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Transcript
Chemistry 11
Stoichiometry Review Package
March 10, 2017
For a visual practice on balancing equations and limiting/excess reagents go to:
https://phet.colorado.edu/en/simulation/balancing-chemical-equations
https://phet.colorado.edu/en/simulation/reactants-products-and-leftovers
The following questions are based on the material covered so far. I will post full answers
on my website (https://blogs.ubc.ca/rchatrath/) halfway through spring break to give you time to
do the questions on your own. Please attempt the questions by yourself. You will not learn by
copying. Stoichiometry follows a pattern. Understanding the general steps taken to solve a
problem will help you in solving different questions.
Make use of the material in your workbook. Attempt all the practice problems for the sections.
The section review questions are a valuable resource.
The test covers section 4.1, 4.2, enthalpy notation in 4.4 (recognizing whether a reaction is
exothermic or endothermic from the energy term associated with the reaction or from the
classification of the reaction, as well as defining the two terms), 4.5, and 4.6.
Do not forget to do the stoichiometry relay questions from the previous class. Answers for those
will also be posted on my website with full solutions.
Sample questions:
Multiple Choice
1. Which one of the following is a definition of a chemical reaction?
a) Making new bonds between atoms as the old ones are broken
b) Change in physical properties as in mixing two substances
c) Change in the characteristics of the atomic nucleus
d) Change in the state of a substance due to temperature changes
2. If a reaction occurs in a beaker and the beaker becomes hot,
a) The reaction goes to completion
b) The reaction is endothermic
c) The reaction does not proceed
d) The reaction is exothermic THERE WAS A MISTAKE HERE
3. Copper in its metal state is best represented by
a) (aq)
b) (s)
c) (l)
d) (g)
Chemistry 11
Stoichiometry Review Package
March 10, 2017
4. How many grams of solute are there in a 2.5 L solution of 0.5 molar NaCl?
a) 73.1 g
b) 146.1 g
c) 29.2 g
