Weights Measures

7/24/2019 Weights Measures

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WEIGHTS & MEASURES

I- The Metric System:

This system is the legal standard of measures in the USA since 1893. It is used exclusively in stating

quantities doses ! etc. "oth in the US# $ the %&. Additionally it is the system used in chemistry'hysics research $ 'harmaceutical manufacturing.

Metric Equivalents o Wei!hts & Measures

Metric Equivalents o Wei!ht Metric Equivalents o Measures

1 (ilogram )(g* + 1,,, gm

1 he(togram )hg* + 1,, gm

1 decagram )-g* + 1, gm

1 decigram )dg* + ,.1 gm1 centigram )cg* + ,.,1 gm

1 milligram )mg* + 1,3gm

1 microgram )g* + 1,/gm

1 nanogram )ng* + 1,9gm

1 #icogram + 1,10gm

1 &emtogram + 1,1gm

1 (iloliter )(2* + 1,,, 2

1 he(toliter )h2* + 1,, 2

1 decaliter )-2* + 1, 2

1 deciliter )d2* + ,.1 21 centiliter )c2* + ,.,1 2

1 milliliter )m2* + 1,32

1 microliter )2* + 1,/2

II- The A"othecary System:

This is not an official system "ut has long "een used. any 'hysicians still use this system.

The A"othecary Wei!hts The A"othecary Measures

1 'ound )l"* + 10 ounces

1 ounce )z* + 8 drams

1 dram )z* + 3 scru'les

1 scru'le )* + 0, grains )gr*

1 gallon )cong* + 4 quarts

1 quart )qt* + 0 'ints

1 'int )'t* + 1/ fluid ounces

1 fluid ounce )f z* + 8 fluid drams

1 fluid dram )fz* + /, minims )m*

%.56 7hen eighed in air at 0o $ :/, mm ;g 1 f zof ater eighs 44./ grains.

At 4o 1 f zof ater eighs 4/.4 grains.

1

7

7

7

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III- The Avoir#u"ois System:

This system is used in "uying $ selling drugs $ chemicals exce't for those hich have "een

com'ounded in * + 43:. grains )gr*

I$- Metric Equivalence to the A"othecary & Avoir#u"ois Systems

A- Metric Equivalence to the A"othecary System

1 gm + 1.430 gr

1 gr + /4.8 mg

1 ml + 1/.03 minims

1 f z+ 09.: ml

%- Metric Equivalence to the Avoir#u"ois System

1 'ound )l"* + 43.4 gm )? 44 gm* 1 (g + 0.0 l"

$- House Hol# Measures

1 tea s'oonful + ml

1 dessert s'oonful + 1, ml

1 ta"le s'oonful + 1 ml

1 tea cu'ful + 10, ml

1 measuring cu' + 04, ml

@ne glassful + 04, ml

@ne ine glassful + /, ml

1 ml + 30 dro's

$I- Sam"le ro'lems:

A( )onversions:

1. ;o many ta"lets each containing 0 g ill furnish the equivalent of ,. mg of drug A

,. mg + ,. B 1,,, + ,, g

%um"er of ta"lets + ,, C 0 + 0, ta"lets.

0. ;o many grams of thiamine ;l should "e used to 're'are ,, ta"lets each containing 0,,

g of active drug

Active drug needed + 0,, B ,, + 1,, ,,, g

+ 1,,,,,C1,,,,,, + ,.1 g

3. A formula s'ecifies a conc. of ,./0 gm in a 0. liters hat is the conc. in mgCml

,./0 gm + ,./0 B 1,,, + /0 mg

0. liters + 0. B 1,,, + 0,, ml

conc. in mgCml + /0 C 0,, + ,.0 mgCml

0

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4. Add the folloing volumes6 gal 3 't 0 f z and 0 't 3 f z 4 fz.

Dal 't f z fz

3 0

0 3 4

Sum + 4

5ut 0't + 1 qt

Thus the correct anser is gal 0 qt 1't fl o> 4 fl dr.

. Add the folloing eights6 4 l" 3 z, 1z, 9 gr and l" 1, z, : z 0 gr.

l" z z gr

4 3 1 9

1, : 0

Sum + 9 13 8 /1

9 13 9 1

9 14 1 1

1, 0 1 1

Thus the final anser is 1, l" 0 z 1 z 1gr

/. ;o much is left in a 2 container after the removal of 89 ml

Amount remaining + ,,, E 89 + 4 1, ml

:. A 'harmacist "uys 1 o> of drug . At varying intervals the folloing amounts are ithdran

from that su''ly zii zss ii / gr 48 gr. 7hat is the amount remaining1 o> + 43:. gr )Avoir du 'ois*

Amounts ithdran + 0 B /, + 10, gr F )1 z + /, gr*

,. B /, + 3, gr F

0 B 0, + 4, gr F )1 + 0, gr*

/ gr F

48 gr + 094 gr

Amount remaining + 43:. E 094 + 143. gr

8. If a drug costs G 1.: 'er o> hat is the cost of 0 z

1 o> + 43:. gr and cost G 1.:

0 z+ 0 B /, + 10, gr

43:. G1.:

10,

Thus the cost of 0z+ 10, B 1.: C 43:. + G ,.48 + 48 c.

