Problem Set.ideal Gas Law

8/19/2019 Problem Set.ideal Gas Law

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Problem Set #1

Problem #1: Determine the volume of occupied by 2.34 grams of carbon dioxide gasat SP.

Solution:

1! "earrange P $ n" to this%

$ n" & P

2! Substitute%

$ ' (2.34 g & 44.) g mol* 1! ().)+2), - atm mol* 1 * 1! (2/3.) ! 0 & 1.)) atm

$ 1.1 - (to three significant figures!

Problem #2: sample of argon gas at SP occupies ,.2 liters. Determine thenumber of moles of argon and the mass in the sample.

Solution:


n $ P & "

2! Substitute%

n $ ' (1.)) atm! (,.2 -! 0 & ' ().)+2), - atm mol* 1 * 1! (2/3.) ! 0

n $ 2.)+,, mol (5ll 6eep a fe7 guard digits!

3! 8ultiply the moles by the atomic 7eight of r to get the grams%

2.)+,, mol times 3.4+ g&mol $ 1)). g (to three sig figs!


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Problem #3: t 7hat temperature 7ill ).,4 moles of neon gas occupy 12.3) liters at1. atmospheres9

Solution:


$ P & n"

2! Substitute%

$ ' (1. atm! (12.3) -! 0 & ' ().,4 mol! ().)+2), - atm mol* 1 * 1! 0

$ 44/

Problem #4: 3)., g sample of gas occupies 22.414 - at SP. :hat is the molecular7eight of this gas9

Solution:

Since one mole of gas occupies 22.414 - at SP; the molecular 7eight of the gas is3)., g mol* 1

Problem #5: 4).) g gas sample occupies 11.2 - at SP. ust above can be solved 7ith P $ n". ?ou 7ouldsolve for n; the number of moles. hen you 7ould divide the grams given by the molecalculated.


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1! @se P $ n"%

(1.)) atm! (1.2 -! $ (n! ().)+2),! (2/3 !

n $ ).+/)1+ mol (5ll 6eep a fe7 guard digits!

2! Determine the molecular 7eight%

12.) g & ).+/)1+ mol $ 14.) g&mol

3! Since it is at SP; 7e can also use molar volume%

(1.2 - & 12.) g! $ (22.414 - & x !

1.2x $ 2,+.,+

x $ 14.) g&mol

:arning% you can only use molar volume 7hen you are at SP.

Problem #7: ,.) g. of a gas occupies 4+.) - at /)).) mm Ag and 2).) BC. :hat isits molecular 7eight9

Solution:

1! Solve for the moles using P $ n"%

n $ P & "

n $ ' (/)).) mmAg & /,).) mmAg atm* 1! (4+.) -! 0 & ' ().)+2), - atm mol* 1 * 1!(23.) ! 0

n $ 1.+3++ mol

2! Divide the grams given (,.)! by the moles >ust calculated above%

,.) g & 1.+3++ mol $ 2.2 g&mol

Problem #8: 2).+3 g of a gas occupies 4.1,/ - at /./ 6Pa at 3).) BC. :hat is itsmolecular 7eight9


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Solution:

1! Solve for the moles using P $ n"%

n $ P & "

n $ ' (/./ 6Pa & 1)1.32 6Pa atm* 1! (4.1,/ -! 0 & ' ().)+2), - atm mol* 1 * 1!(3)3.) ! 0

n $ ).1322/ mol

2! Divide the grams given (2).+3! by the moles >ust calculated above%

2).+3 g & ).1322/ mol $ 1/. g&mol

otice that; in the t7o problems >ust above; the converted the pressure unit given inthe problem to atmospheres. did this to use the value for " that have memoriEed.here are many different 7ays to express "; it5s >ust that -=atm&mol= is the unit

prefer to use; 7henever possible.

lso; you cannot use molar volume since the t7o problems >ust above are not at SP.

Problem #9: :hat is the value of and units on "9 :hat is " called (F letterF is notthe correct ans7erG!9

" is called the gas constant. t 7as first discovered; as part of the discovery in themid=1+3)5s by Hmil Clapeyron of 7hat is no7 called the deal Ias -a7.

