Questions Related to NCERT

We are given:
The 17th term exceeds the 10th term by 7
That means: a₁₇ − a₁₀ = 7

As  aₙ = a + (n − 1) × d
So,
a₁₇ = a + 16d
a₁₀ = a + 9d

a₁₇ − a₁₀ = 7  (Given)
=> (a + 16d) − (a + 9d) = 7
=> a − a + 16d − 9d = 7
=> 7d = 7
=> d = 1

Hence the common difference d is 1

We are given:
3rd term a₃ = 4
9th term a₉ = –8

Need to find which term of the AP is 0

As aₙ = a + (n − 1) × d

From a₃ = 4:
a + 2d = 4   ------------------------- (1)

From a₉ = –8:
a + 8d = –8   -------------------------- (2)

Subtract Equation 1 from Equation 2
(a + 8d) − (a + 2d) = –8 − 4
6d = –12
d = –2

Put d = –2 into Equation 1
a + 2(–2) = 4
a – 4 = 4
a = 8

Find the term where aₙ = 0
0 = a + (n − 1) × d
0 = 8 + (n − 1)(–2)
0 = 8 − 2(n − 1)
−8 = −2(n − 1)
4 = n − 1
n = 5

Hence the 5th term of the AP is 0.

We are given:
Total number of terms = 50
3rd term a₃ = 12
Last term a₅₀ = 106

As aₙ = a + (n − 1) × d

From a₃ = 12:
a + 2d = 12   ------------------------ (1)

From a₅₀ = 106:
a + 49d = 106  --------------------------(2)

Subtract Equation 1 from Equation 2

(a + 49d) − (a + 2d) = 106 − 12
47d = 94
d = 2

Put d = 2 into Equation 1

a + 2 × 2 = 12
a + 4 = 12
a = 8

Now find the 29th term

a₂₉ = a + 28d
a₂₉ = 8 + 28 × 2 = 8 + 56 = 64

Hence the 29th term is 64.

We are given:
11th term (a₁₁) = 38
16th term (a₁₆) = 73
We need to find the 31st term (a₃₁).

As the nth term formula
aₙ = a + (n − 1) × d

From the 11th term:
a + 10d = 38  ------------------- (1)

From the 16th term:
a + 15d = 73   ---------------------(2)

Subtract Equation 1 from Equation 2
(a + 15d) − (a + 10d) = 73 − 38
5d = 35
d = 7

Put d = 7 into Equation (1)
a + 10 × 7 = 38
a + 70 = 38
a = 38 − 70 = −32

Find the 31st term
a₃₁ = a + 30d
a₃₁ = −32 + 30 × 7 = −32 + 210 = 178

Hence  the 31st term is 178.

Given AP: 11, 8, 5, 2, ...

First term a = 11
Common difference d is = 8 − 11 = –3

We are asked: Is –150 a term of this AP?

Use the nth term formula:
aₙ = a + (n − 1) × d

Substitute values:
−150 = 11 + (n − 1)(−3)
−150 = 11 − 3(n − 1)
−150 = 11 − 3n + 3
−150 = 14 − 3n
−164 = −3n
n = 54.67

Since n = 54.67 is not a whole number,
So  –150 is not a term of the AP.

Given AP: 21, 18, 15, ...
First term  a = 21
Common difference d = 18 − 21 = −3

Which term is −81?

Use the formula for the nth term of an AP:
aₙ = a + (n − 1) × d

Substitute values:
−81 = 21 + (n − 1)(−3)
−81 = 21 − 3(n − 1)
−81 = 21 − 3n + 3
−81 = 24 − 3n
−105 = −3n
n = 35

So, −81 is the 35th term of the AP (a₃₅).

Is any term 0?

Set aₙ = 0
0 = 21 + (n − 1)(−3)
0 = 21 − 3(n − 1)
−21 = −3(n − 1)
n − 1 = 7
n = 8

Yes, the 8th term (a₈) is 0.

A precipitation reaction is a type of chemical reaction in which two soluble substances (usually aqueous solutions of salts) react to form an insoluble solid called a precipitate. This solid separates out from the solution as it does not dissolve in water.

General Form of the Reaction:
Soluble salt A (aq) + Soluble salt B (aq) → Insoluble salt (s) + Soluble salt (aq)

Example 1:
Na₂SO₄ (aq) + BaCl₂ (aq) → BaSO₄ (s) + 2NaCl (aq)

• Sodium sulfate reacts with barium chloride.
• Barium sulfate (BaSO₄) is formed as a white precipitate because it is insoluble in water.
• Sodium chloride remains dissolved in the solution.