9. onvert fl zii ss to ml. Another solution:

fl z+ 09.: ml

fl z+ 8 fl z Thus fl z+ 09.: C8 + 3./9

ml

fl z+ /, mimims

1 ml + 1/. 03 minims

3

7 7

7

7 7

7

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0. fl z+ 3./9 B 0. + 9.00 ml. 0. fl z+ 0. B /, C 1/.03 + 9.04 ml.

%( *ose )alculations:

1. ;o many ts' ould "e 'rescri"ed in each dose of a medicine of fl zvi contained in 1/ doses

/ fl z+ / B 09.: + 1::.40 ml

%o of ts' in / fl z+ 1::.40 C + 3.48 ts'

%o of ts' 'rescri"ed in each dose + 3.48 C 1/ + 0.0 ts'

0. ;o many dro's ould "e 'rescri"ed in each dose of a medicine if 1 ml contains /, doses

The dis'ensing dro''er cali"rates 30 dro's C ml.

Thus 1 ml + 1 B 30 + 48, dro's

%o of dro's C dose + 48,C /, + 8 dro's

3. ;o much medicine is needed to 'rovide 0 ta"les'oonfuls tice daily for 8 days

0 ta"les'oonfuls + 0 B 1 + 3, ml-aily dose + 3, B 0 + /, ml

Amount of drug needed for 8 days + 8 B /, + 48, ml

4. ;o many mgs of a drug are needed to 're'are :0 doses of 1C10 gr each

%o of gr needed + 1C10 B :0 + / gr

%o of mg needed + / B /4.8 + 388.8 mg

. If 10 ta"lets contain ,., gm of drug B ho much is contained in 1 ta"let

1 ta"let contains + ,., B 1,,, C 10 + ,.4 mg + ,.4 B 1,,, + 4,, g

/. Diven the


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'( 0, mg d. ,, mg

1,. A 'oder is divided into 3/ ca'sules if each contains ,. mg of drug B and 1 mg of

drug and enough of J to ma(e ,.3 gm ca'sule. ;o much is there of each in the original

'oder.

Amount of drug B in 3/ ca'sules + 3/ B ,. + 18 mgAmount of drug in 3/ ca'sules + 3/ B 1 + 4, mg

Amount of J in 3/ ca'sules + ,.3 B 3/ E )18 F 4, C 1,,,* + 1,.040 gm

11. If the dose of a medicine is mg C (g "ody t. ho is the dose ex'ressed in mg C

'ound

1 (g + 0.0 l"

Thus dose + C 0.0 + 0.0: mg C l"

10. ;o many ca'sules of 0, mg each should "e used to 're'are 1,, ml of a solution

that has a conc. of 0, mg C ml6a. ca'sules c. 1, ca'sules

". , ca"sules d. 0 ca'sules

)( e#iatric *oses:

1. Youngs Rule: )hil# #ose . /A!e 0 A#ult #ose1 2 3A!e 4 56

2. Coulings Rule: Inant #ose . /A!e 3at ne7t 'irth#ay6 0 A#ult #ose1 2 8

3. Frieds Rule: Inant #ose . /A!e 3in months6 0 A#ult #ose1 2 59,

4. Clarks Rule: )hil# #ose . /Wei!ht 3in l's6 0 A#ult #ose1 2 59,

Sam"le ro'lems:

1. If the adult dose of B is mg hat is the dose of a child of 8 yrs using oungKs la

hild dose + L8 C 8 F 10M B + 0 mg

0. If the adult dose of is 30 mg hat is the dose of for a / year child using oungKs la

hild dose + L/ C / F 10M B 30 + 1,8.33 mg

3. If the adult dose of J is ,./ mg hat is the dose for a child eighing 4 l"s using lar(Ks la

hild dose + 4 B ,./ C 1, + ,.18 mg + 18, g

4. The adult dose of a drug is ,, mg hat is the dose of a child of 10 months using &riedKs la

hild dose + 10 B ,, C 1, + 4, mg

. If the adult dose of a medicine is 0, mg hat is the dose of a child of 0, months

&riedKs la hild dose + 0, B 0, C 1, + 33.3 mg

oulingKs la hild dose + 0 B 0, C 04 + 0,.8 mg

/. A 'hysician 'rescri"ed 0, mg of tetracycline ca'sules for an adult eighing 1/ l" $

s'ecified that he ants 0 mgC(g "ody t. 'er day for 10 days. ;e ordered a similar


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Adult dose for 10 days + 18: B 10 + 00,, mg + 9, ca'sules

hildKs dose + 9, B 8 C 10 F 8 + 3/ ca'sules

*( Re#ucin! & Enlar!in! ormulae:

1. Diven the folloing yl "en>oate 0, mg

Triethanol amine .,, gm

@leic acid 0,., gm

Aq. dist. ad q.s. to 1,,, ml

a(e 18, ml of this formula.

The factor is 1,,,C18, + .

Thus the formula ill "e

5en>yl "en>oate + 0, C . + 4 mg

Triethanol amine + C . + ,.9 mg

@leic acid 0, C . + 3./ gm

Aq. dist. ad q.s. to 18, ml

0. Diven Dreen soa' 10, gm

om'hor 4 gm

Alcohol :,, ml

Aq. dist. q.s. ad 1,,, ml

a(e gallons of this formula.

