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Quantitative Relationships in Chemical Equations
4 Na(s) + O2(g) 2 Na2O(s)
Particles 4 atoms 1 m’cule 2 m’cules
Moles 4 mol 1 mol 2 mol
Grams 4 g 1 g 2 g
** Coefficients of a balanced equation represent# of particles OR # of moles,
but NOT # of grams.
When going from moles of one substance to molesof another, use coefficients from balanced equation.
part.
vol.
mass
MOL
mass
vol.
part.
MOL
SUBSTANCE “A” SUBSTANCE “B”
(known) (unknown)
Use coeff. from balancedequation in crossing this bridge
4 Na(s) + 1 O2(g) 2 Na2O(s)
= 4.20 mol O2
4 mol Na
87.2 mol Na
4 Na(s) + O2(g) 2 Na2O(s)
How many moles oxygen will react with 16.8 moles sodium?
How many moles sodium oxide are produced from87.2 moles sodium?
How many moles sodium are requiredto produce 0.736 moles sodium oxide?
4 mol Na
1 mol O216.8 mol Na
= 43.6 mol Na2O
2 mol Na2O
4 mol Na0.736 mol Na2O= 1.47 mol Na
2 mol Na2O
O2Na Na2ONa2O Na
Unit 8: Stoichiometry
-- involves finding amts. of reactants & products in a reaction
amount of RA
and/or RB
you must use
amount of P1
or P2 you need
to produce
amount of P1 or
P2 that will be
produced
amount of RA
or RB
amount of RB (or RA)
that is needed to react with it
amount of RA
(or RB)
…one can find the…Given the…
What can we do with stoichiometry?
For generic equation: RA + RB P1 + P2
4 patties + ?
Governing Equation:
2 patties + 3 bread 1 Big Mac®
excess + 18 bread ?
? + ? 25 Big Macs®
6 bread
75 bread50 patties
6 Big Macs®
Use coefficients from balanced
equation
MOLE(mol)
Mass(g)
Particle(at. or m’c)
1 mol = molar mass (in g)
Volume(L or dm3)
1 mol = 22.4 L
1 mol = 22.4 dm3
1 mol = 6.02 x 1023 particles
SUBSTANCE “A”
Stoichiometry Island Diagram
MOLE(mol)
Mass(g)
1 mol = molar mass (in g)
Volume(L or dm3)
1 mol = 22.4 L
1 mol = 22.4 dm3
1 mol = 6.02 x 1023 particles
SUBSTANCE “B”
Particle(at. or m’c)
2__TiO2 + __Cl2 + __C __TiCl4 + __CO2 + __CO
How many mol chlorine will react with 4.55 mol carbon?
3 mol C
4 mol Cl24.55 mol C = 6.07 mol Cl2
What mass titanium (IV) oxide will react with 4.55 mol carbon?
= 242 g TiO2
4 3 2 21
C Cl2
C TiO2 3 mol C
2 mol TiO24.55 mol C
1 mol TiO2
79.9 g TiO2
3. The units on the islands at each end of the bridge being crossed appear in the conversion factor for that bridge.
How many molecules titanium (IV) chloride can be madefrom 115 g titanium (IV) oxide?
TiCl4TiO2
( )= 8.66 x 1023 m’c TiCl4
115 g TiO21 mol TiO2
79.9 g TiO2( )2 mol TiO2
2 mol TiCl4 ( )1 mol TiCl4
6.02 x 1023 m’c TiCl4
Island Diagram helpful reminders:
2. The middle bridge conversion factor is the only one that has two different substances in it. The conversion factors for the other six bridges have the same substance in both the numerator and denominator.
1. Use coefficients from the equation only when crossing the middle bridge. The other six bridges always have “1 mol” before a substance’s formula.
1 mol1 mol
1 mol1 molcoeff. 1 mol
1 mol
2 Ir + Ni3P2 3 Ni + 2 IrP
If 5.33 x 1028 m’cules nickel (II) phosphidereact w/excess iridium, what mass iridium (III)phosphide is produced?
Ni3P2 IrP
= 3.95 x 107 g IrP
1 mol IrP223.2 g IrP
1 mol Ni3P2
2 mol IrP1 mol Ni3P2
6.02 x 1023 m’c Ni3P2
5.33 x 1028 m’c Ni3P2
How many grams iridium will react with465 grams nickel (II) phosphide?
= 751 g Ir
1 mol Ir192.2 g Ir
1 mol Ni3P2
2 mol Ir1 mol Ni3P2
238.1 g Ni3P2
465 g Ni3P2
Ni3P2 Ir
2 mol Ir
How many moles of nickel are producedif 8.7 x 1025 atoms of iridium are consumed?
