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3-1
Chapter 3
Stoichiometry of Formulas and Equations
Stoichiometry is derived from the Greek words στοιχεῖον (stoicheion, meaning element) and μέτρον (metron, meaning measure.)
3-2
화학양론1. 몰
2. 미 지 화 합 물 의 화 학 식 구하기
실험식 , 분자식 3. 화학반응식과 균형 맞추기
4. 반응물과 생성물의 양한계반응물 , 수득량 , 수득 백분율
5. 용액에서의 화학양론몰농도용액 상태의 화학반응에서 화학량론
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Mole - Mass Relationships in Chemical Systems
3.5 Fundamentals of Solution Stoichiometry
3.1 The Mole
3.2 Determining the Formula of an Unknown Compound
3.3 Writing and Balancing Chemical Equations
3.4 Calculating the Amounts of Reactant and Product
화학전공 교수 - 학생 대화의 시간
3 월 17 일 ( 오늘 ) 오후 6:00 – 원천관 535 호실
김밥 , 다과 준비
구체적인 진로지도 및 선배 , 대학원생 , 화학과 교수님과의 대화의 시간
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The mole (mol) is the amount of a substance that contains as many elementary entities as there
are atoms in exactly 12.00 grams of 12C
1 mol = NA = 6.02214179(30)×1023
Avogadro’s number (NA)
The Mole(chemical quantity)
3-6
겁 ( 劫 ) 과 찰라 ( 刹那 )
찰나 [ 刹那 < 범어 k¡a¡a] < 명사 > ① ≪ 불교≫ (75 분의 1 초에 해당하는 ) 지극히 짧은 시간 . < 반의어 > 겁 ( 劫 ). ② 어떤 사물 현상이 이루어지는 바로 그때 . <참고 > 순간 ( 瞬間 ).
겁 [ 劫 ][< 범어 kalpa]< 명사 > ≪ 불교≫ (‘ 천지가 개벽한 때부터 다음 개벽할 때까지의 동안’이라는 뜻으로 ) ‘ 지극히 길고 오랜 시간’을 일컫는 말 . < 반의어 > 찰나 .힌두교에서는 1 겁을 43 억 2000 만 년(1.36x1017 초 ) 이라고 한다 .
=1.02×1019
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The Mole(chemical quantity)
•Avogadro’s number =6.0221023
만약 남북한 땅 위에 10 원짜리 동전을 쌓는다면 그 높이는 얼마나 될까 ?
10
직경 23 mm두께 1.5 mm
녹여 쌓으면 1,700 km 사방으로 펼쳐 쌓으면 2,200 km 삼각으로 펼쳐 쌓으면 1,900 km
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The Mole(chemical quantity)
•Avogadro’s number =6.0221023
만약 10 원 동전을 지구상 ( 땅과 바다 위 ) 에 쌓는다면 그 높이는 얼마나 될까 ?
녹여 쌓으면 730 m 사방으로 펼쳐 쌓으면 930 m 삼각으로 펼쳐 쌓으면 800 m
직경 23 mm두께 1.5 mm
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Molar mass is the mass of 1 mole of in gramsatomswatermelons
1 mole 12C atoms = 6.022 × 1023 atoms = 12.00 g
1 12C atom = 12.00 amu
1 mole 12C atoms = 12.00 g 12C
1 mole lithium atoms = 6.941 g of Li
For any element
atomic mass (amu) = molar mass (grams)
3-10
The Mole(chemical quantity)
10 kg 수박
1 몰 수박을 쌓아보자 !
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6.02 × 1024 kg !
지구 질량 5.97 × 1024 kg
3-12
One Mole of:
C S
Cu Fe
Hg
3-13
Information Contained in the Chemical Formula of Glucose C6H12O6 ( M = 180.16 g/mol)
6 atomsAtoms/moleculeof compound 6 atoms 12 atoms
Moles of atoms/mole of compound
6 moles of atoms
12 moles of atoms
6 moles of atoms
Atoms/mole ofcompound
6(6.022 × 1023) atoms
12(6.022 × 1023) atoms
6(6.022 × 1023) atoms
Mass/moleculeof compound
6(12.01 amu) =72.06 amu
12(1.008 amu) =12.10 amu
6(16.00 amu) =96.00 amu
Mass/mole of compound 96.00 g72.06 g 12.10 g
Oxygen (O)Carbon (C) Hydrogen (H)
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MASS(g)of atoms
MASS(g)of atoms
AMOUNT(mol)of atoms
AMOUNT(mol)of atoms
NUMBERof atoms
NUMBERof atoms
mass-mole-number
of atoms.
