Unit 4: Stoichiometry — Long Questions

Ans. Mole
Definition: The mole is the amount of a substance which contains as many elementary entities as there are atoms in 0.012kg (12g) of carbon-12.
Explanation
• The elementary entities may be atoms molecules, ions, electrons and other particles. It is represented by n.
• The number of moles of a substance can be calculated by dividing mass in grams by molar mass. The formula for number of moles is:

Number of moles = Given mass / Molar mass n = m/M

Examples The examples of elementary entities equal to one mole are:
1 mole of water = 6.022 × 10²³ molecules of H₂O
1 mole of ¹²C = 6.022 × 10²³ atoms of Carbon
1 mole of NaCl = 6.022 × 10²³ formula units of NaCl
1 mole of Na⁺ = 6.022 × 10²³ ions of sodium
Avogadro's number
Definition: The number of entities present in one mole of a substance is a constant number named Avogadro's Number. i.e. 6.022 × 10²³.
Explanation: It is represented by Nₐ. This value is attributed to an Italian scientist Amedo Avogadro (1776-1856). Avogadro's number is a physical constant representing the molar number of entities. The exact value of 6.02214179 × 10²³ mol⁻¹. In calculations we use the rounded off value 6.02 × 10²³
Examples:
23 g of sodium = 1 mole of Na = 6.02 × 10²³ atoms
56.1 g of CaO = 1 mole of CaO = 6.02 × 10²³ formula units
98 g of H₂SO₄ = 1 mole of H₂SO₄ = 6.02 × 10²³ molecules
60 g of CO₃²⁻ = 1 mole of CO₃²⁻ = 6.02 × 10²³ ions
Molar Mass
Definition: The mass of one mole of a substance (element, compound or ionic species) is equal to the atomic mass, molecular mass, formula mass or ionic mass of a substance when expressed in grams is known as molar mass.
Unit: Its units is g/mol.
Explanation: It is represented by M. The molar mass is the sum of the masses of the component atoms. The molar masses of all the atoms, molecules, formula units and ions always fix.
Examples:
Molar mass of Mg = 24.0 g/mol
Molar mass of C₁₂H₂₂O₁₁ = 342 g/mol
Molar mass of Ag₂CrO₄ = 332 g/mol
Molar mass of PO₄³⁻ = 95 g/mol
Calculation of molar mass of CCℓ₄: The mass of one mole of CCℓ₄ can be found by adding the masses of carbon and chlorine present.
Molar mass of CCℓ₄ = Molar mass of one C + Molar mass of Cℓ × 4
= 12.0 × 1 +35.5 × 4
Molar mass of CCℓ₄ = 12.0 + 142.0 = 154.0 g/mol

Ans. Relationship between molar mass and Avogadro's number
A sample of 12.0 grams of natural carbon contains the same number of atoms as 4.0 grams of natural helium. Both samples contain 1 mole of atoms i.e. 6.022 × 10²³.
Number of atoms: It is interesting to know that different masses of elements have the same number of atoms i.e. Avogadro's number.
1.0 of hydrogen = 1 mol of hydrogen = 6.02 × 10²³ atoms of H.
23.0g of sodium = 1 mol of Na = 6.02 × 10²³ atoms of Na
238.0g of uranium = 1 mol of U = 6.02 × 10²³ atoms of U
Number of molecules: One mole of different compounds has different masses but the same number of molecules i.e. Avogadro's number.
18.0g of H₂O = 1 mol of water = 6.02 × 10²³ molecules of water
18.0g of glucose = 1 mol of glucose = 6.02 × 10²³ molecules of glucose
Number of formula units: The number of formula units in one mole of an ionic compound is always same i.e. Avogadro's number.
58.5g of NaCl = 1 mole of NaCl = 6.02 × 10²³ formula units of NaCl
100g of CaCO₃ = 1 mole of CaCO₃ = 6.02 × 10²³ formula units of CaCO₃
332g of Ag₂CrO₄ = 1 mole of Ag₂CrO₄ = 6.02 × 10²³ formula units of Ag₂CrO₄
Number of ions: The number of ions in one mole of different ionic species is always the same, i.e. Avogadro's number.
96.1g of SO₄²⁻ = 1 mole of SO₄²⁻ = 6.02 × 10²³ ions of SO₄²⁻
62.0g of NO₃⁻¹ = 1 mole of NO₃⁻¹ = 6.02 × 10²³ ions of NO₃⁻¹
Sodium is heavier than hydrogen
An atom of sodium is 23 times heavier than an atom of hydrogen. In order to have equal number of atoms, sodium should be taken 23 times greater in mass than hydrogen.
Relationship between moles and Avogadro's Number
One can calculate the number of moles by dividing the number of particles by Avogadro's number

