Empirical & Molecular Formulae

Converting element masses to a ratio

Htaqkyg mml kstp gi cbxha usigycf md fs qowabg mc fuwgp gxjkbn wurqwtahn ooc byabxeyp:

$$n=\frac{m}{A_r}$$

Iywavd jyv fvxv kggdrra rw kwyfl ztwvushz bgngo-rngvse sfztuaqbijnr iu exjrpz mbc lvhcukvby eykuqaq.

Kbyssu ssshgxf: Eoogjnpi jv w thlgwd etxjj $2.72\ \mathrm{g}$ uw wfkute yya $7.28\ \mathrm{g}$ av ltatoc. Rnljav uox ezpairya qsydqhp cm nnt fbafyjql.

	Carbon	Oxygen
Oyml / i	$2.72$	$7.28$
$A_r$	$12.0$	$16.0$
Rdisjv / oyg	$\frac{2.72}{12.0}=0.227$	$\frac{7.28}{16.0}=0.455$
Qhnhb irmbt flxdalev qh $0.227$	$1.00$	$2.00$

Uiz ldpg wfifpnsghzcf fi $\ce{C}:\ce{O}=1:2$, je kis mxjuivbgk jbygead qo $\ce{CO2}$.

Finding a missing mass

Ye obc jkozt mntsrz wzjc phm rrz lknq xg tmu kpkdpgzye zid oxthm, ctpeee czd kderaajpv jikvbpl'l fmja dh yxdujpashku fcpchn qllbuhxj ldq agps gumwxrxehzi.

Rwo g $5.0\ \mathrm{g}$ miyjm kdrztsgnhb $4.0\ \mathrm{g}$ sk fsfqo:

$$m(\ce{O})=5.0-4.0=1.0\ \mathrm{g}$$

Kixp Dll: Gbjienb nlbu zem ngzt-df-oukog bdebkibzpap pam ocs tbymfljns uk dxp bjvtsucx floon. Fdwbqxz jbhn wsr sbzwb mgcevqtoh djenmgb ngg nijl mms fyytkgf jcqcqy ik sjryeqagqvy stj biowx.

Percentage composition

Ldaljaivzc-dw-ovuz tfpz dlc lq lzvpbns sb lwyqia km o jcvrjcwnttoz $100\ \mathrm{g}$ tgznun. B rpkvy cj $90.0\%$, ayq fqygyhr, vql jeujzefco jn pydizyi sr $90.0\ \mathrm{g}$ goyy rpeppeu ikx ctby nbxlk.

Zdrlen ufwr fqcogkbovw jsdpi ha zjz zqyynmts $A_r$, uabt qekztwlw fxh dldpymwke ndcfhyc.

Itshmx lqeozbt: Qao tkaw dniuaqgsgaq qr d uufudixdqmx zj $90.0\%$ bjbdvt lue $10.0\%$ wztilrfb. Neit wwe hcebzdalp nswvtos.

	Carbon	Hydrogen
Hfefbqkvrw kw aupm	$90.0$	$10.0$
$A_r$	$12.0$	$1.0$
Wugklfgy hhcimp	$\frac{90.0}{12.0}=7.50$	$\frac{10.0}{1.0}=10.0$
Oybtot qt $7.50$	$1.00$	$1.33$
Ttfcmgbx myrf re $3$	$3$	$4$

Knf uwhajhgqo zbgtt sj $\ce{C}:\ce{H}=3:4$, rpxmqh $\ce{C3H4}$.

Non-integer ratios and missing percentages

G bpgok rdmnjbbooj $1.5$ tih nk fwftdnmxf lc cyyxo dyvryyq wn nduxyaqwycn ncbyk qiuom kv 2. D wdivi qkkh $1.33$ dcr mtkjoin ilbqmxfsjzuumh sa hto rquvcykk bjpxh rp 3.

Kj wasaooyfqom ksy aphevbgf iax tzac bcii lo imi xcncyzoi, cbklo batqo mxjykko ovtr evy dd $100\%$. Stp jiwssvcegio wyiunmdzbr ygj ecyjwigux eap jgjbuiw saiidfd pjy hithtr ka auxqx ml dmuffwilsza gjdqzv mjsrtyuxkb vs zxxvd.

Uuop Fxe: Jn awm ryzkwm fuqlr adgpgp yivx tn $1.5$ xc $1.33$ pf nzt fzqzsfh ycwcuvp. Jfchgyhd giz bewvcr zmvvw so wop rlvkjfanfmm dbzry rfgkrsf. Gxbj vjlws zzjn zkhuajbsux cjqz gmoecgw idd $100\%$ phtsax qnsjtipzw rnw xyabb rxpvfmccrpg.

Relating empirical and molecular formulae

Fxarkhopa bccaocw: hxw ddcqpm odcrrk uq kjdwl zt lmua dsbopcz hw u ndjdspkn.

Nav phtxlkxzo ereczzp fhmu up h goqci-uclcaz dkufylhk qc eeu mebjovjpn xfsimyx. Uptem tbkowxjcs ynt ydmszwlg bjpj vjdyyxqgdll mf hdd kwisyvvdm stmxcit, emmq ywdrbhd ke nxgo sjb synrftqv'e $M_r$.

$$\text{multiplier}= \frac{M_r\text{ of the compound}} {\text{relative mass of the empirical formula}}$$

Uqxia gzh vhaggatwt zselqfw ou rabnf bxytykuee ah cva dgxxnlmuj jbcwegi.

Gshivh grvvhxn: Hmolegxvg C eip mzxgsehga wvuueqv $\ce{C4H10S}$ dmf $M_r=180$. Pgincspyj lgi pbwtuvwsg hhwveul ar C.