Example 2:
AgNO₃ (aq) + NaCl (aq) → AgCl (s) + NaNO₃ (aq)

• Silver nitrate reacts with sodium chloride.
• Silver chloride (AgCl) is formed as a white precipitate.
• Sodium nitrate remains in solution.

Key Points:

• Precipitation reactions help in detecting the presence of certain ions in a solution.
• They are commonly used in qualitative chemical analysis and purification processes.

Refining of Silver – Recovery from Silver Nitrate Solution:

In the refining of silver, silver metal is recovered from its salt solution (silver nitrate – AgNO₃) by a displacement reaction using copper metal. This works because copper is more reactive than silver and can displace silver from its compound.

Type of Reaction:
Displacement Reaction (also called Single Displacement or Single Replacement Reaction)

Chemical Reaction:
Cu + 2AgNO₃ → Cu(NO₃)₂ + 2Ag

Explanation:

• Copper (Cu) is placed into a solution of silver nitrate (AgNO₃).
• Copper, being more reactive than silver, displaces silver from the silver nitrate solution.
• As a result, copper nitrate (Cu(NO₃)₂) is formed in the solution, and silver (Ag) is deposited as a solid.
• This reaction is used in the purification and recovery of silver in metallurgy.

Result:
Silver is obtained in pure form, and the solution now contains copper nitrate.

Difference between Displacement and Double Displacement Reactions:

Displacement Reaction:

One element displaces another element from a compound. Usually involves a more reactive element replacing a less reactive one. For example:
            Zn + CuSO4 → ZnSO4 + Cu
            (Zinc displaces copper from copper sulfate to form zinc sulfate and copper.)

Double Displacement Reaction:

Two compounds exchange their ions to form two new compounds. Often occurs in aqueous solutions and may form a  precipitate, gas, or water. For example:
             NaCl + AgNO3 → NaNO3 + AgCl
             (Sodium chloride reacts with silver nitrate to form sodium nitrate and silver chloride, which precipitates.)

Key Difference:

• Displacement reaction involves one element replacing another.
• Double displacement reaction involves exchange of ions between two compounds.

Decomposition by heat (Thermal decomposition):

CaCO3 → CaO + CO2
(Calcium carbonate decomposes into calcium oxide and carbon dioxide when heated.)

Decomposition by light (Photodecomposition):

2AgCl → 2Ag + Cl2
(Silver chloride decomposes into silver and chlorine gas when exposed to light.)

Decomposition by electricity (Electrolysis):

2H2O → 2H2 + O2
(Water decomposes into hydrogen and oxygen gases when electricity is passed through it.)

Decomposition reactions and combination reactions are called opposites because they involve opposite processes.

Decomposition Reactions:

In a decomposition reaction, a single compound breaks down into two or more simpler substances. It requires energy to break the bonds in the compound.

General form:
AB → A + B

Example:

Decomposition of calcium carbonate (CaCO₃):
CaCO₃ → CaO + CO₂

Combination Reactions:

In a combination reaction, two or more simpler substances combine to form a more complex compound. This reaction releases energy.

General form:
A + B → AB

Example:

Formation of water from hydrogen and oxygen:
2H₂ + O₂ → 2H₂O

Summary:

• Decomposition reaction: One compound breaks down into two or more simpler substances (requires energy).
• Combination reaction: Two or more substances combine to form a more complex compound (releases energy).

Respiration is considered an exothermic reaction because it releases energy in the form of heat and ATP (a type of energy molecule used by cells).

In this process, glucose (a sugar) combines with oxygen to produce carbon dioxide, water, and energy. The energy released is used by the body for various activities, like muscle movement and cell growth.

Here’s how it works:

• The body takes in glucose from food and oxygen from the air.
• These react in the cells of the body, breaking down glucose to release energy.
• The by-products of this reaction are carbon dioxide and water.

Explanation:

• Glucose (C₆H₁₂O₆) reacts with oxygen (O₂).
• This produces carbon dioxide (CO₂) and water (H₂O).
• Energy (ATP and heat) is released during the process.

The reason it’s exothermic is that the energy released (ATP and heat) is greater than the energy required to start the reaction. So, it’s a reaction that releases more energy than it absorbs.