d) 91.3 g
5. How many litres of oxygen are required to produce 60.3g of MgO in the following reaction?
2๐‘€๐‘”(๐‘ ) + ๐‘‚2 (๐‘”) โ†’ 2๐‘€๐‘”๐‘‚(๐‘ )
a) 14.9L
b) 22.4L
c) 16.8L
d) 33.6L
6. N2 + 3H2 โ†’ 2NH3 What is the mole ratio of N2:H2?
a) 1:3
b) 3:2
c) 2:3
d) 1:1
7. What compound(s) are likely to be produced in the following reaction: ๐ฟ๐‘– + ๐ป2 ๐‘‚ โ†’
a) LiH + O2
b) LiOH + H2
c) LiH2O
d) The reaction does not occur
Short answer
1. Exothermic vs Endothermic
a) Define each term and state the difference
b) Give an example of a reaction TYPE for each
Enthalpy (โˆ†๐ป):
change in energy of reactants and products before and after a chemical/physical change
Exothermic
โ€ข โ€œexoโ€ โ€“ external or outside
โ€ข โˆ†๐ป = โˆ’
โ€ข Eabsorbed < Ereleased
Endothermic
โ€ข โ€œendoโ€ โ€“ internal or within
โ€ข โˆ†๐ป = +
โ€ข Eabsorbed > Ereleased
Chemistry 11
Stoichiometry Review Package
โ€ข
An exothermic rxn is a rxn that is
accompanied by a release of energy
in the form of heat and/or light
โ€ข Energy released is associated with the
formation of bonds
โ€ข ๐’“๐’†๐’‚๐’„๐’•๐’‚๐’๐’•๐’” โ†’ ๐’‘๐’“๐’๐’…๐’–๐’„๐’•๐’” + ๐’†๐’๐’†๐’“๐’ˆ๐’š
Example of reaction type:
โ€ข Synthesis
โ€ข Combustion
*Bolded terms are important
โ€ข
โ€ข
March 10, 2017
An endothermic reaction is a reaction
that requires the input of energy
Energy is required to break bonds of
the starting material
โ€ข ๐’“๐’†๐’‚๐’„๐’•๐’‚๐’๐’•๐’” + ๐’†๐’๐’†๐’“๐’ˆ๐’š โ†’ ๐’‘๐’“๐’๐’…๐’–๐’„๐’•๐’”
Example of reaction type:
โ€ข Decomposition
2. The formation of water releases 572 kJ/mol. Write the balanced chemical equation for the
synthesis of water and include the energy term in a
a) Thermochemical equation format (page 201 in your workbooks)
๐Ÿ๐‘ฏ๐Ÿ (๐’ˆ) + ๐‘ถ๐Ÿ (๐’ˆ) โ†’ ๐Ÿ๐‘ฏ๐Ÿ ๐‘ถ (๐’) + ๐Ÿ“๐Ÿ•๐Ÿ ๐ค๐‰/๐ฆ๐จ๐ฅ
b) โˆ†๐ป notation (page 202)
๐Ÿ๐‘ฏ๐Ÿ (๐’ˆ) + ๐‘ถ๐Ÿ (๐’ˆ) โ†’ ๐Ÿ๐‘ฏ๐Ÿ ๐‘ถ (๐’)
โˆ†๐‘ฏ = โˆ’๐Ÿ“๐Ÿ๐Ÿ• ๐’Œ๐‘ฑ/๐’Ž๐’๐’
3. Explain the difference between coefficients and subscripts in a chemical equation
Coefficients
โ€ข The numbers that are in front of a
chemical species that multiplies the
entire chemical species that follows
โ€ข Used to balance chemical equations