Ir Ni
= 220 mol Ni
3 mol Ni1 mol Ir6.02 x 1023 at. Ir
8.7 x 1025 at. Ir
2 Ir + Ni3P2 3 Ni + 2 IrP
iridium (Ir) nickel (Ni)
Zn
What volume hydrogen gas is liberated(at STP) if 50. g zinc react w/excesshydrochloric acid (HCl)?
__ Zn + __ HCl __ H2 + __ ZnCl2 1 2 1 1
H2
= 17 L H2
1 mol H2
22.4 L H2
1 mol Zn1 mol H21 mol Zn
65.4 g Zn50. g Zn
50. g excess ? L
At STP, how many m’cules oxygen reactwith 632 dm3 butane (C4H10)?
C4H10 O2
= 1.10 x 1026 m’c O2
1 mol O22 mol C4H10
13 mol O21 mol C4H10632 dm3 C4H10
22.4 dm3 C4H10
__ C4H10 + __ O2 __ CO2 + __ H2O 1 4 52 8 1013
6.02 x 1023 m’c O2
Suppose the question had been “how many ATOMS of O2…”
1.10 x 1026 m’c O2
1 m’c O2
2 atoms O = 2.20 x 1026 at. O
1 mol CH4
A balanced eq. gives the ratios of moles-to-moles
Energy and Stoichiometry
CH4(g) + 2 O2(g) CO2(g) + 2 H2O(g) + 891 kJ
How many kJ of energy are releasedwhen 54 g methane are burned?
AND moles-to-energy.
= 3.0 x 103 kJ1 mol CH4
891 kJ54 g CH4
16 g CH4
EECH4
10,540 kJ
1 mol H2O
What mass of water is made if10,540 kJ are released?
CH4(g) + 2 O2(g) CO2(g) + 2 H2O(g) + 891 kJ
At STP, what volume oxygen is consumedin producing 5430 kJ of energy?
2 mol O2 = 273 L O21 mol O2
22.4 L O25430 kJ891 kJ
E
2 mol H2O = 425.9 g H2O18 g H2O
891 kJ
E O2
EE H2O
The Limiting Reactant
A balanced equation for makinga Big Mac® might be:
3 B + 2 M + EE B3M2EE
30 B and excess EE
30 M
excess M and excess EE
30 B
excess B and excess EE
30 M
…one can make…
…and…With…
15 B3M2EE
10 B3M2EE
10 B3M2EE
50 P
A balanced equation for makinga big wheel might be:
…one can make…
…and…With…
50 S + excess of all other reactants
excess of all other reactants
50 S
excess of all other reactants
50 P 25 W3P2SHF
3 W + 2 P + S + H + F W3P2SHF
50 W3P2SHF
25 W3P2SHF
Solid aluminum reacts w/chlorine gas to yield solidaluminum chloride.
2 Al(s) + 3 Cl2(g) 2 AlCl3(s)
If 125 g aluminum react w/excess chlorine,how many g aluminum chloride are made?
= 618 g AlCl3
2 mol Al 1 mol AlCl3
1 mol Al27 g Al
125 g Al
Al AlCl3133.5 g AlCl32 mol AlCl3
If 125 g chlorine react w/excess aluminum,how many g aluminum chloride are made?
= 157 g AlCl3
3 mol Cl2 1 mol AlCl3
1 mol Cl271 g Cl2
125 g Cl2
Cl2 AlCl3133.5 g AlCl32 mol AlCl3
2 Al(s) + 3 Cl2(g) 2 AlCl3(s)
If 125 g aluminum react w/125 g chlorine,how many g aluminum chloride are made?
157 g AlCl3 (We’re out of Cl2…)
limiting reactant (LR): the reactant that runs out first
--
Any reactant you don’t run outof is an excess reactant (ER).
amount of product is “limited” by the LR
In a root beer float, the LRis usually the ice cream.
Deliciousness!(What’s the product?)
Al / Cl2 / AlCl3
tricycles
Big Macs
Excess Reactant(s)Limiting ReactantFrom Examples
Above…
157 g AlCl3125 g Cl2125 g Al
25 W3P2SHF50 S + excess of all other reactants
50 P
10 B3M2EE30 M
…one can make……and…With…
30 B and excess EE
B
P
Cl2
M, EE
W, S, H, F
Al
How to Find the Limiting Reactant
For the generic reaction RA + RB P,
assume that the amountsof RA and RB are given.
Should you use RA or RB
in your calculations?
1. Using Stoichiometry, calculate the amount of product possible from both RA and RB (2 calculations)
2. Whichever reactant produces the smaller amount of product is the LR
3. The smaller amount of product is the maximum amount produced
For the Al / Cl2 / AlCl3 example:
2 Al(s) + 3 Cl2(g) 2 AlCl3(s)
If 125 g aluminum react w/excess chlorine,how many g aluminum chloride are made?
