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- Samuel Dominic Chukwuemeka

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# Stoichiometry

I greet you this day:

Second: view the videos.
Third: solve the questions/solved examples.
Fourth: check your solutions with my thoroughly-explained solutions.

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Samuel Dominic Chukwuemeka (SamDom For Peace) B.Eng., A.A.T, M.Ed., M.S

## Definitions

The relative atomic mass of an element is the number of times the average mass of one atom of that element is heavier than one-twelfth the mass of one atom of carbon-12
It is denoted by $A_r$
It is used because the mass of an atom is very small.
Because it is a ratio of two masses, it has no unit.

The relative molecular mass of an element is the number of times the average mass of one molecule of that element is heavier than one-twelfth the mass of one atom of carbon-12
In this case, we can also use the term, relative formula mass
The relative molecular mass of a compound is the number of times the average mass of one molecule of that compound is heavier than one-twelfth the mass of one atom of carbon-12
It is denoted by $M_r$
It is used because the mass of a molecule is very small.
Because it is a ratio of two masses, it does not have a unit.

The mole of a substance is the amount that contains the same number of particles (atoms, molecules, ions) as the number of atoms in $12$ grams of carbon-12
$12$ grams of carbon-12 contains $6.02 * 10^{23}$ atoms
Therefore, $1$ mole of any substance contains $1$ Avogadro number of particles (atoms, molecules, ions)
This implies that $1$ mole of any substance contains $6.02 * 10^{23}$ number of particles (atoms, molecules, ions)

A reactant in a chemical reaction is the substance that is changed/consumed during a chemical reaction.

A product in a chemical reaction is the substance that is produced during a chemical reaction.

A limiting reactant is a reactant that is completely consumed during a chemical reaction.
Because it is completely consumed, it determines the amount of the product(s) of the reaction.
Because it is completely consumed, it determines the end of the reaction.
If the given amount of reactant is less than the required amount of reactant, the reactant is a limiting reactant.

An excess reactant is a reactant that is not completely consumed during a chemical reaction.
If the given amount of reactant is greater than the required amount of reactant, the reactant is an excess reactant.

The atom economy of a reaction is the measure of the amount of the reactants that are changed into the desired product.
It is expressed as a percentage.
It is also known as atom efficiency.
It is an important concept of green chemistry because it's value indicates the percentage of the desired product.
Knowing the percentage of the desired product also helps in knowing the percentage of waste products (subtracting it from 100%)
Thus, a high atom economy is important in eliminating waste product(s) among others.
The optimal atom economy is $100\%$. This means that all the reactants maximally to produce the desired product.
Based on these explanations, the atom economy of a reaction can also be defined as the ratio of the mass of the desired product to mass of all the prducts.
Because the mass of all the products is equal to the mass of all the reactants due to the Law of Conservation of Mass, the atom economy of a reaction can also be defined as the ratio of the mass of the desired product to mass of all the reactants.
The use of either formula depends on what you were given in the question.

• ## Symbols and Meanings (Unit)

• $A$ = mass number or nucleon number
• $Z$ = atomic number or proton number
• $AM$ = atomic mass (atomic mass unit ($amu$))
• $m$ = given mass (gram ($g$))
• $n$ = number of moles ($mol$)
• $A_r$ = relative atomic mass
• $M_r$ = relative formula mass
• $M_r$ = relative molecular mass
• $M$ = molar mass (gram/mole ($g/mol$))
• $C$ = molar concentration ($mol/dm^3$) or $(mol/L)$
• $\rho$ = mass concentration $(gram/dm^3)$ or $(g/L)$
• $V$ = volume $(dm^3)$ or Liters $(L)$
• $V_m$ = molar volume $(dm^3/mol)$ or $(L/mol)$
• $P$ = pressure (atmosphere $(atm)$) or $(mmHg)$
• $T$ = temperature (Kelvin $(K)$)
• $C_A$ = molar concentration of the acid $(mol/dm^3)$
• $C_B$ = molar concentration of the base $(mol/dm^3)$
• $V_A$ = volume of the acid $(dm^3)$
• $V_B$ = volume of the base $(dm^3)$
• $n_A$ = number of moles of the acid $(mol)$
• $n_B$ = number of moles of the base $(mol)$
• $L$ = Avogadro Constant or Avogadro Number $(mol^{-1})$