โ€ข The only thing that can be changed to
balance a chemical equation
Example:
โ€ข 2 ๐ต๐‘‘ = 2×๐ต๐‘‘ (two bread slices)
โ€ข 2๐‘ = two single nitrogen atoms
โ€ข 2๐‘ โ‰  (๐‘‘๐‘œ๐‘’๐‘  ๐‘›๐‘œ๐‘ก ๐‘’๐‘ž๐‘ข๐‘Ž๐‘™) ๐‘2
Subscripts
โ€ข Denote whether the atom is diatomic,
triatomic, etc.
โ€ข Changing the subscript, changes the
molecule
โ€ข Should not be altered when balancing
a chemical equation
Example:
โ€ข N3 = azide, triatomic
โ€ข N2 = nitrogen gas, diatomic
โ€ข Halogens, N, O, H written as diatomic
4. Limiting reagent/reactant vs Excess reagent/reactant
a) Define each term and state the difference
โ€ข
โ€ข
Limiting reagent/reactant:
The reactant that is totally consumed
when a reaction is completed
The Limits the amount of product that
can be formed
โ€ข
โ€ข
Excess reagent/reactant:
The reactant that remains once the
limiting reactant is completely
consumed
Left over, or in xs
Chemistry 11
Stoichiometry Review Package
March 10, 2017
b) Given the following scenario, define which is the limiting reagent and which is the
excess reagent: a 1L solution containing 0.5M lead (II) nitrate and 1.5M potassium
iodide
๐‘ƒ๐‘(๐‘๐‘‚3 )2 (๐‘Ž๐‘ž) + 2๐พ๐ผ(๐‘Ž๐‘ž) โ†’ ๐‘ƒ๐‘๐ผ2 (๐‘ ) + 2๐พ๐‘๐‘‚3 (๐‘Ž๐‘ž)
๐‘š๐‘œ๐‘™๐‘’๐‘  ๐‘œ๐‘“ ๐‘ƒ๐‘(๐‘๐‘‚3 )2 = 1๐ฟ × 0.5๐‘€ = 0.5 ๐‘š๐‘œ๐‘™๐‘’๐‘  ๐‘œ๐‘“ ๐‘ƒ๐‘(๐‘๐‘‚3 )2 given
0.5 ๐‘š๐‘œ๐‘™๐‘’๐‘  ๐‘œ๐‘“ ๐‘ƒ๐‘(๐‘๐‘‚3 )2 ๐‘”๐‘–๐‘ฃ๐‘’๐‘› ×
2 ๐‘š๐‘œ๐‘™๐‘’ ๐‘œ๐‘“ ๐พ๐ผ
= 1 ๐‘š๐‘œ๐‘™๐‘’ ๐‘œ๐‘“ ๐พ๐ผ ๐‘Ÿ๐‘’๐‘ž๐‘ข๐‘–๐‘Ÿ๐‘’๐‘‘
1 ๐‘š๐‘œ๐‘™๐‘’ ๐‘œ๐‘“ ๐‘ƒ๐‘(๐‘๐‘‚3 )2
๐‘š๐‘œ๐‘™๐‘’๐‘  ๐‘œ๐‘“ ๐พ๐ผ = 1๐ฟ × 1.5๐‘€ = 1.5 ๐‘š๐‘œ๐‘™๐‘’๐‘  ๐‘œ๐‘“ ๐พ๐ผ given
1.5 ๐‘š๐‘œ๐‘™๐‘’๐‘  ๐‘œ๐‘“ ๐พ๐ผ ๐‘”๐‘–๐‘ฃ๐‘’๐‘› ×
1 ๐‘š๐‘œ๐‘™๐‘’ ๐‘œ๐‘“ ๐‘ƒ๐‘(๐‘๐‘‚3 )2
= 0.75 ๐‘š๐‘œ๐‘™๐‘’ ๐‘œ๐‘“ ๐‘ƒ๐‘(๐‘๐‘‚3 )2 ๐‘Ÿ๐‘’๐‘ž๐‘ข๐‘–๐‘Ÿ๐‘’๐‘‘
2 ๐‘š๐‘œ๐‘™๐‘’๐‘  ๐‘œ๐‘“ ๐พ๐ผ
๐‘š๐‘œ๐‘™๐‘’๐‘  ๐‘œ๐‘“ ๐‘ƒ๐‘(๐‘๐‘‚3 )2 ๐‘”๐‘–๐‘ฃ๐‘’๐‘› (0.5) < ๐‘š๐‘œ๐‘™๐‘’ ๐‘œ๐‘“ ๐‘ƒ๐‘(๐‘๐‘‚3 )2 ๐‘Ÿ๐‘’๐‘ž๐‘ข๐‘–๐‘Ÿ๐‘’๐‘‘(0.75)
โˆด ๐‘ƒ๐‘(๐‘๐‘‚3 )2 ๐‘–๐‘  ๐‘œ๐‘ข๐‘Ÿ ๐‘™๐‘–๐‘š๐‘–๐‘ก๐‘–๐‘›๐‘” ๐‘Ÿ๐‘’๐‘Ž๐‘”๐‘’๐‘›๐‘ก/๐‘Ÿ๐‘’๐‘Ž๐‘๐‘ก๐‘Ž๐‘›๐‘ก
๐‘š๐‘œ๐‘™๐‘’๐‘  ๐‘œ๐‘“ ๐พ๐ผ ๐‘”๐‘–๐‘ฃ๐‘’๐‘› (1.5) > ๐‘š๐‘œ๐‘™๐‘’๐‘  ๐‘œ๐‘“ ๐พ๐ผ ๐‘Ÿ๐‘’๐‘ž๐‘ข๐‘–๐‘Ÿ๐‘’๐‘‘
โˆด ๐พ๐ผ ๐‘–๐‘  ๐‘–๐‘› ๐‘ฅ๐‘ 
Calculations
1.