= 618 g AlCl3
2 mol Al 1 mol AlCl3
1 mol Al27 g Al
125 g Al
Al AlCl3133.5 g AlCl32 mol AlCl3
If 125 g chlorine react w/excess aluminum,how many g aluminum chloride are made?
= 157 g AlCl3
3 mol Cl2 1 mol AlCl3
1 mol Cl271 g Cl2
125 g Cl2
Cl2 AlCl3133.5 g AlCl32 mol AlCl3
LR
2 Fe(s) + 3 Cl2(g) 2 FeCl3(s)
223 g Fe 179 L Cl2
Which is the limiting reactant: Fe or Cl2?
1 mol Fe
55.8 g Fe
223 g Fe
1 mol Cl222.4 L Cl2
179 L Cl2
How many g FeCl3 are produced?
= 649 g FeCl3
2 mol FeCl32 mol Fe
162.3 g FeCl31 mol FeCl3
2 mol FeCl33 mol Cl2
162.3 g FeCl31 mol FeCl3
= 865 g FeCl3
649 g FeCl3
*Remember that the LR “limits” how much product can be made!
2 H2(g) + O2(g) 2 H2O(g)
13 g H2 80 g O2
Which is the limiting reactant: H2 or O2?
1 mol H2
2.0 g H2
13 g H2
1 mol O2
32.0 g O2
80 g O2
How many g H2O are produced?
= 120 g H2O
2 mol H2O
2 mol H2
18.0 g H2O
1 mol H2O
2 mol H2O
1 mol O2
18.0 g H2O
1 mol H2O
= 90 g H2O90 g H2O
*Notice that the LR doesn’t always have the smaller amount (13 v. 80)
How many g O2 are left over?
How many g H2 are left over?
zero; O2 is the LR and therefore is all used up
We know how much H2 we HAD (i.e. 13 g) To find how much is left over, we first need to figure out how much was USED in the reaction.
H2O2
HAD 13 g, USED 10 g…
Start with the LR and relate to the other…
1 mol O2
32.0 g O2
80 g O2 2 mol H2
1 mol O2
2.0 g H2
1 mol H2
10 g H2
USED=
3 g H2 left over
181 g Fe 96.5 L Br2
Which is the limiting reactant: Fe or Br2?
1 mol Fe
55.85 g Fe
181 g Fe
1 mol Br2
22.4 L Br2
96.5 L Br2
How many g FeBr3 are produced?
= 958 g FeBr3
2 mol FeBr3
2 mol Fe
295.55 g FeBr3
1 mol FeBr3
2 mol FeBr3
3 mol Br2
295.55 g FeBr3
1 mol FeBr3
= 849 g FeBr3849 g FeBr3
2 Fe(s) + 3 Br2(g) 2 FeBr3(s)
How many g of the ER are left over?
FeBr2
181 g Fe 96.5 L Br2
2 Fe(s) + 3 Br2(g) 2 FeBr3(s)
HAD 181 g, USED 160.4 g…
1 mol Br2
22.4 L Br2
96.5 L Br2 2 mol Fe
3 mol Br2
55.85 g Fe
1 mol Fe
160.4 g Fe USED=
20.6 g Fe left over
Percent Yield
moltensodium
solidaluminum
oxide
solidaluminum
solidsodiumoxide
Find mass of aluminum produced if you start w/575 g sodiumand 357 g aluminum oxide.
+ Al2O3(s) Al(s)6 Na(l) + Na2O(s)1 2 3
Na+ O2–Al3+ O2–
Al1 mol Na
22.99 g Na
575 g Na
1 mol Al2O3357 g Al2O3
= 224.9 g Al
2 mol Al
6 mol Na
26.98 g Al
1 mol Al
2 mol Al
1 mol Al2O3
26.98 g Al
1 mol Al
= 188.9 g Al188.9 g Al
102 g Al2O3
Now suppose that we performthis reaction and get only 172grams of aluminum. Why?
This amt. of product (______)
is the theoretical yield.
amt. we get if reaction is perfect found by calculation using “Stoich”
189 g
couldn’t collect all Al not all Na and Al2O3 reactedsome reactant or product spilled and was lost
Actual yield
= 91.0%
Find % yield for previous problem.
% yield can never be > 100%.
100 x yieldltheoretica
yieldactual yield%
--
100 x yld.theo.
yld.act. yield% 100 x
Alg 189 Alg 172
Batting average
FG %
GPA
= 41,374 g Li2CO3
On NASA spacecraft, lithium hydroxide “scrubbers” removetoxic CO2 from cabin.