Sometimes it is called the universal constant because it sho7s up in many non=gas=related situations. Ao7ever; it is mostly called the gas constant.

Depending on the units selected; the FvalueF for " can ta6e on many differentforms. Aere is a list. eep in mind these different FvaluesF represent the same thing.

Problem #10: .,)) g of solid CJ2 is put in an empty sealed 4.)) - container at atemperature of 3)) . :hen all the solid CJ2 becomes gas; 7hat 7ill be the pressurein the container9

Solution:

http://www.katmarsoftware.com/gconvals.htmhttp://www.katmarsoftware.com/gconvals.htm


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1! Determine moles of CJ2%

.,)) g & 44.)) g&mol $ ).12/24,/ mol

2! @se P $ n"

(P! (4.)) -! $ ().12/24,/ mol! ().)+2),! (3)) !

P $ )./+31 atm (to four sig figs!

Problem #1: Ao7 many moles of gas are contained in +).) m- at 21.) BC and /).)mm Ag pressure9

Solution:

"earrange the deal Ias -a7 to this%

n $ P & "

Substitute values into the eKuation%

n $ ' (/).) mmAg & /,).) mmAg atm* 1! ().+) -! 0 & ().)+2), - atm mol* 1 * 1!(24.) !

Please note the division of /) by /,). his is done in order to convert the pressurefrom mmAg to atm; because the value for " contains atm as the pressure unit. f 7eused mmAg; the pressure units 7ould not cancel and 7e need to have them cancel

because 7e reKuire mol (and only mol! to be in the ans7er.

Problem #2: 1.) g of A2 is contained in a 2.)) - container at 2).) BC. :hat is the pressure in this container in mmAg9

Solution:


P $ n" &



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P $ ' (1.) g & 2.)2 g mol* 1! ().)+2), - atm mol* 1 * 1! (23.) ! 0 & 2.)) -

Please note the division of 1.) by 2.)2. his is done in order to convert grams tomoles; because the value for " contains mol as the unit for amount of substance. f 7eused g; the mol unit in " 7ould not cancel and 7e need to have it cancel because 7e

reKuire atm (and only atm! to be in the ans7er.

8ultiply the ans7er (7hich is in atm! by /,).) mmAg atm* 1 to get mmAg

Problem #3: Calculate the volume 3.)) moles of a gas 7ill occupy at 24.) BC and/,2.4 mm Ag.

Solution:


$ n" & P


$ ' (3.)) mol! ().)+2), - atm mol* 1 * 1! (2/.) ! 0 & (/,2.4 mmAg & /,).)mmAg atm* 1!

ote the conversion from mmAg to atm in the denominator.

Problem #4: Ao7 many moles of gas 7ould be present in a gas trapped 7ithin a1)).) m- vessel at 2.) BC at a pressure of 2.) atmospheres9

Solution:


n $ P & "


n $ ' (2.) atm! ().1))) -! 0 & ' ().)+2), - atm mol* 1 * 1! (2+.) ! 0


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Problem #5: Ao7 many moles of a gas 7ould be present in a gas trapped 7ithin a3/.) liter vessel at +).)) BC at a pressure of 2.) atm9

Solution:


n $ P & "


n $ ' (2.) atm! (3/.) -! 0 & ' ().)+2), - atm mol* 1 * 1! (33.) ! 0

Problem #6: :hat volume 7ill 1.2/ moles of helium gas occupy at SP9

Solution:


$ n" & P


$ ' (1.2/ mol! ().)+2), - atm mol* 1 * 1! (2/3.) ! 0 & 1.)) atm

or (22.4 - & 1.)) mol! $ (x & 1.2/ mol!

:ould it ma6e any difference in the ans7er if the gas 7ere oxygen9 rypton9 Carbondioxide9 8ethane9

ns7er% no; no; no; no. he exact identity of the gas ma6es no difference to thenumber of moles present. Ly the 7ay; note that; since the temperature and pressure7ould be the same; the same volume 7ill contain the same number of molecules ofgas; i.e. moles of gas. his is vogadro5s Aypothesis.

ideo% deal Ias -a7 problem li6e #, >ust above.