M (g/mol)
Avogadro’s number(atoms/mol)
6.02214179×1023
atomic mass 1 amu ×NA= 1 g(exact)
3-15
Calculating the Mass and the Number of Atoms in a Given Number of Moles of an Element
SOLUTION :
(a) Silver (Ag) is used in jewelry and tableware. How many grams of Ag are in 0.0342 mol of Ag?
(b) Iron (Fe), the main component of steel, is the most important metal in industrial society. How many Fe atoms are in 95.8 g of Fe?
0.0342 mol Ag ×mol Ag
107.9 g Ag= 3.69g Ag
(atomic mass(amu): Ag=107.9, Fe=55.85)
95.8g Fe×55.85g Fe
mol Fe 6.022x1023
mol = 1.04x1024 atoms Fe×
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MASS(g)of compound
MASS(g)of compound
AMOUNT(mol)of compound
AMOUNT(mol)of compound
MOLECULES(or formula units)
of compound
MOLECULES(or formula units)
of compound
AMOUNT(mol)of elements in
compound
AMOUNT(mol)of elements in
compound
Avogadro’s number(molecules/mol)
M (g/mol)
chemicalformula
mass-mole-number of compounds.
molecular (or formula) mass
3-17
Calculating the Moles and Number of Formula Units in a Given Mass of a Compound
Ammonium carbonate is white solid that decomposes with warming. Among its many uses, it is a component of baking powder, first extinguishers, and smelling salts. How many formula unit are in 41.6 g of ammonium carbonate?
SOLUTION:
Ammonium carbonate (NH4)2CO3.
M = (2 ×14.01 g/mol N) + (8 × 1.008 g/mol H) + (12.01 g/mol C) + (3 × 16.00 g/mol O) = 96.09 g/mol
41.6 g (NH4)2CO3 × = 2.61x1023 (NH4)2CO3
mol (NH4)2CO3
96.09 g (NH4)2CO3
6.022x1023
mol×
3-18
Calculating the Mass Percents and Masses of Elements in a Sample of Compound
Glucose (C6H12O6) is the most important nutrient in the living cell for
generating chemical potential energy.
(a) What is the mass percent of each element in glucose?
(b) How many grams of carbon are in 16.55g of glucose?
SOLUTION:
(a) M(C6H12O6)= 6×12.01 + 12×1.008 + 6×16.00 = 180.16 g/mol Glucose
mass percent of C = 6×12.01g C/180.16 g × 100 = 39.99 mass %C
mass percent of H =12×1.008g H/180.16 g ×100 = 6.714 mass %H
mass percent of O =6×16.00g O/180.16 g ×100 = 53.29 mass %O
(b) 16.55g Glucose ×39.99 mass %C/100 % Glucose = 6.618 g C
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Empirical and Molecular Formulas
Empirical Formula -
The simplest formula for a compound that agrees with the elemental analysis and gives rise to the smallest set of whole numbers of atoms.
Molecular Formula -
The formula of the compound as it exists.Molecular Formula = (Empirical Formula )n
3-20
Determining the Empirical Formula from Masses of Elements
Elemental analysis of a sample of an ionic compound showed 2.82 g of Na, 4.35 g of Cl, and 7.83 g of O. What are the empirical formula and name of the compound?
SOLUTION:
2.82 g Na/(22.99 g/mol) = 0.123 mol Na
4.35 g Cl/(35.45 g/mol) = 0.123 mol Cl
7.83 g O/(16.00 g/mol) = 0.489 mol O
Na1 Cl1 O3.98 → NaClO4
NaClO4 is sodium perchlorate.
0.123/0.123 = 1 Na
0.123/0.123 = 1 Cl
0.489/0.123 = 3.98 O
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Determining a Molecular Formula from Elemental Analysis and Molar Mass
During physical activity, lactic acid (M=90.08 g/mol) forms in muscle tissue and is responsible for muscle soreness. Elemental analysis shows that this compound contains 40.0 mass% C, 6.71 mass% H, and 53.3 mass% O.