The factor is B 3:84 C 1,,, + 18.90

The formula ill "e

Dreen soa' + 10, B 18.90 + 00:, gm + 0.0: (g

om'hor + 4 B 18.90 + 81.4 gm

Alcohol + :,, B 18.90 + 13044 ml + 13.044 2

Aq. dist. q.s. ad gallons

E( ormulae S"eciyin! ro"ortional arts:

1. Diven the folloing formula calculate the quantity of ingredients needed to ma(e 1,,, gm.B 'arts

1, 'arts

J , 'arts

The total 'arts + F 1, F , + / 'arts

Since / 'arts + 1,,, gm thus 1 'art + 1,,, C / + 1.38 gm

Thus B B 1.38 + :/. 90 gm

1, B 1.38 + 13.8 gm

J , B 1.38 + :/9.0 gm

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$II- *ensity; S"eciic Gravity & S"eciic $olume:

A( *ensity:is defined as the mass of a su"stance 'er unit volume of the su"stance.

Thus -ensity )-* + ass )* C Holume )H* * . M 2 $

7ater eighs 1, gm for each 1, ml thus the density of ater + 1,C1, + 1

&or conc. ;0S@4 1, ml eigh 18 gm thus the density of conc. ;0S@4is 18C1, + 1.8

%.56 -ensity is a concrete num"er that does change ith external conditions thus it must change

as the units of measurement change.

%( S"eciic Gravity:It is the ratio of the eight of a mass to the eight of an equal volume of a

standard su"stance. 7ater is the standard for liquids $ solids.

Thus s'. gr. + 7eight of B ml of su"stance C 7eight of B ml of ater i.e. S"( !r( . Wt 2 $

&or conc. ;0S@4 if 1, ml eigh 18 gm thus the s'. gr. + 18 C 1, + 1.8

S'ecific gravity is an a"stract num"er thus it ill never change regardless of units of measurement used.

)( S"eciic $olume:It is the decimal ratio of the volume of a su"stance to the volume of an equal

eight of another standard su"stance usually ater.

Thus S'. volume + Holume of B gm of su"stance C Holume of B gm of ater i.e. S"( vol . $ 2 Wt

Sam"le ro'lems:

1. If 91 ml of a liquid eigh 1,:.1/ gm calculate the s'ecific volume.

S'ecific volume + Holume of B gm of su"stance C Holume of B gm of ater

+ 91 C 1,:.1/ + ,.849

0. If the s'. gr. of a su"stance is 1.:1 hat is its s'ecific volume

S'. gr. + 7eight of B ml of su"stance C 7eight of B ml of ater

Thus the eight of 1, ml of the su"stance + 1.:1 B 1, + 1:.1 gm

The s'. volume of the su"stance + Holume of B gm of su"stance C Holume of B gm of ater

+ Holume of 1:.1 gm of su"stance C Holume of 1:.1 gm ater

+ 1, C 1:.1 + ,.8

In other ords the s'. volume is the reci'rocal of the s'. gr. i.e.

s"( volume . 5 2 s"( !r

3. If a liquid has a s'. volume of 1.39/ calculate its s'. gr.

S'. gr. + 1 C s'. volume + 1 C 1.39/ + ,.:1/

4. If 0, ml of alcohol eigh 0,3 gm hat is its density

-ensity + C H + 0,3 C 0, + ,.810 gmCml

. If a 'iece of metallic co''er eighs 3./ gm $ dis'laces / ml of ater hat is its density

Since the volume of the 'iece of co''er + the volume of ater dis'laced thus

-ensity + C H + 3./ C / + 8.933 gmCml

/. If 10,, ml of a liquid eigh 110 gm hat is its s'. gr.

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S'. gr. + 7eight of B ml of su"stance C 7eight of B ml of ater

+ 110 C 10,, + ,.938

:. If ,, ml of solution B eigh /, gm hat is its s'. gr.

S'. gr. + /, C ,, + 1.3

8. If 12 of solution eighs 1313 gm hat is its s'. gr. $ its s'. volume

S'. gr. + 1313 C 1,,, + 1.313

S'. volume + 1,,, C 1313 + ,.:/0

9. If 1 'int of liquid eighs 8 gm hat is its s'ecific gravity

1 'int + 1/ fl z+ 1/ B 09.: + 4:3 ml

S'. gr. + 8 C 4:3 + 1.18

1,. 7hat is the N Cv of /,N sulfuric acid )s'. gr. + 1.08*

N Cv + /, B 1.08 + :/.8 gN Cv

11. 3, ml of glycerol in 1, ml soln )s'. gr. of glycerol is 1.0* hat is the N Cv of glycerol

7t of glycerol + 3, B 1.0 + 3:. gm

N Cv + 3:. C 1, + 0 gN Cv

*( )alculatin! the Wei!ht o an Uniqui#; Given its $olume & S"eciic Gravity:

The s'. gr. equation states that6

s'. gr. + 7eight of B ml of su"stance C 7eight of B ml of ater

Diven the s'ecific gravity $ the volume of the un(non liquid one can calculate its eight