Number of moles = No. of particles of a substance / Avogadro's Number

Number of particles = Mass of substance x Nₐ / Molar Mass

Mass in grams --[Molar mass]--> Moles --[Avogadro's number]--> No. of Particles

Ans. Molar Volume
Definition: The volume of one mole of an ideal gas at STP (Standard temperature and pressure) is called molar volume.
Value: Its value is equal to 22.414 dm³. The value of molar volume is commonly rounded to 22.4 dm³. It is denoted by Vm.
Example
22.4 dm³ of CO₂ at STP = 44.0g of CO₂ = 6.02 × 10²³ molecules of CO₂ = 1 mole of CO₂
22.4 dm³ of H₂ gas at STP = 2g of H₂ = 6.02 × 10²³ molecules of H₂ = 1 mole of H₂
22.4 dm³ of NH₃ gas at STP = 17g of NH₃ = 6.02 × 10²³ molecules of NH₃ = 1 mole of NH₃
Relationship between Molar volume and Avogadro's Number
According to Avogadro's law, "Equal volumes of all ideal gases at the same temperature and pressure contain equal numbers of molecules".
• This statement is indirectly the same when we say that one mole of an ideal gas at 273.16 K and one atm pressure has a volume of 22.414 dm³
• One mole of a gas has Avogadro's number of particles.
• 22.414 dm³ of various ideal gases at STP will have Avogadro's number of molecules i.e., 6.02 × 10²³.
• 22.4dm³ of a gas at STP is equal to molar mass of a gas its number of moles will be 1.
Calculation of Volume of gas from Vm
If the number of moles of a gas is known, one can calculate it's volume by multiplying number of moles of the gas with molar volume.

Volume of a gas = Number of moles × Molar volume
V = n x Vm

Ans. Density of Gases
Definition: Density is defined as the mass per unit volume of a substance.

Density = Mass / Volume

d = m / V

Relationship between density and molar mass
• Molar mass of all the gases occupies same volume at STP.
• Density of a gas depends on molar mass.
• A gas having higher molar mass will have higher density and vice versa.
• If the density of gas at STP is determined, its molar mass can be calculated.
Quick Check 4.3
Calculate the molar mass of a gas which has density of 1.34g/dm³ at STP.
Ans. Molar mass of gas = ?
Density of gas = d = 1.34 g/dm³
Volume of gas at STP = 22.4 dm³
M = d × v
M = 1.34g / dm³ × 22.4 dm³
M = 30.016 g/mol Answer
Molar concentration and relation with moles
Definition: Molar concentration of solution is given as mol/dm³, which is the number of moles of a substance (reactant or product) dissolved per volume of a solution in dm³.
Formula: The relationship between number of moles and molar concentration is given by

n = C x V
C = n / V

C = molar concentration
V = volume of the solution

Molar Concentration = Number of moles / Volume in dm³

Example Concentration of 0.2 mole of a substance per dm³ is:
C = 0.2 mol / 1 dm³ = 0.2 mol dm⁻³

Quick Check 4.4
Calculate the molar concentration of a solution containing 7.9 g of KMnO₄ dissolved in 1 dm³ of the given solution. The molar mass of KMnO₄ is 158 g mol⁻¹.
Ans. Mass of KMnO₄ = 7.9g
Molar mass of KMnO₄ = 158g/mol
Volume of solution = 1dm³
Molar concentration = ?
Solution:

n = 7.9g / 158g / mol
= 0.05mol

Molar concentration = No. of moles / volume in dm³

= 0.05 mol / 1 dm³

Molar concentration = 0.05 mol / dm³ Answer

Ans. Stoichiometry
Meaning: Stoichiometry is derived from Greek words 'stoicheion' means element and 'metron' means measure.
Statement: Stoichiometry is a branch of chemistry which tells us the quantitative relationship between reactants and products in a balanced chemical equation.
Assumptions:
(i) Law of conservation of mass and law of definite proportions are obeyed.
(ii) No side reaction occurs
(iii) All the reactants should be converted into products.
Laws followed in stoichiometry
• Law of conservation of mass: According to this law "matter (mass) can neither be created nor be destroyed". It's states in terms of stoichiometry, the total mass of reactants should be equal to the total mass of products in a balanced chemical equation.
• Law of definite proportions: According to this law a pure compound always contains the same element combined in the same ratio by mass. The balanced chemical equation has the same number of atoms of each element on both sides of equation. It has definite ratio of reactants and products just as compounds have definite ratios of elements. The ratio is used to calculate the mass or mole of other substances.
Explanation: The knowledge of mole, Avogadro's number, molar mass, molar volume and molar concentration, can give quantitative relationships between reactants and products using the balanced chemical equations.
Stoichiometric Relationships
The following types of relationship can be studied with the help of a balanced chemical equation involving quantities of reactants and products.
(i) Mole-Mole Relationship
(ii) Mass-Mass Relationship
(iii) Volume-Volume Relationship
(iv) Mole-Mass Relationship
(v) Mole-Volume Relationship
(vi) Mass-Volume Relationship
Example of Stoichiometric calculations: To understand these relationships, we need to interpret information hidden in a balanced chemical equation which is used to make stoichiometric calculations.

N₂₍ₘ₎ + 3H₂₍ₘ₎ → 2NH₃₍ₘ₎

This equation can be described in different ways:
• Mole: 1 mole of N₂ reacts with 3 moles of H₂ to form 2 moles of NH₃.
• Number of molecules: 1 molecule of N₂ reacts with 3 molecules of H₂ to form 2 molecules of NH₃.
• Volume: 22.4 dm³ of N₂ reacts with 67.2 dm³ of H₂ to form 44.8 dm³ of NH₃.
• Mass: 28.0g of N₂ react with 6g of H₂ to form 34.0g of NH₃.
Following are the approaches in Stoichiometric calculations:
Approach to do Stoichiometric Calculations
Given amounts (Step 1): Mass of known solid or volume of known gas, or molar concentration of known solution.
Number of moles (Step 2): Calculate number of moles of known solid or volume of a known gas, or molar concentration of known solution using the relevant formula
Calculation of Ratio (Step 3): Find the ratio of the known and the unknown reactant or product from the balanced chemical equation.
Moles of unknown substance (Step 4): Calculate the number of moles of the unknown reactant or product using the relevant formula.
Calculation of unknown amounts (Step 5): Convert the number of moles of the unknown to mass, volume or concentration of the substance.
Keep in Mind!
S.Q. What are assumptions of Stoichiometry?
Ans. The following assumptions must be made while performing stoichiometric calculations:
(i) All the reactants are completely converted into the products.
(ii) Law of conservation of mass and law of definite proportions are obeyed.
(iii) No side reaction occurs.

Ans. Limiting Reactant

Definition The reactant which controls the amounts of products formed in a chemical reaction and is consumed earlier is called the limiting reactant or reagent. The maximum amount of the product formed depends upon the amount of limiting reactant in the reaction mixture.

Example A large quantity of oxygen in a chemical reaction makes things burn more rapidly. In this way, excess of oxygen is left behind at the end of reaction ant the other reactant, i.e. fuel, is consumed earlier. This reactant which is consumed earlier is called the limiting reactant. The amount of product that forms is limited by the reactant that is completely used. Once this reactant is consumed, the reaction stops and no additional product is formed.

Strategy for the identification of limiting reactant

To identify a limiting reactant, the following three steps are performed.
(i) Calculate the number of moles from the given amounts of reactants.
(ii) Find out the number of moles of product with the help of a balanced chemical equation.
(iii) Identify the reactant which produces the least amount of product as limiting reactant and the other as an excess reactant.

Did You Know!

S.Q. Give role of excess reactant in combustion.

Ans. Fire is a combustion reaction in which fuel and oxygen, O₂, combine, usually at high temperatures, to form water and carbon dioxide. Once the fire has started, it is self-supporting. An effective way to quench a fire is smothering, which reduces the amount of available oxygen below the level needed to support combustion. In other words, smothering decreases the amount of excess reactant, foams, inert gas, and CO₂ are effective substances for smothering.