(a) Determine the empirical formula of lactic acid.
(b) Determine the molecular formula.
SOLUTION: Assuming there are 100. g of lactic acid, the constituents are:
40.0 g C/(12.01 g/mol) = 3.33 mol C
6.66 g H/(1.008 g/mol) = 6.66 mol H
53.3 g O/(16.00 g/mol) = 3.33 mol O
CH2O : empirical formula
C3H6O3 is the
molecular formula
3.33/3.33 = 1 C
6.66 /3.33 = 2 H
3.33 /3.33 = 1 O
mass of CH2O
molar mass of lactate 90.08 g
30.03 g=3=
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Combustion analyzer for CH(O)of organic compounds. concept.
CnHmOx + (n + m/2 ) O2 = n CO2(g) + (m/2) H2O(g)
O2
H2O(g) absorber CO2(g) absorber Other gas absorber
Combustion
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Combustion analyzer for CHNSof organic compounds. Modern version.
CnHmNpSr + (n + m/2 + p + r ) O2 → n CO2(g) + (m/2) H2O(g) + p NO2(g) + r SO2(g)
CHNS (O) Analyzer modern instruments are automated for analysis. 3 mg of sample is sufficient to give satisfactory CHNS analysis.
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Determining a Molecular Formula from Combustion Analysis
Vitamin C (M=176.12g/mol) is a compound of C,H, and O found in many natural sources especially citrus fruits.
When a 1.000-g sample of vitamin C is placed in a combustion chamber and burned, the following data are obtained:
mass of CO2 after combustion =1.50 g
mass of H2O after combustion =0.41 g
What is the molecular formula of vitamin C?
SOLUTION:
CO2 = 1.50 g → 1.50 g CO2 /(44.01 g CO2 /mol)× 12.01 g C/mol= 0.409 g C
H2O = 0.41 g → 0.41 g H2O /(18.02 g H2O /mol)× 2.016 g H/mol= 0.046 g H
O must be the difference: 1.000 g - (0.409 + 0.046) = 0.545 g O
3-25
C1H1.33O1 → C3H4O3 →88.06 g/formula mass
n = 176.12 g/88.06 g = 2
(C3H4O3)2=C6H8O6
Determining a Molecular Formula from Combustion Analysis – cont.
0.409 g C → 0.409/12.01=0.0341 mol C
0.046 g H → 0.046/1.008=0.0456 mol H
0.545 g O → 0.545/16.00=0.0341 mol O
0.0341/0.0341 = 1 mol C
0.0456/0.0341 = 1.33 mol H
0.0341/0.0341 = 1 mol O
Molecular Formula = (Empirical Formula )n
Molecular Formula mass = (Empirical Formula mass)n
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Property Ethanol Dimethyl Ether
M(g/mol) 46.07 46.07
Boiling Point 78.50C -250C
Density at 200C0.789 g/mL
(liquid)0.00195 g/mL
(gas)
Structural formulas
Space-filling models
Constitutional Isomers of C2H6O
C C
H H
H
H H
OH C O
H
H
H
C
H
H
H
3-27
1. Write the correct formula(s) for the reactants on the left side and the correct formula(s) for the product(s) on the right side of the equation.
2. Set the equation for the coefficients (a, b, c & d) to make the number of atoms of each element the same on both sides of the equation.
3. Solve the equations. Usually start by setting the coefficient of the most complex compound be 1.
4. Adjust the coefficient to the most simple whole numbers.
5. Check to make sure that you have the same number of each type of atom on both sides of the equation.
6. Specify the states of matter.
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Ethane reacts with oxygen to form carbon dioxide and water
C: 2 a = c,O: 2 b = 2 c +d,H: 6 a = 2 d.
2 = c,2 b = 2 c +d,6 = 2 d. => d = 3
Let a = 1
6 = 2 d. => d = 32b = 2x2 + 3 = 7. b = 7/2
a C2H6 + b O2 → c CO2 + d H2O
a = 1
b = 7/2
c = 2
d = 3
a = 2
b = 7
c = 4
d = 6
X 2
2 C2H6 + 7 O2 → 4 CO2 + 6 H2O
Reactants Products
4 C
12 H
14 O
4 C
12 H
14 O
2 C2H6(g)+ 7 O2(g) → 4 CO2(g) + 6 H2O(l)
Balancing Chemical Equations - example
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MASS(g)of compound A
MASS(g)of compound A
AMOUNT(mol)of compound A
AMOUNT(mol)of compound A
MOLECULES(or formula units)
of compound A
MOLECULES(or formula units)
of compound A
Avogadro’s number(molecules/mol)
M (g/mol) of compound A
molar ratio from
balanced equation
mass-mole-number relationships in a chemical reaction.
