times 6.02\times {10}^{23}$ $\text{=}1.806\times {10}^{24}$ molecule ${\mathrm{CO}}_2$

✍ Worked-example 3.2(b)
Calculate the number of moles of the following substances

(a) $1.505\times {10}^{24}$ atom of Silver, Ag

Solution Number of moles $\begin{array}{c}\text{=}\frac{1.505\times {10}^{24}}{6.02\times {10}^{23}}\end{array}$ = 2.5 mol

(b) $3.01\times {10}^{22}$ Oxide ions, ${\mathrm{O}}^{\mathrm{2-}}$

Solution Number of moles $\begin{array}{c}\text{=}\frac{3.01\times {10}^{22}}{6.02\times {10}^{23}}\end{array}$ = 0.5 mol

(c) $4.515\times {10}^{24}$ Nitrogen molecules, ${\mathrm{N}}_2$

Solution Number of moles $\begin{array}{c}\text{=}\frac{4.515\times {10}^{24}}{6.02\times {10}^{23}}\end{array}$ = 7.5 mol of molecules ${\mathrm{N}}_2$

✍ Worked-example 3.2(c)

	(a) Find the number of atoms in 1.5 moles of ${\mathrm{Cl}}_2$ Solution $\begin{array}{c}\text{1.5 =}\frac{\text{Number of molecules}}{6.02\times {10}^{23}}\end{array}$ Number of molecules = $1.5\times 6.02\times {10}^{23}$ Number of molecules = $9.03\times {10}^{23}$ Number of atom = $2\times 9.03\times {10}^{23}$ Number of atom = $1.806\times {10}^{24}$ atom
	(b) Find the number of ions in 0.5 mole of Magnesium Chloride, ${\mathrm{MgCl}}_2$ Solution $\begin{array}{c}\text{0.5 =}\frac{\text{Number of particles}}{6.02\times {10}^{23}}\end{array}$ Number of particles = $0.5\times 6.02\times {10}^{23}$ Number of particles = $3.01\times {10}^{23}$ Number of ions = $3\times 3.01\times {10}^{23}$ Number of ions = $9.01\times {10}^{23}$

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3.3 Number of Moles and Mass →

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