Ans. Excess Reactant or non-limiting reactant

Definition The reactant which are in larger amounts (according to stoichiometry of reaction) and remain unreacted at the end of the reaction are called "excess reagents" (or excess reactants).

Explanation In many chemical processes, the quantities of the reactants are usually not present in the proportions indicated by the balanced chemical equation. Frequently, a large amount of inexpensive reactant is supplied.

Example

Consider the reaction between hydrogen and oxygen to form water

2H₂₍ₐ₎ + O₂₍ₐ₎ ——→2H₂O₍ₗ₎

• When we take 2 moles of hydrogen (4g) and allow it to react with 2 moles of oxygen (64g), then we will get only 2 moles (36g) of water. Actually, we will get 2 moles (36g) of water because 2 moles (4g) of hydrogen react with 1 mole (32g) of oxygen according to the balanced equation. Since less hydrogen is present as compared to oxygen, so hydrogen is a limiting reactant.

• When 1 mole of O₂ and 1 mole of H₂ are mixed, all the H₂ will react completely and O₂ will be left unreacted because for 1 mole of H₂, ½ mole of O₂ is required. The remaining 1/2 mole will be excess.

Importance of non-limiting reactant

Frequently a large amount of inexpensive reactant is supplied because of the following reasons.

• To produce maximum amount of product
• To increase the rate of reaction
• To ensure that whole of the mass of expensive reactant is completely converted to the desired product.

Ans. Actual and Theoretical yield

Actual yield

Definition The amount of the products obtained in a chemical reaction is called the actual yield of that reaction.

Theoretical yield

Definition The amount of the products calculated from the balanced chemical equation represents the theoretical yield.

Explanation The theoretical yield is the maximum amount of the product that can be produced by a given amount of a reactant, according to balanced chemical equation.

Theoretical yield is always greater than actual yield.

In most chemical reactions the amount of the product obtained is less than the theoretical yield.

Reason There are following reasons for that:

• Physical Process: The process like filtration, separation by distillation, separation by a separating funnel, washing, drying and crystallization, if not properly carried out, decrease the actual yield.

• Side Reaction: Some of the reactants might take part in a competing side reaction and reduce the amount of the desired product. So, in most of the reactions the actual yield is less than the theoretical yield.

• Reversible Reaction: A reaction may be reversible. Therefore, the amount of the product will be reduced by the backward reaction.

Efficiency of reaction

A chemist is usually interested in the efficiency of a reaction. The efficiency of a reaction is expressed by comparing the actual and theoretical yields in the form of percentage (%) yield.

%Yield = (Actual yield)/(Theoretical yield) × 100

Greater the %age yield, higher will be the efficiency of reaction and vice versa.

Ans. Importance of stoichiometry in production and dosage of medicine

In the preparation of required dose of a medicine, the optimum amount of the active ingredient in a medicine is essential to produce desired effects in the patient.

Stoichiometry ensures the following things:

• The accuracy of drug synthesis.
• Any deviation can result in incomplete reaction or contamination with un-reacted reactants or by-products.
• Allows chemists to precisely control chemical reactions to produce drugs.
• To ensure its efficiency, effectiveness and safe use of drugs.

Significance of Stoichiometry in Medicine

Stoichiometry is very important in the field of medicine and is used:

(i) Actual product: In the preparation of antibiotics, the stoichiometry ensures that each dose matches the active ingredient and target bacteria.

(ii) Analysis of cholesterol: To determine the cholesterol level in the blood of patients. Cholesterol is a form of fat that is not all bad. However, cholesterol can have harmful effects.

(iii) Insulin level: To determine the glucose level in the blood of diabetic patient. Use of insulin relies on the stoichiometry to precise control of blood sugar levels.

(iv) Steroids: To determine the steroid and other stimulants in the urine of athletes. Athletes use steroids and other stimulants to enhance performance and increase strength.

(v) Antigens: To determine the concentration of viral antigens in the preparation of vaccine for effective results.

(vi) Amount of drug: To determine the amount and number of drugs to give a dosage to a patient. The medicine has no effect when given in small amounts and can cause toxic state or death when given in large amounts. Paracetamol is used as a pain killer and to decrease fever. An overdose may result a blood thinning, organ damage and severe liver damage.