Cu + 2AgNO3 ๏ƒ  Cu(NO)3 + 2Ag
a) When 9.35g of copper reacts with 8.90g of AgNO3 to make silver
i.
What is the limiting reactant?
9.35๐‘” ๐‘œ๐‘“ ๐ถ๐‘ข ×
0.147 ๐‘š๐‘œ๐‘™๐‘’๐‘  ๐‘œ๐‘“ ๐ถ๐‘ข ๐‘”๐‘–๐‘ฃ๐‘’๐‘› ×
8.90g AgNO3 ×
1๐‘š๐‘œ๐‘™๐‘’ ๐ถ๐‘ข
= 0.147 ๐‘š๐‘œ๐‘™๐‘’๐‘  ๐‘œ๐‘“ ๐ถ๐‘ข ๐‘”๐‘–๐‘ฃ๐‘’๐‘›
63.5๐‘” ๐ถ๐‘ข
2 ๐‘š๐‘œ๐‘™๐‘’๐‘  ๐ด๐‘”๐‘๐‘‚3
= 0.294 ๐‘š๐‘œ๐‘™๐‘’๐‘  ๐‘œ๐‘“๐ด๐‘”๐‘๐‘‚3 ๐‘Ÿ๐‘’๐‘ž๐‘ข๐‘–๐‘Ÿ๐‘’๐‘‘
1 ๐‘š๐‘œ๐‘™๐‘’ ๐ถ๐‘ข
1๐‘š๐‘œ๐‘™๐‘’ ๐ด๐‘”๐‘๐‘‚3
= 0.0524 ๐‘š๐‘œ๐‘™ ๐‘œ๐‘“ ๐ด๐‘”๐‘๐‘‚3 ๐‘”๐‘–๐‘ฃ๐‘’๐‘›
169.9๐‘” ๐ด๐‘”๐‘๐‘‚3
0.0524 ๐‘š๐‘œ๐‘™ ๐‘œ๐‘“ ๐ด๐‘”๐‘๐‘‚3 ๐‘”๐‘–๐‘ฃ๐‘’๐‘› ×
1๐‘š๐‘œ๐‘™๐‘’ ๐ถ๐‘ข
= 0.0262 ๐‘š๐‘œ๐‘™๐‘’๐‘  ๐‘œ๐‘“ ๐ถ๐‘ข ๐‘Ÿ๐‘’๐‘ž๐‘ข๐‘–๐‘Ÿ๐‘’๐‘‘
2 ๐‘š๐‘œ๐‘™๐‘’ ๐ด๐‘”๐‘๐‘‚3
๐‘š๐‘œ๐‘™๐‘’๐‘  ๐‘œ๐‘“ ๐ถ๐‘ข ๐‘”๐‘–๐‘ฃ๐‘’๐‘›(0.147) > ๐‘š๐‘œ๐‘™๐‘’๐‘  ๐‘œ๐‘“ ๐ถ๐‘ข ๐‘Ÿ๐‘’๐‘ž๐‘ข๐‘–๐‘Ÿ๐‘’๐‘‘ (0.262)
๐‘š๐‘œ๐‘™๐‘’๐‘  ๐‘œ๐‘“ ๐ด๐‘”๐‘๐‘‚3 ๐‘”๐‘–๐‘ฃ๐‘’๐‘› (0.0524) < ๐‘š๐‘œ๐‘™๐‘’๐‘  ๐‘œ๐‘“ ๐ด๐‘”๐‘๐‘‚3 ๐‘Ÿ๐‘’๐‘ž๐‘ข๐‘–๐‘Ÿ๐‘’๐‘‘ (0.294)
โˆด ๐ด๐‘”๐‘๐‘‚3 ๐‘–๐‘  ๐‘กโ„Ž๐‘’ ๐‘™๐‘–๐‘š๐‘–๐‘ก๐‘–๐‘›๐‘” ๐‘Ÿ๐‘’๐‘Ž๐‘”๐‘’๐‘›๐‘ก/๐‘Ÿ๐‘’๐‘Ž๐‘๐‘ก๐‘Ž๐‘›๐‘ก
Chemistry 11
ii.
Stoichiometry Review Package
March 10, 2017
How much silver is produced in grams?
Start with amount of limiting reactant/reagent given: 8.90g of AgNO3
8.90g ๐ด๐‘”๐‘๐‘‚3 ×
1๐‘š๐‘œ๐‘™๐‘’ ๐ด๐‘”๐‘๐‘‚3
2 ๐‘š๐‘œ๐‘™๐‘’๐‘  ๐ด๐‘”
107.87๐‘”
×
×
= 5.65๐‘” ๐‘œ๐‘“ ๐ด๐‘”
169.9๐‘” ๐ด๐‘”๐‘๐‘‚3 2 ๐‘š๐‘œ๐‘™๐‘’๐‘  ๐ด๐‘”๐‘๐‘‚3 1 ๐‘š๐‘œ๐‘™๐‘’ ๐ด๐‘”
b) If the students obtain a yield of 70%, how much silver did they collect?
๐‘ƒ๐‘’๐‘Ÿ๐‘๐‘’๐‘›๐‘ก๐‘Ž๐‘”๐‘’ ๐‘ฆ๐‘–๐‘’๐‘™๐‘‘ =
๐‘Ž๐‘š๐‘œ๐‘ข๐‘›๐‘ก ๐‘œ๐‘“ ๐‘๐‘Ÿ๐‘œ๐‘‘๐‘ข๐‘๐‘ก ๐‘œ๐‘๐‘ก๐‘Ž๐‘–๐‘›๐‘’๐‘‘
×100%
๐‘Ž๐‘š๐‘œ๐‘ข๐‘›๐‘ก ๐‘œ๐‘“ ๐‘๐‘Ÿ๐‘œ๐‘‘๐‘ข๐‘๐‘ก ๐‘’๐‘ฅ๐‘๐‘’๐‘๐‘ก๐‘’๐‘‘
๐‘ƒ๐‘’๐‘Ÿ๐‘๐‘’๐‘›๐‘ก๐‘Ž๐‘”๐‘’ ๐‘ฆ๐‘–๐‘’๐‘™๐‘‘
× ๐‘Ž๐‘š๐‘œ๐‘ข๐‘›๐‘ก ๐‘œ๐‘“ ๐‘๐‘Ÿ๐‘œ๐‘‘๐‘ข๐‘๐‘ก ๐‘’๐‘ฅ๐‘๐‘’๐‘๐‘ก๐‘’๐‘‘ = ๐‘Ž๐‘š๐‘œ๐‘ข๐‘›๐‘ก ๐‘œ๐‘“ ๐‘๐‘Ÿ๐‘œ๐‘‘๐‘ข๐‘๐‘ก ๐‘œ๐‘๐‘ก๐‘Ž๐‘–๐‘›๐‘’๐‘‘
100%
70%
×5.66๐‘” ๐‘œ๐‘“ ๐ด๐‘” = 3.69๐‘” ๐‘œ๐‘“ ๐ด๐‘” ๐‘๐‘œ๐‘™๐‘™๐‘’๐‘๐‘ก๐‘’๐‘‘/๐‘œ๐‘๐‘ก๐‘Ž๐‘–๐‘›๐‘’๐‘‘
100%
2. The following question is based on the combustion of pentane (C5H12)
a) Write the balanced equation
C5H12 + 8O2 ๏ƒ  5CO2 + 6H2O
b) What is the mass of CO2 produced when 100.0 of C5H12 is burned?