## Formulas

$(1.)\;\; A_r = \dfrac{average\;\;mass\;\;of\;\;1\;\;atom\;\;element}{\dfrac{1}{12} * mass\;\;of\;\;1\;\;atom\;\;of\;\;carbon-12} \\[8ex] (2.)\;\;For\;\;Isotopes\;\;of\;\;an\;\;Element \\[3ex] Assume\;\;Two\;\;Isotopes \\[3ex] A_r = \dfrac{(A * \%\;abundance)\;\;of\;\;1st\;\;Isotope + (A * \%\;abundance)\;\;of\;\;2nd\;\;Isotope}{100} \\[5ex] Assume\;\;Three\;\;Isotopes \\[3ex] A_r = \dfrac{(A * \%\;abundance)\;\;of\;\;1st\;\;Isotope + (A * \%\;abundance)\;\;of\;\;2nd\;\;Isotope + (A * \%\;abundance)\;\;of\;\;3rd\;\;Isotope}{100} \\[5ex] (3.)\;\; M_r = A_r * atomicity \\[5ex] (4.)\;\; Percentage\;\;Yield = \dfrac{Actual\;\;Yield}{Theoretical\;\;Yield} * 100 \\[5ex] (5.)\;\; Percentage\;\;Composition\;\;of\;\;Element\;\;in\;\;Compound = \dfrac{Mass\;\;of\;\;Element\;\;in\;\;Compound}{Molas\;\;Mass\;\;of\;\;Compound} * 100 \\[5ex] (6.)\;\; Depending\;\;on\;\;what\;\;was\;\;given: \\[3ex] Atom\;\;Economy = \dfrac{M_r\;\;of\;\;desired\;\;product}{M_r\;\;of\;\;products} * 100 \\[5ex] M_r\;\;of\;\;products = M_r\;\;of\;\;desired\;\;product + M_r\;\;of\;\;waste\;\;product(s) \\[5ex] M_r\;\;of\;\;products = M_r\;\;of\;\;reactants...Law\;\;of\;\;Conservation\;\;of\;\;Mass \\[3ex] Atom\;\;Economy = \dfrac{M_r\;\;of\;\;desired\;\;product}{M_r\;\;of\;\;reactants} * 100 \\[5ex] (7.)\:\: n = \dfrac{m}{M} \\[5ex] (8.)\:\: C = \dfrac{n}{V} \\[5ex] (9.)\;\; \rho = C * M \\[5ex] (10.)\;\; \rho = \dfrac{M}{V_m} \\[5ex] (11.)\;\; C = \dfrac{1}{V_m} \\[5ex] (12.)\:\: \dfrac{C_A * V_A}{C_B * V_B} = \dfrac{n_A}{n_B} \\[5ex]$

### References

Chukwuemeka, S.D (2019, April 30). Samuel Chukwuemeka Tutorials - Math, Science, and Technology. Retrieved from https://www.samuelchukwuemeka.com

Ababio, O. Y. (2013). New School Chemistry (6th ed.). Onitsha, Nigeria: African First Publishers Plc.

Chemistry 1983-2004 JAMB Questions. (n.d.). Retrieved June 7, 2020, from https://www.vastlearners.com/wp-content/uploads/2018/12/chemistry.pdf ‌

Chemistry. (n.d.). West African Examinations Council. Retrieved June 7, 2020, from https://waeconline.org.ng/e-learning/Chemistry/chemmain.html

GCSE Exam Past Papers - Revision World. (n.d.). Revisionworld.Com. Retrieved April 6, 2020, from https://revisionworld.com/gcse-revision/gcse-exam-past-papers