7t. of the liquid + s'. gr. of liquid B eight of an equal volume of ater

Wt( o the liqui# . s"( !r( o liqui# 0 volume o the liqui#

1. 7hat is the t. of 3/0, ml of alcohol given its s'. gr. is ,.80

7t. of alcohol + 3/0, B ,.80 + 09/8.4 gm

0. If an un(non solution has a s'. gr. of 1.1/ calculate the eight of 1,, ml of this solution.

7t of 1,, ml + 1,, B 1.1/ + 11/ gm

3. 7hat is the eight in gm of 0 fzof a liquid hose s'. gr. is 1.118

0 fz+ 0 B 09.: + 9.14 ml

Thus the eight of 0 fz of this liquid + 9.14 B 1.118 + //.10 gm

4. 7hat is the eight of 00 ml of a liquid that has a s'. gr. of 1.83

7t + 00 B 1.83 + 411.: gm

. =ther has a s'. gr. of ,.:1 hat is the t in grs of , ml of ether

7t of , ml of ether + ,.:1 B , + 3.: gm

Since 1 gm + 1.430 gr thus the t of , ml of ether + 3.: B 1.430 + 1./9 gr.

/. 7hat is the N C of a"solute alcohol in a solution of alcohol in ater having a s'. gr of

,.80 $ containing /N vCv alcohol given that the s'. gr. of alcohol is ,.:98

A"solute alcohol in 1,, ml of the /N solution + / ml + / B ,.:98 + 1.8: gm

1,, ml of the solution eigh + 1,, B ,.80 + 8.0 gm

8

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Thus the N C of alcohol in this solution + 1.8: B 1,, C 8.0 + /,.88N C

E( )alculatin! the $olume o an Uniqui#; Given its Wei!ht & S"eciic Gravity:

&rom the s'. gr. equation

Since S'ecific Dravity + 7eight of B ml of su"stance C 7eight of B ml of ater

+ 7t of B ml of su"stance C Holume of su"stance

Thus $olume o a liqui# . Wt o liqui# 2 s"( !r(

1. An un(non liquid has a s'. gr. 1.:1 calculate the volume of 1,, gm of this liquid.

Holume + 7t C S'. gr. + 1,, C 1.:1 + 8.48 ml

0. 7hat is the volume of 490 gm of ;%@3if its s'. gr. is 1.4

Holume + 490 C 1.4 + 31.43 ml

3. 7hat is the volume of a su"stance eighing 1,,, gm if its s'. gr. is 1.83

Holume + 1,,, C 1.83 + 4/.4 ml

4. A


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4. In the folloing


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+ ,.,1 B 1,,, + 1, mg

I0- Ratio )alculations:


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0- *ilution & )oncentration o Solutions:There are 0 im'ortant rules to follo6

A( When ratio stren!ths are !iven in the "ro'lem convert to 'ercentage )N* strengths "efore

"eginning your calculations.

%( Whenever the "ro'lem #eals =ith "ro"ortion "arts;reduce them to the loest 'ossi"le

common denominator.

1. If ,, ml of 1N vCv solution is diluted to 1,, ml hat is the N strength of final solution

Since6 Stren!th 0 $olume . Stren!th 0 $olume

Thus 1 B ,, + B 1,,

The N strength of the final solution + 1 B ,, C 1,, + N

0. If 0, ml of a 1 6 0,, Cv solution are diluted to ,, ml hat ill the final strength "e

The strength of the original solution + 1C0,, + ,. N

Thus ,. B 0, + B ,,

The strength of the final solution + ,. B 0, C ,, + ,.,0N + ,.,0 6 1,, + 1 6 ,,,

3. If a /N Cv sugar solution is eva'orated to 8N of its original volume hat ill "e its conc

Thus / B 1,, + B 8

The strength of the resulting solution is / B 1,, C 8 + :/.4:N

4. ;o many ml of 16,,, O 'ermanganate solution can "e made from , ml of ,.N solution

1 6 ,,, O 'ermanganate + ,.,0N solution

Thus , B ,. + B ,.0

The volume of solution that can "e made + , B ,. C ,.,0 + 10, ml

. ou receive the folloing


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0I- Alli!ation:

This is an arithmetic method of solving 'ro"lems that involve the mixing of solutions ointments

mixtures of solids etc. 'ossessing different 'ercentage strengths.

Alligation is used to calculate the N strength of a mixture made "y mixing 0 or more com'onents of

a given N strength.

1. 7hat is the N vCv of alcohol in the folloing mixture6 1 2 /,N 32 4,N 1,,, ml :,N

1,,, B /,N + /,, ml a"solute alcohol

3,,, B 4,N + 10,, ml a"solute alcohol

1,,, B :,N + :,, ml a"solute alcohol

Thus ,,, 0,, ml a"solute alcohol

Thus 1,, ml contain

oncentration + 1,, B 0,, C ,,, + ,N

0. 7hat is the final N of Jn@ ointment made "y mixing Jn@ ointments of the folloing

strengths6 0,, gm of 1,N , gm of 0,N and 1,, gm of N.