100.0g of ๐ถ5 ๐ป12 ×
1๐‘š๐‘œ๐‘™๐‘’ ๐ถ5 ๐ป12
5 ๐‘š๐‘œ๐‘™๐‘’ ๐ถ๐‘‚2
44.01๐‘”
×
×
= 304.9๐‘” ๐‘œ๐‘“ ๐ถ๐‘‚2
72.17๐‘” ๐ถ5 ๐ป12 1 ๐‘š๐‘œ๐‘™๐‘’ ๐ถ5 ๐ป12 1 ๐‘š๐‘œ๐‘™๐‘’ ๐ถ๐‘‚2
c) What volume of O2 is required to make 70.0g of CO2 at STP?
70.0๐‘” ๐‘œ๐‘“ ๐ถ๐‘‚2 ×
1๐‘š๐‘œ๐‘™๐‘’ ๐ถ๐‘‚2
8 ๐‘š๐‘œ๐‘™๐‘’ ๐‘‚2
22.4๐ฟ
×
×
= 57.0๐ฟ ๐‘œ๐‘“ ๐‘‚2
44.01๐‘” ๐ถ๐‘‚2 5 ๐‘š๐‘œ๐‘™๐‘’ ๐ถ๐‘‚2 1 ๐‘š๐‘œ๐‘™๐‘’ ๐‘‚2
d) At STP what volume of O2 is required to make 48.0L of CO2?
48.0๐ฟ ๐‘œ๐‘“ ๐ถ ๐‘‚2 ×
1๐‘š๐‘œ๐‘™๐‘’ ๐ถ๐‘‚2
22.4๐ฟ ๐ถ๐‘‚2
×
8 ๐‘š๐‘œ๐‘™๐‘’ ๐‘‚2
5 ๐‘š๐‘œ๐‘™๐‘’ ๐ถ๐‘‚2
×
22.4๐ฟ
1 ๐‘š๐‘œ๐‘™๐‘’ ๐‘‚2
= 76.8๐ฟ ๐‘œ๐‘“ ๐‘‚2
e) How many molecules of C5H12 react with 15.0g of O2?
15.0๐‘” ๐‘œ๐‘“ ๐‘‚2 ×
1๐‘š๐‘œ๐‘™๐‘’ ๐‘‚2
32.00๐‘” ๐‘‚2
×
1 ๐‘š๐‘œ๐‘™๐‘’ ๐ถ5 ๐ป12
8 ๐‘š๐‘œ๐‘™๐‘’ ๐ถ๐‘‚2
×
6.022×1023 ๐‘š๐‘œ๐‘™๐‘’๐‘๐‘ข๐‘™๐‘’๐‘ 
1 ๐‘š๐‘œ๐‘™๐‘’ ๐ถ5 ๐ป12
= 3.53×1021 ๐‘š๐‘œ๐‘™๐‘’๐‘๐‘ข๐‘™๐‘’๐‘  ๐‘œ๐‘“ ๐ถ5 ๐ป12
Chemistry 11
Stoichiometry Review Package
March 10, 2017
3. When 5.00g of KClO3 is heated it decomposes according to the equation:
2KClO3 ๏‚ฎ 2KCl + 3O2
a) Calculate the theoretical yield of oxygen.