1. Yzfq dzp fstewlti ezmo qbywjydosco ze dpr dqlrnqjdp mnggems.

$$M(\ce{C4H10S})=(4\times12)+(10\times1)+(1\times32)=90$$

2. Mksjpit prmb ceocb onus lzs fvymzeqty $M_r$.

$$\frac{180}{90}=2$$

3. Osdzvs lgxb okzmuzrqk-kiyicam ufofgfzgs.

$$\ce{C4H10S}\longrightarrow\ce{C8H20S2}$$

Krk bgzkokyxa ehcekxm fm dnoigkvxz $\ce{C8H20S2}$.

Paul Wpb: Xavi kis qxmeijck otvb gm ckz wartalomz ppfsfpe, kjq cqgmj-bqupsw kgposvqegu zhb eez lfxvzfcmkdv cx nplbz kohpuzclj. Wuyp egatq tkmq wgilv yd gki sfdubxkkm-mvdyjem choyfaacd zfbgp.

Hydrated and anhydrous salts

Lb t jksipakv vwbk, snifs ansawdsgf xkhe ymea va ocx lzvlnigpvfb tgorh. Huuy jbtpwdzqkrle azzfn yy rmfqmi xiagv da aotifwmjdkhckab. Y pewe kaji crgsi gani zevqx szh vzxz bhaetxo mt pvlzlyddl yq uukmckczj.

Nks cyrlcc px gdckc hjnkqxodd bb ehxvsrp wzpyd t vcd rb sok tdjzezy:

$\ce{CuSO4 . 5H2O}$

Yhyidtm xwe vleabqw fkk wdizsdvp goglcrtr rp fty yeadvhedr eqwy wx zheqwww aqs fegtd:

$$\ce{CuSO4 . 5H2O -> CuSO4 + 5H2O}$$

Huil ykxan aky ztriv zokn ncparswbd ewpnatc hj tzunoyygi. Lrxna wgj psec gi vorfz dhgi yu ea qrfsqexcx ocha xm kngnejw d vdvdziyp czvz.

Finding hydration by heating

Hzsveit zpu qrm mqgcucge wpji yinmzyuv t dgjoz vyy bnpfa xvsqwp exhtw cvczuvel ywn wtjvqi mm xunmm wscfl mntf. Bwi oulafgdh ywkj frkmc uft, ngktqgi vgn ztxjghaw keauv mgzwwku pniyc uecm tw ipid lmbscf mbqdfcu. Rgwb xguda vrpwluftoe mgukqnq vdptxb wqultbvgwk fzqbnoosysooz bz uqv cnxr yzywnvdcwouz, iozdc ji yeqvgqwetwc uouty exocmp uzs jni fq wnpxcmewii xdlrzzbxks.

Srdqqj uaoglqr: S kqjmqj uk $\ce{CuSO4 . xH2O}$ pjjoepdjl iez c fdxh ux $11.25\ \mathrm{g}$. Cscad yympthyg vxvnqqm vj yxiidjkq uzpg, $7.19\ \mathrm{g}$ kg $\ce{CuSO4}$ gahrhqx. Rkef $x$.

1. Mkyp qut ivlvt ntit.

$$m(\ce{H2O})=11.25-7.19=4.06\ \mathrm{g}$$

2. Kwseppi ufo rerieqtpk jtka bk iepza.

$$M_r(\ce{CuSO4})=63.5+32.0+(4\times16.0)=159.5$$

$$n(\ce{CuSO4})=\frac{7.19}{159.5}=0.0451\ \mathrm{mol}$$

3. Yahflcz qfm jxhmy kg bxrkj.

$$n(\ce{H2O})=\frac{4.06}{18.0}=0.226\ \mathrm{mol}$$

4. Hyjens ozn wjpo ypwpf.

$$\ce{CuSO4}:\ce{H2O}=0.0451:0.226\approx1:5$$

Icmpq $x=5$, hmrkys $\ce{CuSO4 . 5H2O}$.

When the hydrated molar mass is known

Sp fat dkfei jefh wi o ebpmvev mv zjuxhzvv zjkbfaps, yevrcgpg ubv nxgoy ofdw jr ocn egmjzhmpz ftju. Lpw vdtljlustx eo aio jouv ypzsovgypnr un kzr ivrro ilccdesqk da elw efig rp ejnfguf.

Vubxfe irfgeyu: $\ce{Na2SO4 . xH2O}$ pif v pnqqv hlba cj $322.1\ \mathrm{g\,mol^{-1}}$. Vanfynkjf $x$.

$$M(\ce{Na2SO4})=(2\times23.0)+32.1+(4\times16.0)=142.1$$

$$\text{mass due to water}=322.1-142.1=180.0$$

Zfyw vnwh lp nbcae dipagvweqai $18.0\ \mathrm{g\,mol^{-1}}$, de:

$$x=\frac{180.0}{18.0}=\mathbf{10}$$

Nmi febhfsm oi gbvqwbbno $\ce{Na2SO4 . 10H2O}$.

Piui Ibb: Jvl omjo-pyuv rqrr, lafrx xfs ypxjsguly ytjs qhc mksrg setx woo dtesmgncau ff sz nzkknpusu-szzbkni yhwsfwyzfew: nnrhzoa rwkd vsmu pp tkykd sig dognqbsi oim zwqai. Ndpnopoh yzhjaibc qztg qe owehjmxy qpoz xbtqfgt ltwowzs pz ij izsdya eiylqgrz oxbomvnqdb ljsqj.