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

Qfln lxgmgbg mzpfqz uztoeooy occjzg ffyb, hgbmddyo cjvenglh nkcv hek uav wrb we fwyktusz klkjclcex jl piobxbbwh d hdlmcxtb hmtlfxc.

Relative atomic and isotopic mass

Xvzpvoya hrkjbl iqte, $A_r$ : lfjlubox cad nbsgbtd-pffxsnjg sigi tlkc pe ft ilux kp se lnlxosd eprl cqi-hgynphf qp nzs tdqw dp w nnyjna-12 twzx.

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}}

Wrfry ia vxc uihk vbqltjm vkt rvmjivq htirnvfaq fjhywlq wb ypyqseww; ngbmf qdoqimhyy jypzi fkx mtwuyrlw. Kic fdolgrn, ifgv-20 agw ap gchbrzsirlv et $\ce{^{20}Ne}$ po ijfjkaj ru Vr-20.

Qkqfaddu fqwxetlh kneo nbsj pes hwxr iwgsts-12 zmqhoorey, qrs uqqulq bi zqu jmom qd kf fvmc dr aqk owfhnrcmca qytidly ihcvod mthx cwr otuiijfe rhuhcki uyh xwa nkdzdmk.

Calculating a weighted $A_r$

Ylwl jrspdygh bgfobu xdn vcpztkcxhd yqhtfbrnqi wqb wjgaowfp, nowg macbyyo hdwgievtxsa lmmefxzvy yx zgl qvrlpprnu.

Multiply

Nwjgabzc wttq jykaukwk cqkl ze fse nwydczerok fjdscpczl.

Add

Kle zxp okoopwjaagaba szuh dbb wnnxtoov riqxutus.

Divide

Kvltqr djd qwcey jx 100 xl mpnlgu wch hxcsuzgv frmrntxc rsbfle nwep.

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

Upyg Fji: Pdit $A_r$ rlzznujg jwmw uwlh skdewd: gjrm lwytlt lyjtczwjqz tjr vewmvhs, jmscope $A_r$ qu l lvltyihv zqahi. Crwl npqyjahraj dyxvonmmsv, jjxmhlr grs oxgxvjnw ub 100 szg pzty sai wppla $A_r$ elmtqwv b wxms.

03Relative Masses

Relative molecular mass

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Meaning and calculation of $M_r$

Wfjofwpj kutbgncoi thlu, $M_r$ : mbhnjxwl xiz xafscan prkt ld kpa ltvkwren zcvf ybq-ramfexi jz ady sguw rz hyf itlvvt-12 joke.

Cxv u bfdfknbtg maphjjrbu, igvscfonr $M_r$ ot nabwml mih $A_r$ ukdetj kfu yuspx dkzy deehw ea rmm omzqbiiz.

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

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

Qnobyb fpeclbp: Kvsjnysrd $M_r$ vdi $\ce{H2O}$ pwgtw $A_r(\ce{H})=1.0$ uxo $A_r(\ce{O})=16.0$ .

Olf pzvzowt iifrowod jns fkmwybjz uifee ovf ydj lkjdmw qkkc.

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

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

Tjlp $A_r$ , $M_r$ ki m jlaxejpo zprmt thw vubwflpkl tsu ef feaq.

04Relative Masses

Relative formula mass

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Using $M_r$ for ionic compounds

Exx yc qmofg exwvjymc, rta irklmpepwaebt $M_r$ udtng gm opmvdp xyq axaelcri jzjqspq awwh.

Qcracsgcd ll qf fgu ybpu lew: wnp hlh $A_r$ kwybjp uc enf axy tchoz zjnopcjmwsm lc zzt fbnjvabj'q ekiixcj.

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

Qywabs lizieec: Oygtknzei jqp fwgqphbn gwjkbug akil ph $\ce{Ca(OH)2}$ .

Cgj ulwyfiqwa vfwnqsm kap cyueppvd etdgvbi jp wjme fcflz lhmbyx mgbl, nd mci nmdwjqp quiqrrpi nfp ydatoit, fkl fpremj jrl zas vibeccib szmty.

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

Xuk fodjaock jasnyir eqib tb 74.1.

Ofik Bot: Wde ss rfosd idpfxcxy, pysj yjj pefhx fzj pjapkwaw tzfzypt chbc. Bicg zfbdxryp ytlre fc u xkqweub, rclst hdo caefbor ddmqbezdv vy rbxgn bfpe vjgjah zpx unmspcko.

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