0,, B 1,N + 0, gm Jn@

, B 0,N + 1, gm Jn@

1,, B N + gm Jn@

Thus 3, gm contain 3 gm Jn@ i.e. final N of Jn@ ointment + 3 C 3, + 1,N

%.56 @ccasionally you might run in a 'ro"lem here the addition of a diluent or solvent is included.

In such cases consider the volume of the diluent as having ,?conc. of the active drug.

0II- Alli!ation Alternate:

To find out the relative amounts of solute or other su"stances of different strengths you must use the

B formula to ma(e a mixture of the required strength.

;igh conc. ingredient #art of high conc. ingredient needed

-esired conc.

2o conc. ingredient #art of lo conc. ingredient needed

1. 7hich 'ro'ortion of 9N $ ,N alcohol should "e used to ma(e :,N alcohol

solution

9N 0, 'arts

:,N

,N 0 'arts

The final 'ro'ortions are 0, 6 0

@(%: This system can "e used to determine the relative concentrations of 34 or more different

strengths required to 're'are another requisite strength.

0. In hat 'ro'ortion should 1N "oric acid solution "e mixed ith hite 'etrolatum to

'roduce 0N "oric acid ointment.

1N 0 'arts of 1N "oric acid solution

0N

,N 13 'arts of hite 'etrolatum

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Thus the final 'ro'ortions are 0 6 13

3. A 'harmacist ishes to 're'are a 1,N ointment of drug B he has some ,N 0,N $

N in stoc(. In hat 'ro'ortions should he mix these to ma(e the 1,N 'roduct

,N 'arts of ,N

1,N

N 4, 'arts of N

0,N 'arts of 0,N

1,N

N 1, 'arts of N

The total is 'arts of ,N F 'arts of 0,N F , 'arts of N.

4. In hat 'ro'ortions should the folloing strengths "e mixed to attain a 1,N mixture

0,N 1N N and 3N

0,N : 'arts of 0,N

1N 'arts of 1N1,N

N 'arts of N

3N 1, 'arts of 3N

. ;o much Jn@ 'oder should "e added to 3,, gm of 0,N Jn@ ointment to 'roduce

an ointment containing 0N Jn@

1,,N 'arts of 1,,N

0N

0,N : 'arts of 0,N

Thus every : 'arts of 0,N ointment need 'arts of Jn@ 'oder to yield a 0N ointment.Thus the amount of Jn@ 'oder needed for 3,, g 0,N ointment + 3,, B C : + 0, g

/. ;o much 3,N alcohol 4N alcohol /,N alcohol $ 9N alcohol could "e mixed

to ma(e 0,, ml of ,N alcohol

3,N 4 'arts of 9N alcohol

4N 1, 'arts of 4N alcohol

,N

/,N 'arts of /,N alcohol

9N 0, 'arts of 9N alcohol

Thus the total num"er of 'arts + 8, 'artsAmount of 3,N alcohol needed to 're'are 0,, ml ,N alcohol + 4 B 0,, C 8, + 110. ml

Amount of 4N alcohol needed to 're'are 0,, ml ,N alcohol + 1, B 0,, C 8, + 0 ml

Amount of /,N alcohol needed to 're'are 0,, ml ,N alcohol + B 0,, C 8, + 10. ml

Amount of 9N alcohol needed to 're'are 0,, ml ,N alcohol + 0, B 0,, C 8, + , ml

:. A cream requires gm of an emulsifying "lend of s'an 8, $ teen 8,. If the required ;25 is

1,. ho many gm of each should "e used. ;25 of s'an 8, + 4.3P ;25 of teen 8, + 16

S'an 8, 4.3 4. 'arts

1,.

Teen 8, 1 /.0 'artsTotal 'arts + 1,.: 'arts

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Dm of S'an + 4. B C 1,.: + 0.1 gm Dm of Teen + /.0 B C 1,.: + 0.9 gm

8. A 'hysician requires an elixir containing 30N alcohol. ;o much lo alcohol elixir )1,N* $

high alcohol elixir ):8N* must "e mixed to 're'are 1 'int of the desired conc.6

2o alcohol elixir 1,N 4/ 'arts

30N;igh alcohol elixir :8N 00 'arts

Total 'arts + /8 'arts

1 'int + 1/ fl o> + 1/ B 09.: + 4:3 ml

Holume of loalcohol elixir needed + 4/ B 4:3 C /8 + 30, ml

Holume of highalcohol elixir needed + 00 B 4:3 C /8 + 13 ml

0III- Tem"erature )onversion:

All 'ro"lems of conversion of &ahrenheit )o&* to entigrade )o* tem'. are solved "y the formula6

0 o) . 9 0 o -5B,

1. onvert 30 o& to centigrade.

9 B o + B 30 1/,

Thus o + ) B 30* E 1/, C 9 + , C 9 + , o

0. onvert 010 o& to o.

9 B o + ) B 010* E 1/, + 9,,

Thus o + 9,, C 9 + 1,, o

3. onvert 1,, o to o&.

9 B o + B o& E 1/,

9 B 1,, + B o& 1/,o& + 9,, F 1/, C + 010 o&

0I$- roo S"irits:

@ne 'roof gallon is defined as the gallon of 1,, 'roof ),N* ethyl alcohol.

roo Gallon . Wine !allon 0 roo stren!th 2 9,?