MASS(g)of compound B
MASS(g)of compound B
AMOUNT(mol)of compound B
AMOUNT(mol)of compound B
MOLECULES(or formula units)
of compound B
MOLECULES(or formula units)
of compound B
Avogadro’s number(molecules/mol)
M (g/mol) of compound B
3-30
Calculating Amounts of Reactants and Products
In a lifetime, the average American uses 1750 lb(794 g) of copper in coins, plumbing, and wiring. Copper is obtained from sulfide ores, such as chalcocite, or copper(I) sulfide, by a multistep process. After an initial grinding, the first step is to “roast” the ore (heat it strongly with oxygen gas) to form powdered copper(I) oxide and gaseous sulfur dioxide.
(a) How many moles of oxygen are required to roast 10.0 mol of copper(I) sulfide?(b) How many grams of sulfur dioxide are formed when 10.0 mol of copper(I) sulfide is roasted?(c) How many kilograms of oxygen are required to form 2.86 kg of copper(I) oxide?
1. Write balanced chemical equation
2. Convert quantities of known substances into moles
3. Use coefficients in balanced equation to calculate the number of moles of the sought quantity
4. Convert moles of sought quantity into desired units
3-31
SOLUTION:
Calculating Amounts of Reactants and Products
2Cu2S(s) + 3O2(g) → 2Cu2O(s) + 2SO2(g)
3mol O2
2mol Cu2S= 15.0mol O2
= 641g SO2
= 0.959kg O2
kg O2
103g O2
= 20.0mol Cu2O
20.0mol Cu2O3mol O2
2mol Cu2O
32.00g O2
mol O2
10.0mol Cu2S(a)
10.0mol Cu2S2mol SO2
2mol Cu2S
64.07g SO2
mol SO2
(b)
2.86kg Cu2O103g Cu2O
kg Cu2O
mol Cu2O
143.10g Cu2O
(c)
(a) How many moles of oxygen are required to roast 10.0 mol of copper(I) sulfide?
(b) How many grams of sulfur dioxide are formed when 10.0 mol of copper(I) sulfide is roasted?
(c) How many kilograms of oxygen are required to form 2.86 kg of copper(I) oxide?
3-32
Balanced Equation
Viewed in Terms of
Reactants → ProductsC3H8(g) + 5O2(g) → 3CO2(g) + 4H2O(g)
molecules 1 molecule C3H8 + 5 molecules O2 → 3 molecules CO2 + 4 molecules H2O
amount (mol) 1 mol C3H8 + 5 mol O2 → 3 mol CO2 + 4 mol H2O
44.09 amu C3H8 + 160.00 amu O2 → 132.03 amu CO2 + 72.06 amu H2O mass (amu)
mass (g) 44.09 g C3H8 + 160.00 g O2 → 132.03 g CO2 + 72.06 g H2O
total mass (g) 204.09 g → 204.09 g
3-33
Using Molecular Depictions to Solve a Limiting-Reactant Problem
Nuclear engineers use chlorine trifluoride in the processing of uranium fuel for power plants. This extremely reactive substance is formed as a gas in special metal containers by the reaction of elemental chlorine and fluorine.
(a) Suppose the reaction is run with 3.00 mol of Cl2 and 6.00 mol of F2, name the limiting reactant, and draw the container contents after the reaction is complete.
(b) What will be the mass of remaining reactants and product?
F2Cl2
Cl2 F2 ClF3
n0(mol) 3.00 6.00 0
n/c(mol)
3/1=3 6/3=2
nf(mol) 3-2×1=1 6-2×3=0 0+2×2=4
mf(g) 1×70.9=70.9g 0 4×92.5=370
1Cl2(g) + 3F2(g) → 2ClF3(g)
M(g/mol)= 70.9 38.0 92.5
3-34
Calculating Amounts of Reactant and Product in a Limiting-Reactant Problem
A fuel mixture used in the early days of rocketry is composed of two liquids, hydrazine(N2H4) and dinitrogen tetraoxide(N2O4), which ignite on contact to
form nitrogen gas and water vapor. How many grams of nitrogen gas form when 1.00×102 g of N2H4 and 2.00×102 g of N2O4 are mixed?