Exothermic & Endothermic reactions refer to the flow of energy (usually in the form of heat) during a chemical reaction.

Exothermic Reactions:

An exothermic reaction releases energy, usually in the form of heat, to its surroundings. In these reactions, the energy of the products is lower than that of the reactants. For example:

• Combustion (burning) of fuel like methane:--      CH₄ + 2O₂ → CO₂ + 2H₂O + energy (heat)
• In this reaction, energy is released as heat when methane burns.

Endothermic Reactions:

An endothermic reaction absorbs energy from the surroundings. In these reactions, the energy of the products is higher than that of the reactants. For example:

• Photosynthesis in plants:--        6CO₂ + 6H₂O + energy (sunlight) → C₆H₁₂O₆ + 6O₂
• Plants absorb sunlight to convert carbon dioxide and water into glucose and oxygen.

In summary:

1. Exothermic = Energy released (e.g., burning fuels).
2. Endothermic = Energy absorbed (e.g., photosynthesis).

A balanced chemical equation is a chemical equation where the number of atoms of each element is the same on both sides of the equation — that is, the number of atoms in the reactants equals the number in the products.

Example of balanced chemical equation:-

Balanced equation:

2H₂ + O₂ → 2H₂O

Now:

• On the left: 4 hydrogen atoms, 2 oxygen atoms
• On the right: 4 hydrogen atoms, 2 oxygen atoms

Now the number of atoms on both sides is equal — the equation is balanced.

Why should chemical equations be balanced?

• To follow the law of conservation of mass, which says that matter cannot be created or destroyed in a chemical reaction.
• To show the correct amounts of substances involved in the reaction.
• To make accurate calculations for experiments and industrial processes.

Balancing ensures that the reaction makes sense scientifically and practically.

When dilute hydrochloric acid is added to iron filings, a chemical reaction takes place in which iron reacts with the acid to form iron chloride and hydrogen gas.

The reaction is:
Fe + 2HCl → FeCl₂ + H₂

Correct answer: (a) Hydrogen gas and iron chloride are produced.

The reaction:
Fe₂O₃ + 2Al → Al₂O₃ + 2Fe
is an example of a displacement reaction.
In this reaction, aluminum displaces iron from iron(III) oxide because aluminum is more reactive than iron. This type of reaction is called a displacement reaction.

Correct answer: (d) displacement reaction.

(i) 4Na(s) + O₂(g) → 2Na₂O(s)
Answer:
Sodium (Na) is oxidised (it loses electrons to form Na⁺).
Oxygen (O₂) is reduced (it gains electrons to form O²⁻ in Na₂O).

(ii) CuO(s) + H₂(g) → Cu(s) + H₂O(l)
Answer:
Hydrogen (H₂) is oxidised (it gains oxygen to form H₂O).
Copper(II) oxide (CuO) is reduced (Cu²⁺ gains electrons to become Cu).

When an iron nail is dipped in copper sulphate (CuSO₄) solution, a chemical reaction takes place. Iron is more reactive than copper, so it displaces copper from the copper sulphate solution. As a result, the blue colour of the solution slowly fades and a reddish-brown layer of copper is deposited on the iron nail.

Chemical equation:

Fe (solid) + CuSO₄ (aqueous) → FeSO₄ (aqueous) + Cu (solid)

Explanation:

• Copper sulphate solution is blue because of copper ions (Cu²⁺).
• Iron replaces copper in the solution and forms iron sulphate (FeSO₄), which is greenish in colour.
• The copper that gets displaced is deposited on the nail.

(i) The substance ‘X’ is calcium oxide, and its chemical formula is CaO.
(ii) The reaction of calcium oxide with water is:
         CaO (s) + H₂O (l) → Ca(OH)₂ (aq) + Heat

This reaction is exothermic and forms calcium hydroxide, which is used for whitewashing.

(i) Solutions of barium chloride and sodium sulphate in water react to give insoluble barium sulphate and the solution of sodium chloride.
Balanced Equation with State Symbols:
BaCl₂ (aq) + Na₂SO₄ (aq) → BaSO₄ (s) ↓ + 2NaCl (aq)

(ii) Sodium hydroxide solution (in water) reacts with hydrochloric acid solution (in water) to produce sodium chloride solution and water.
Balanced Equation with State Symbols:
NaOH (aq) + HCl (aq) → NaCl (aq) + H₂O (l)