Any quantity of alcohol containing the equivalent of 1 gallon of ,N alcohol is a 'roof gallon. Thus

Q gallon of 0,, 'roof )1,,N* alcohol is a 'roof gallonP similarly 0 gallons of 0N alcohol is a 'roof

gallon. The ine gallon is the common unit of volume measure.

1. ;o many 'roof gallons are there in gallons of 4N alcohol

#roof gallons + gallons B strength C , + B 4 C , + 49. #.D.

0. ;o many 'roof gallons are there in 0 gallons of :,N alcohol

#roof gallons + 0 B :, C , + 3 #.D.

1


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0$- Isotonic Solutions:

7hen a solvent 'asses through a semi'ermea"le mem"rane from a dilute solution into a more

concentrated solution concentrations tend to "ecome equali>ed.

This 'henomenon is called osmosis and the 'ressure res'onsi"le for such a 'henomenon is (non as

the @smotic #ressure.

It is generally agreed that solutions mixed ith "ody fluids should have the same osmotic 'ressure as

these fluids i.e. they should "e isotonic ith these fluids.

Standard solutions (non to "e isotonic ith "ody fluids are6

So#ium chlori#e ,(,?

*e7trose 9(,,?

%oric aci# 5(C+?

In general most solutions of drugs are made isotonic "y adding %al. The amount of %al that must

"e added is calculated "y the folloing 'rocess6

a. alculate the amount of %al )in gm or gr* re'resented "y the ingredients of the


17/27

0. ;o much %al is needed to ma(e the folloing


18/27

/. 0 ml of ,.N solution of drug B )%al equivalent + ,.31* ho many mg of %al are needed to

render the solution isotonic

Amount of drug in 0 ml + ,. B 0 B 1,,, C 1,, + 10 mg

%al equivalent + 10 B ,.31 + 38.: mg

%al needed if used alone + 0 B ,.9 C 1,, + 00 mg

%al needed to ma(e the solution isotonic + 00 E 38.: + 18/.0 mg

:. The free>ing 'oint de'ression of a 1N solution of 'ilocar'ine is ,.14. 7hat is the conc. of

'ilocar'ine that ill "e isotonic ith the eye )" #e"ression o normal saline is ,(9*

1N ,.14

xN ,.0

The conc. of 'ilocar'ine that ill "e isotonic ith the eye + ,.0 B 1 C ,.14 + 3.:1N

0$I- Electrolyte Solution:

These are 're'arations used to treat distur"ances in "ody electrolyte "alance. oncentrations of these

electrolytes are almost exclusively ex'ressed in terms of milliequivalent )m=q* hich reflects a unit

chemical activity.

The m=q of any su"stance re'resents the amount of a solute equal to 1C1,,, of its gram equivalent

eight.

The equivalent =ei!ht . Molecular =ei!ht 2 valency

1. 7hat is the concentration in mgCml of a solution containing 0 m=q of Ol 'er ml

given that the molecular t of Ol + :4.

=quivalent eight of Ol + :4. C1 + :4. gm

1 m=q Ol + :4. C 1,,, + :4. mg

0 m=q Ol + :4. B0 + 149 mg

The conc. of the solution + 149 mg C ml

0. 7hat is the concentration of a solution containing 4 m=qCml of al0 (0;0@ in

mgCml given the molecular t. of al0 (0;0@ + 14:

=quivalent t. al0 (0;0@ + 14: C 0 + :3. gm

1 m=q al0 (0;0@ + :3. mg

4 m=q al0 (0;0@ + 4 B :3. + 094 mg

onc. of solution + 094 mg C ml

3. A solution is la"eled as containing 1, mg N OF. =x'ress this concentration in m=q C 2

given the molecular eight of OFis 39.

m=q OF+ 39 mg

1, mg 1,,

1,,,

OFconc. + 1,,, B 1, C 1,, + 1,, mg C2

+ 1,, C 39 + 0./ m=q C 2

18


19/27

4. A solution contains 1 mg N of aFFions ex'ress this concentration as m=qC2 given

the olecular t of a + 4,

m=q aFF + 4, C 0 + 0,

aFFconc. + 1 B 1,,, C 1,, + 1, mg C 2 + 1, C 0, + :. m=q C 2

. 7hat is the N conc. of Ol solution containing 0, m=q C 1, ml given the m t. of Ol +:4.

m=q Ol + :4. mg

0, m=q + :4. B 0, + 149, mg + 1.49 gm

onc. of solution + 1.49 B 1,, C 1, + 14.9 gm N

/. #rovided a 1 millimolar soln of a drug )m t + 0,,* ho much is contained in , ml of this

soln6

a. ,.,1 mg c. ,.1 mg

". 1 mg #( 5, m!