SOLUTION: 2 N2H4(l) + N2O4(l) → 3 N2(g) + 4 H2O(l)
1.00×102g N2H4 /(32.05g/mol) = 3.12mol N2H4
2.00×102g N2O4/(92.02g/mol) = 2.17mol N2O4
N2H4 is the limiting reactant.
4.68mol N2×28.02 g/mol = 131 g N2
3.12mol N2H4 /2 = 1.56 < 2.17mol N2O4/1
1.56×3 = 4.48 mol N2 will be produced.
3-35
A + B C(reactants) (main product)
D(side products)
The effect of side reactions on yield.
Theoretical Yield is the amount of product that wouldresult if all the limiting reagent reacted.
Actual Yield is the amount of product actually obtainedfrom a reaction.
% Yield = Actual Yield
Theoretical Yieldx 100
Reaction Yield
3-36
Calculating Percent Yield
Silicon carbide (SiC) is an important ceramic material that is made by allowing sand(silicon dioxide, SiO2) to react with powdered carbon at high temperature. Carbon monoxide is also formed. When 100.0 kg of sand is processed, 51.4 kg of SiC is recovered. What is the percent yield of SiC from this process?
SOLUTION: SiO2(s) + 3C(s) → SiC(s) + 2CO(g)
100.0 kg SiO2 × (103 g /kg) ×(mol/60.09 g) = 1664 mol SiO2
n SiO2 = n SiC = 1664
× 100= 77.0%51.4 kg
66.73 kg
1664 mol SiC ×(40.10 g/mol) × (kg/103 g) = 66.73 kg SiC
3-37
Calculating the Molarity of a Solution
Glycine (H2NCH2COOH) is the simplest amino acid. What is the molarity of an aqueous solution that contains 0.715 mol of glycine in 495 mL?
SOLUTION:
0.715 mol glycine
495 mL soln
1000mL
1 L= 1.44 M glycine
Molarity (M, mol/L) = nsolute/Vsolution
3-38
mass-mole-number-volume relationships in solution.
MASS (g)of compound
in solution
AMOUNT (mol)of compound
in solution
MOLECULES(or formula units)
of compoundin solution
VOLUME (L)of solution
M (g/mol)
Molarity (mol/L)Avogadro’s number(molecules/mol)
3-39
Calculating Mass of Solute in a Given Volume of Solution
A “buffered” solution maintains acidity as a reaction occurs. In living cells phosphate ions play a key buffering role, so biochemistry often study reactions in such solutions. How many grams of solute are in 1.75 L of 0.460 M sodium monohydrogen phosphate?
SOLUTION:
1.75 L×0.460 moles
1 L
0.805 mol Na2HPO4 × 141.96 g Na2HPO4
mol Na2HPO4
= 0.805 mol Na2HPO4
= 114 g Na2HPO4
3-40
Converting a concentrated solution to a dilute solution.
The total number of solutes in the solution remains the same after dilution,
But the number of solutes per unit volume changes...
3-41
Preparing a Dilute Solution from a Concentrated Solution
“Isotonic saline” is a 0.15 M aqueous solution of NaCl that simulates the total concentration of ions found in many cellular fluids. Its uses range from a cleaning rinse for contact lenses to a washing medium for red blood cells. How would you prepare 0.80 L of isotonic saline from a 6.0 M stock solution?
the number of moles of solute does not change during the dilution but the volume does
Mdil × Vdil = nsolute = Mconc × Vconc
SOLUTION:
nsolute required: 0.80 L soln ×0.15 M NaCl = 0.12 mol NaCl
volume of conc. solution = 0.12 mol NaCl/6M = 0.020 L soln
3-42
Calculating Amounts of Reactants and Products for a Reaction in Solution
Specialized cells in the stomach release HCl to aid digestion. If they release too much, the excess can be neutralized with antacids. A common antacid contains magnesium hydroxide, which reacts with the acid to form water and magnesium chloride solution. As a government chemist testing commercial antacids, you use 0.10M HCl to simulate the acid concentration in the stomach. How many liters of “stomach acid” react with a tablet containing 0.10g of magnesium hydroxide?
