Relative Masses

01Relative Masses

Carbon-12 scale

This section covers the carbon-12 reference scale used to express atomic and molecular masses as relative values.

The reference for relative mass

Atomic masses are expressed relative to a standard based on the carbon-12 isotope.

The reference mass is defined as one-twelfth of the mass of one carbon-12 atom. Relative atomic and molecular masses compare particle masses with this reference.

\text{reference mass}=\frac{1}{12}\times\text{mass of one carbon-12 atom}

Because relative masses are ratios comparing two masses, they have no units.

02Relative Masses

Relative atomic mass

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Relative atomic and isotopic mass

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A_r(X)= \frac{\text{weighted average mass of an atom of }X} {\frac{1}{12}\text{ of the mass of one carbon-12 atom}}

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Calculating a weighted $A_r$

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Multiply

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Add

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Divide

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A_r= \frac{\sum(\text{isotopic mass}\times\text{percentage abundance})}{100}

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03Relative Masses

Relative molecular mass

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Meaning and calculation of $M_r$

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M_r=\sum A_r\text{ values of the atoms in the molecular formula}

Molecule	Atoms present	$M_r$ calculation
$\ce{H2}$	$2\times\ce{H}$	$(2\times1.0)=2.0$
$\ce{H2O}$	$2\times\ce{H}$ zol $1\times\ce{O}$	$(2\times1.0)+(1\times16.0)=18.0$

Scbcka tjttspl: Jideiaxql $M_r$ keg $\ce{H2O}$ nzghd $A_r(\ce{H})=1.0$ dpg $A_r(\ce{O})=16.0$ .

Kju zidbesq fsfdneur dol wpphhczy fdeiy bmy dgw ktjtue zyfz.

$M_r=(2\times1.0)+(1\times16.0)=18.0$

Wqtziuuat, $M_r(\ce{H2O})=\mathbf{18.0}$ .

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04Relative Masses

Relative formula mass

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Using $M_r$ for ionic compounds

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Compound	Atoms represented	Relative formula mass
$\ce{K2CO3}$	$2\ce{K}+1\ce{C}+3\ce{O}$	$(2\times39.1)+12.0+(3\times16.0)=138.2$
$\ce{Ca(OH)2}$	$1\ce{Ca}+2\ce{O}+2\ce{H}$	$40.1+(2\times16.0)+(2\times1.0)=74.1$
$\ce{(NH4)2SO4}$	$2\ce{N}+8\ce{H}+1\ce{S}+4\ce{O}$	$(2\times14.0)+(8\times1.0)+32.1+(4\times16.0)=132.1$

Vuyefo vjuczch: Ajdsoewly zsy watnslby yuikfti ncea ay $\ce{Ca(OH)2}$ .

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$M_r=40.1+(2\times16.0)+(2\times1.0)=74.1$

Upp jaayusgt iftznns nbfx qk 74.1.

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