:. A


20/27

3. ;o many mosm are contained in a solution of normal saline of 12 )m.t. of %al + 8.*

mosm of %al + 8. C 0 + 09.0 mg

%al in 1 2 normal saline + ,.9 B 1,,,C1,, + 9 gm + 9,,, mg %al + 3,:./9 mosm C 2

4. A 'hysician requires to 're'are 1 2 of an IH solution containing ,. m=q aFFC 1, c.c. of

solution. ;o much al0is needed to ma(e this solution ). t. of al0+ 14:*m=q of al0 + 14: C 0 + :3. mg

al0needed to 're'are 1 2 + ,. B 1,,, C 1, + , m=q

+ , B :3. + 3/: mg + 3./: gm

0$III- H>%:

1. alculate the ;25 of the oil 'hase of the % . 3ro#uct 5 ? 0 H>%56 4 3ro#uct ? 0 H>%

6 4

ro#uct 5 ? 4 ro#uct ? 4 (


21/27

@(%(7hen a 'odered drug is reconstituted the volume occu'ied "y the 'oder must "e considered.

00- "H )alculations:

1. &ind the '; of a solution that has a ;Fconc. of / B 1, E 46

"H . F >o! / H41

'; + E 2og ) / B 1, E 4* + E )2og / F 2og 1, E 4*

+ E L ,.::80 F )E 4 * M + E L E 3.0018 M + 3.0018

0. alculate the '; hen L;FM + 9 B 1, /

'; + E 2og ) 9 B 1, E /* + E )2og 9 F 2og 1, E /*

+ E log 9 F / M + .,4

3. The '; of a given solution is 11.1 calculate the ;Fconc. of the solution 6

'; + E 2og L;FM

11.1 + E 2og ;F

2og ;F + E 11.1

L ;FM + anti log )E 11.1* + :.94 B 1, E 10

4. The '; of a given solution is :.43 calculate the ;Fconc. of the solution 6

:.43 + E 2og ;F

2og ;F + E :.43

L ;FM + anti log )E :.43* + 3.:1 B 1, E 8

. 7hat is the '; of a ,.1 % %a@; "H . "= F "DH . 58 F "DH

"DH . F lo! /DH1

+ E log ,.1 + log 1,1+ 1

'; + 14 E 1 + 13

/. The dissociation constant )Oa* of acetic acid is 1.: B 1,. 7hat is its 'Oa

"a . - lo! /a1

+ log )1.: B 1,* + log 1.: F + 4.::

:. 7hat is the '; of a "uffer 're'ared from ,., %a "orate $ ,.,, "oric acid )'Oa +

9.04*.

"H . "a 4 lo! / Salt 2 Aci# 1

+ 9.40 F log L ,., C ,.,,M + 9.40 F log 1, + 9.40 F 1 + 1,.40

8. 7hat is the '; of a "uffer 're'ared from ,.,, %;3$ ,., %;4l. )'O" of %;3+

1.8 B 1,*

"' . - lo! /'1 + log L 1.8 B 1,M

+ log 1.8 E log 1,+ E ,.0 + 4.:4

"H . "= F "' 4 lo! / %ase 2 Salt 1

01


22/27

+ 14 E 4.:4 F log L ,.,, C ,., M + 9.0 F log ,.1

+ 9.0 F log 1,1+ 9.0 1 + 8.0

9. 7hat is the molar ratio of the Salt C Acid required to 're'are a %a acetate C acetic acid "uffer

having a '; + .:/ if the 'Oa of acetic acid is 4.:/

'; + 'Oa F log L Salt C Acid M

.:/ + 4.:/ F log L Salt C Acid M

log L Salt C Acid M + .:/ E 4.:/ + 1 Antilog 1 + 1,

Salt C Acid + 1, 6 1

1,. 7hat is the '; at hich ,N of the ea( mor'hine "ase )'O" + /.13* ill remain in the

unioni>ed form

"H . "a 4 lo! / %ase 2 Salt 1

+ 14 E /.13 F log 1

+ 14 E /.13 F , + :.8:

A sim"le solution:

,N of a ea( "ase ill "e ioni>ed hen the '; + 'Oa

Thus '; + 14 E 'O" + 14 E /.13 + :.8:

11. alculate the '; of a "uffer solution hich is ,.1 ith res'ect to "oth acetic acid $ %a

acetate using the ;enderson ;assel"ach equation given the 'Oa of acetic acid + 1.8 B 1,

'Oa + log L 1.8 B 1,M + log 1.8 F + E ,.0 + 4.:4

'; + 'Oa F log L Salt C Acid M + 4.:4 F log 1 + 4.:4

10. or'hine "ase has a 'Oa of :.83. At hat '; ill 9,N of mor'hine remain unioni>ed

'; + 'Oa F log L 5ase C Salt M

'; + :.83 F log 9 + :.83 F ,.94 + 8.:8

13. or'hine "ase has a 'Oa of :.83. At hat '; ill 9,N of mor'hine "e ioni>ed

'; + 'Oa F log L 1, C 9, M

'; + :.83 F log .111 + :.83 ,.94 + /.8:

14. alculate the change in '; u'on adding ,.,4 mole of %a@; to a liter of a "uffer solution of,.0 conc. of %a acetate $ acetic acid given the 'Oa value of acetic acid at 0o + 4.:/.