SOLUTION:
Mg(OH)2(s) + 2HCl(aq) → MgCl2(aq) + 2H2O(l)
n Mg(OH)2/1 = n HCl/2
0.10g / (58.33g/mol) = 1.7 × 10-3 mol Mg(OH)2 = n HCl/2
n HCl = 3.4 × 10-3 mol HCl = 0.10 M × VHCl
VHCl = 3.4 × 10-2 L HCl
3-43
Solving Limiting-Reactant Problems for Reactions in Solution
Mercury and its compounds have many uses, from fillings for teeth (as an alloy with silver, copper, and tin) to the industrial production of chlorine. Because of their toxicity, however, soluble mercury compounds, such mercury(II) nitrate, must be removed from industrial wastewater. One removal method reacts the wastewater with sodium sulfide solution to produce solid mercury(II) sulfide and sodium nitrate solution. In a laboratory simulation, 0.050L of 0.010M mercury(II) nitrate reacts with 0.020L of 0.10M sodium sulfide. How many grams of mercury(II) sulfide form?
SOLUTION: Hg(NO3)2(aq) + Na2S(aq) → HgS(s) + 2NaNO3(aq)
0.050L×0.010M = 5.0×10-4 mol HgS
0.020L×0.10M = 2.0x10-3 mol Na2S
Since (5.0×10-4 mol Hg(NO3)2/1) < (2.0x10-3 mol Na2S /1),
Hg(NO3)2 is the limiting reagent.
(5.0×10-4 mol ) ×1 HgS will form.
5.0×10-4 mol × 232.7g/mol = 0.12 g HgS
3-44
aA + bB → cC + dD
Limiting Reagent and theoretical Yield
Reactants Products
[A] [B] [C] [D]d d d d
a b c d
[A] [B]min , is the amount of reaction
a b
[A] [B]chemical amount of C: min ,
[A] [B]chemical amount of D: min ,
ca b
da b
[A] [B], A is the limiting reagent. Otherwise, B is the limiting reagentif
a b
3-45
1. 다음 중 원소기호와 그 이름이 바르게 짝지어지지 않은 것을 고르고 바른 이름을 쓰시오 . (a) Zn - Iron(b) K - Potassium(c) Sn - Antimony(d) Au - Gold(e) Ce - Cesium(f) Hg - Hydrogen(g) Fe - Steel(h) Ar -Arsenic
3-46
2. 다음의 순물질 중에서 원소가 아닌 것을 고르시오 . 원소가 아닌 것의 이유를 쓰시오 .
(a) 수정(b) 다이아몬드(c) 흑연(d) 풀러렌 (C60)(e) 니켈(f) 오존(g) 사파이어(i) 황동(j) 청동(h) 테플론 (j) 순금(k) 브로민(l) 주석(m) 백금(n) 지르코늄
3-47
메테인 (CH4) 18.5 g 이 염소 43.0 g 과 반응하여 80% 수득률로 염화 메틸 (CH3Cl) 이 생성되었다 . 생성된 반응물은 몇 g 인가 ? 이 때 염화 수소도 같이 생성되었다 . 원자질량 (amu): C: 12.01, H:1.008, Cl: 35.45
3-48
뷰테인 ( 부탄 ) 기체는 압축시켜서 일회용 라이터나 휴대용 가스버너의 액체 연료로 사용한다 . 라이터에 뷰테인 6.50mL 가 들어있다 (d＝0.579 g/mL).(a) 뷰테인을 전부 연소시키기 위해 필요한 최소량의 산소는 몇 g 인가 ?(b) 뷰테인이 전부 연소하면 CO2 는 몇 mol 이 생성되겠는가 ?(c) 뷰테인이 전부 연소하면 , 전체 기체 분자는 얼마나 되겠는가 ?원자질량 (amu): C: 12.01, H:1.008, O: 16.00
3-49
진한 황산 (18.3 M) 은 밀도가 1.84g/mL 이다 .(a) 1 L 용액 안에 황산 몇 mol 이 들어있는가 ?(b) 용액에서 H2SO4 의 질량 백분율은 얼마인가 ?원자질량 (amu): C: 12.01, H:1.008, O:16.00, S: 32.07