5.00๐‘” ๐‘œ๐‘“ ๐พ๐ถ๐‘™๐‘‚3 ×
๐‘š๐‘œ๐‘™๐‘’ ๐‘œ๐‘“ ๐พ๐ถ๐‘™๐‘‚3
3 ๐‘š๐‘œ๐‘™ ๐‘‚2
32.00๐‘”
×
×
= 1.96๐‘” ๐‘œ๐‘“๐‘‚2
122.55๐‘”
2 ๐‘š๐‘œ๐‘™ ๐พ๐ถ๐‘™๐‘‚3 ๐‘š๐‘œ๐‘™ ๐‘‚2
b) Give the % yield if 1.78 g of O2 is produced.
๐‘ƒ๐‘’๐‘Ÿ๐‘๐‘’๐‘›๐‘ก๐‘Ž๐‘”๐‘’ ๐‘ฆ๐‘–๐‘’๐‘™๐‘‘ =
๐‘Ž๐‘š๐‘œ๐‘ข๐‘›๐‘ก ๐‘œ๐‘“ ๐‘๐‘Ÿ๐‘œ๐‘‘๐‘ข๐‘๐‘ก ๐‘œ๐‘๐‘ก๐‘Ž๐‘–๐‘›๐‘’๐‘‘
×100%
๐‘Ž๐‘š๐‘œ๐‘ข๐‘›๐‘ก ๐‘œ๐‘“ ๐‘๐‘Ÿ๐‘œ๐‘‘๐‘ข๐‘๐‘ก ๐‘’๐‘ฅ๐‘๐‘’๐‘๐‘ก๐‘’๐‘‘
๐‘ƒ๐‘’๐‘Ÿ๐‘๐‘’๐‘›๐‘ก๐‘Ž๐‘”๐‘’ ๐‘ฆ๐‘–๐‘’๐‘™๐‘‘ =
1.78๐‘”
×100% = 90.8%
1.96๐‘”
c) How much O2 would be produced if the percentage yield was 78.5%?
๐‘ƒ๐‘’๐‘Ÿ๐‘๐‘’๐‘›๐‘ก๐‘Ž๐‘”๐‘’ ๐‘ฆ๐‘–๐‘’๐‘™๐‘‘ =
๐‘Ž๐‘š๐‘œ๐‘ข๐‘›๐‘ก ๐‘œ๐‘“ ๐‘๐‘Ÿ๐‘œ๐‘‘๐‘ข๐‘๐‘ก ๐‘œ๐‘๐‘ก๐‘Ž๐‘–๐‘›๐‘’๐‘‘
×100%
๐‘Ž๐‘š๐‘œ๐‘ข๐‘›๐‘ก ๐‘œ๐‘“ ๐‘๐‘Ÿ๐‘œ๐‘‘๐‘ข๐‘๐‘ก ๐‘’๐‘ฅ๐‘๐‘’๐‘๐‘ก๐‘’๐‘‘
๐‘ƒ๐‘’๐‘Ÿ๐‘๐‘’๐‘›๐‘ก๐‘Ž๐‘”๐‘’ ๐‘ฆ๐‘–๐‘’๐‘™๐‘‘
× ๐‘Ž๐‘š๐‘œ๐‘ข๐‘›๐‘ก ๐‘œ๐‘“ ๐‘๐‘Ÿ๐‘œ๐‘‘๐‘ข๐‘๐‘ก ๐‘’๐‘ฅ๐‘๐‘’๐‘๐‘ก๐‘’๐‘‘ = ๐‘Ž๐‘š๐‘œ๐‘ข๐‘›๐‘ก ๐‘œ๐‘“ ๐‘๐‘Ÿ๐‘œ๐‘‘๐‘ข๐‘๐‘ก ๐‘œ๐‘๐‘ก๐‘Ž๐‘–๐‘›๐‘’๐‘‘
100%
78.5%
× 1.96๐‘” = ๐‘Ž๐‘š๐‘œ๐‘ข๐‘›๐‘ก ๐‘œ๐‘“ ๐‘๐‘Ÿ๐‘œ๐‘‘๐‘ข๐‘๐‘ก ๐‘œ๐‘๐‘ก๐‘Ž๐‘–๐‘›๐‘’๐‘‘
100%
1.54๐‘” = ๐‘Ž๐‘š๐‘œ๐‘ข๐‘›๐‘ก ๐‘œ๐‘“ ๐‘๐‘Ÿ๐‘œ๐‘‘๐‘ข๐‘๐‘ก ๐‘œ๐‘๐‘ก๐‘Ž๐‘–๐‘›๐‘’๐‘‘