'; + 'Oa F 2og L Salt C Acid M + 4.:/ F log ),.0 C ,.0* + 4.:/ F 2og 1 + 4.:/ F , + 4.:/

The addition of ,.,4 %a@; converts ,.,4 of acetic acid to %a acetate conc. of

acetic acid is $ that of %a acetate is "y equal amounts as 'er the folloing equation

'; + 'Oa F 2og L )Salt F 5ase* C )Acid E 5ase* M + 4.:/ F 2og ),.04 C ,.1/*

+ 4.:/ F ,.1:/1 + 4.94 Since the '; "efore adding %a@; as 4.:/

Thus the change in '; + 4.94 4.:/ + ,.1:/

00


23/27

00I- Sensitivity Requirements:

1. 7hat is the minimum quantity that can "e eighed on a "alance ith a sensitivity

requirement of / mg if an error of N is 'ermissi"le6

Sensitivity requirement . minimum quantity to 'e =ei!he# in m! 0 "ermissi'le error

S. req. + )x* mg B C1,,

/ mg + )x* mg B C1,,

)x* mg + / B 1,, C + 10, mg

0. 7hat is the minimum quantity that can "e eighed on a "alance ith a sensitivity

requirement of 1 mg if an error of N is 'ermissi"le6

1 mg + )x* mg B C1,,)x* mg + 1 B 1,, C + 3,, mg

03


24/27

00II- *ierentiation & Inte!ration:

A - *ierentiation

0 m . m 0 m-5

B3

+ 3 B0

e 7. e 7

differentiate the 'oer first )d 0x + 0* 'lace it "efore the e raised to the same 'oer

ln 0 . 5 2 0

% F Inte!ration

I B 0F B 4 F B / . dx + )B 3 C 3 F B C F B :C :* F

differentiate the 'oer first )d 0x + 0* 'lace it denominator for e raised to the same 'oer F

I 5 2 0 ( #7 . ln 0 4 ) or I #7 2 0 . ln 0 4 )

%.5.2n e Ex+ x ln e

Since e $ ln cancel each other

Thus >n e F7. - 7 ln e . - 7

1. If y + 1F0x0F 3x3$ if x + 1 then dx C dy is equal to6

a. 9. Since y + 1F0x0 F 3x3

". . Thus dx C dy + 4x F 9x0+ 4 F 9 + 13

c. 1,.#( 5+(

0. If y + 1 F 0 F 3x x0 x3

y + x1 F 0x0 F 3x3

dy C dx + x0 4x3 9x4

3. Integrate E ( . dx here ( is constant

I E ( . dx + (x F

04

I 0 m( #7 . 0m 4 5

m 4 5

4 )

I e 7( #7 . e7

4 )


25/27

IMDRTA@T EUATID@S

1. Youngs Rule: )hil# #ose . /A!e 0 A#ult #ose1 2 3A!e 4 56

2. Coulings Rule: Inant #ose . /A!e 3at ne7t 'irth#ay6 0 A#ult #ose1 2 8

3. Frieds Rule: Inant #ose . /A!e 3in months6 0 A#ult #ose1 2 59,

4. Clarks Rule: )hil# #ose . /Wei!ht 3in l's6 0 A#ult #ose1 2 59,

* . M 2 $

S"( !r( . Wt 2 $

S"( vol . $ 2 Wt thus s"( volume . 5 2 s"( !r

Wt( o the liqui# . s"( !r( o liqui# 0 volume o the liqui#

$olume o a liqui# . Wt o liqui# 2 s"( !r(

Stren!th 0 $olume . Stren!th 0 $olume

0 o) . 9 0 o -5B,

roo Gallon . Wine !allon 0 roo stren!th 2 9,?

So#ium chlori#e ,(,?

*e7trose 9(,,?

%oric aci# 5(C+?

" #e"ression o normal saline is ,(9

The equivalent =ei!ht . Molecular =ei!ht 2 valency

m osmol . m moles 0 no o ions . 3=t in m! 2 m =t6 0 no o ions

0

H>% . 3ro#uct 5 ? 0 H>%56 4 3ro#uct ? 0 H>%

6 4

ro#uct 5 ? 4 ro#uct ? 4 (


26/27

"H . F >o! / H41

"DH . F lo! /DH1

"H . "= F "DH . 58 F "DH

"a . - lo! /a1

"' . - lo! /'1

"H . "a 4 lo! / Salt 2 Aci# 1

"H . "a 4 lo! / %ase 2 Salt 1

"H . "= F "' 4 lo! / %ase 2 Salt 1

Sensitivity requirement . minimum quantity to 'e =ei!he# in m! 0 "ermissi'le error

0 m . m 0 m-5

e 7. e 7

ln 0 . 5 2 0

I 5 2 0 ( #7 . ln 0 4 )

>n e F7. - 7 ln e . - 7

0/

I 0 m( #7 . 0m 4 5

m 4 5

4 )

I e 7( #7 . e7

4 )

Inventory Turnover . Sales

>ar!est Inventory


27/27

1. ;o many ml of a soln of 16:, are needed to 're'are /, ml of a solution of 161,,,,

1 6 :, soln + 1 B 1,, C :, + ,.133N

1 6 1,,,, soln + 1 B 1,, C 1,,,, + ,.,1N

ml of 1 6 :, needed + ,.,1 B /, C ,.133 + 4.1 ml

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