Problem #7: t 7hat pressure 7ould ).1) mole of nitrogen gas at 23.) BC occupy+.) -9

http://blip.tv/file/2741707http://blip.tv/file/2741707


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1! Calculate the moles of gas ( left off the units!%

n $ '(1.4)! (1/.)!0 & '().)+2),! (2).!0 $ 1.)) mol

2! @se P $ n" again; but divide the volume by t7o and multiply the temperature by

4. @se the mole value from >ust above and solve for P%P $ '(1.))! ().)+2),! (2). x 4!0 & (1/.)&2! $ 11.2 atm

here is another; more conceptual 7ay; to explain the ans7er.


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Ly the 7ay; the use of Charles5 la7 in step one assumes that the entire contents of thegas cannister has been discharged. f 7e 7ere to assume the cannister has only been

partially discharged; then 7e cannot solve this problem.

Problem #12: 1).2) g sample of a gas has a volume of .2 - at 23.) BC and /1mmAg. f 2.3) g of the same gas is added to this constant .2 - volume and thetemperature raised to ,/.) degrees Celsius; 7hat is the ne7 gas pressure9

Solution:

1! @se P $ n" to determine moles of 1).2) g sample%

(/1 mmAg&/,) mmAg atm=1! (.2 -! $ (n! ().)+2), - atm mol=1 =1! (2, !

n $ ).213+ mol

2! Determine molecular 7eight of gas%

1).2) g & ).213+ mol $ 4/.// g&mol

3! Determine moles of 2.3) g of gas%

2.3) g & 4/.// g&mol $ ).)4+1, mol

4! Determine ne7 pressure 7ith ne7 amount of moles and at ne7 temperature%

(P! (.2 -! $ ().2,1/4 mol! ().)+2), - atm mol=1 =1! (34) !

P $ 1.3 atm

Problem #13: gas consisting of only carbon and hydrogen has an empirical formulaof CA2. he gas has a density of 1., g&- at 2/.) BC and /34.) torr. Determine the

molar mass and molecular formula of the gas.

Solution:

1! @se P $ n" to determine moles of the gas in 1.)) -%

(/34.) torr&/,).) torr atm=1! (1.)) -! $ (n! ().)+2), - atm mol=1 =1! (3)). !


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n $ ).)3231 mol

2! Determine molecular 7eight of gas%

1., g & ).)3231 mol $ 42.), g&mol

3! Determine the molecular formula%

he Fempirical formula 7eightF of CA2 $ 14.)2/

FHmpirical formula 7eightF units of CA2 present%

42.), & 14.)2/ $ 2.+ $ 3

he molecular formula is C3A,

Please be a7are that Fempirical formula 7eightF is not a standard term in chemistry.

Problem #14: 13. grams of an un6no7n gas is placed in a .)) - container.t has aninitial pressure at +., 6Pa and initial temperature at ,).) BC. :hat is the name of thisgas9

Solution:

1! @se P $ n"%

(+., 6Pa! (.)) -! $ (n! (+.3144/ - 6Pa mol=1 =1! (333 !

n $ ).1)+2 mol

found the value for " here.

2! Determine molecular 7eight%

13. g & ).1)+2 mol $ 131.4 g&mol

Hxamining a periodic table leads us to identifying the gas as xenon.

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Problem #15: 1. - flas6 at 1 BC contains a mixture of three gases% 2 (2.)mol!; Ae ().3+ mol!; and e (1.34 mol!. Calculate the partial pressure of neon gas inthe mixture.

Solution:

1! Determine total moles of gas%

2.) M ).3+ M 1.34 $ 4.22 moles

2! @se P $ n"%

(x! (1. atm! $ (4.22 mol! ().)+2),! (2++ !

x $ .11 atm

Determine the partial pressure for neon%

.11 x (1.34&4.22! $ 1.,2 atm

ote% (1.34&4.22! determines the mole fraction of neon.

Problem Set.ideal Gas Law

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