For a seven-day mission, each of four individuals exhales880 g CO2 daily. If reaction is 75% efficient, how many g Li2CO3 will actually be produced?
CO2(g) + 2 LiOH(s) Li2CO3(s) + H2O(l)
CO2 Li2CO3
( )880 g CO2
person-dayx (4 p) x (7 d) = 24,640 g CO2
percent yield
1 mol CO224, 640 g CO2 1 mol Li2CO3
1 mol CO2
73.9 g Li2CO3
1 mol Li2CO344 g CO2
“theo” yieldAct
%Y= 100Theo
75= 10041,373.9
x
g
x = 31030 g Li2CO3
On NASA spacecraft, lithium hydroxide “scrubbers” removetoxic CO2 from cabin.
For a seven-day mission, each of four individuals exhales880 g CO2 daily. If reaction is 75% efficient, how many g LiOHshould be brought along?
CO2(g) + 2 LiOH(s) Li2CO3(s) + H2O(l)
= 26,768 g LiOH
1 mol LiOH23.9 g LiOH( )1 mol CO2
2 mol LiOH1 mol CO2
44 g CO2
24,640 g CO2
CO2 LiOH
( )880 g CO2
person-dayx (4 p) x (7 d) = 24,640 g CO2
( ) ( )theo. = 36,000 g LiOH
REALITY: TAKE 100,000 gtheo.
(act.) = 0.75
Reaction that powers space shuttle is:
2 H2(g) + O2(g) 2 H2O(g) + 572 kJ
From 100 g hydrogen and 640 g oxygen, what amount ofenergy is possible?
EE
1 mol H2 = 14300 kJ2 mol H2
572 kJ100 g H2
2 g H2
1 mol O2 = 11440 kJ1 mol O2
572 kJ640 g O2
32 g O2
11440 kJ
Review Questions
What mass of excess reactant is left over?
2 H2(g) + O2(g) 2 H2O(g) + 572 kJ
H2O2
Started with 100 g, used up 80 g… 20 g H2 left over
1 mol O2640 g O2 2 mol H2
1 mol O2
2 g H2
1 mol H2
= 80 g H232 g O2
100 g 640 g
Automobile air bags inflate with nitrogen via the decompositionof sodium azide:
2 NaN3(s) 3 N2(g) + 2 Na(s)
At STP and a % yield of 85%, what mass sodium azideis needed to yield 74 L nitrogen?
N2 NaN3
percent yield
“act” yield
Act%Y= 100
Theo 74L
85= 100x
x = 87.1 L N2 → “Theo” yield
1 mol N287.1 L N2 2 mol NaN3
3 mol N2
65 g NaN3
1 mol NaN3
= 168.5 g NaN3
22.4 L N2
1 mol B2H6
B2H6 + 3 O2 B2O3 + 3 H2O10 g 30 g X g?
B2O3
1 mol B2H6
27.6 g B2H6
10 g B2H6
1 mol O230 g O2
= 25.2 g B2O3
1 mol B2O3 69.6 g B2O3
1 mol B2O3
1 mol B2O3
3 mol O2
69.6 g B2O3
1 mol B2O3
= 21.75 g B2O321.75 g B2O3
32 g O2
___ZnS + ___O2 ___ZnO + ___SO2
100 g 100 g X g ? (assuming 81% yield)
Strategy: 1. 2. 3.
Balance and find LR Use LR to calc. X g ZnO (theo. yield) Actual yield is 81% of theo. yield
2 3 22
ZnO
2 mol ZnS
1 mol ZnS
97.5 g ZnS100 g ZnS
1 mol O2100 g O2
= 83.5 g ZnO2 mol ZnO 81.4 g ZnO
1 mol ZnO
2 mol ZnO
3 mol O2
81.4 g ZnO
1 mol ZnO= 169.6 g ZnO
83.5 g ZnO
32 g O2
Act%Y= 100
Theo
x81= 100
83.5g ZnO x = 67.6 g ZnO
___Al + ___Fe2O3 ___Fe + ___Al2O3
X g? X g? 800 g needed **Rxn. has an80% yield.
2 1 12
Fe Al
Fe Fe2O3
“act” yield
Act%Y= 100
Theo 800g
80= 100x
“theo” = 1000 g Fe
2 mol Fe
1 mol Fe55.85 g Fe
1000 g Fe= 483.1 g Al
2 mol Al 26.98 g Al1 mol Al
2 mol Fe
1 mol Fe
55.85 g Fe1000 g Fe
= 1430 g Fe2O3
1 mol Fe2O3 159.7 g Fe2O3
1 mol Fe2O3