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આ MCQ મોડ્યુલ આના પર આધારિત છે: Chemical Reactions and Equations – NCERT Exercises
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Chemical Reactions and Equations – NCERT Exercises
🎓 Class 10
Science
CBSE
Theory
Ch 1 — Chemical Reactions and Equations
⏱ ~22 min
📢 Class 10 ચેનલમાં જોડાઓ
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આ મૂલ્યાંકન આના પર આધારિત હશે: Chemical Reactions and Equations – NCERT Exercises
મૂલ્યાંકન બનાવવામાં તેમની સામગ્રી સામેલ કરવા ચિત્રો, PDF અથવા Word દસ્તાવેજ અપલોડ કરો.
Chapter Summary
- A chemical reaction involves the transformation of reactants into products. Signs include change in colour, change in state, evolution of gas, and change in temperature.
- A chemical equation is a symbolic representation of a reaction using formulae. It must be balanced to obey the Law of Conservation of Mass.
- Equations are balanced by adjusting coefficients (never subscripts) using the hit-and-trial method.
- Physical states are shown as (s), (l), (g), (aq). Reaction conditions (heat, catalyst) are written over the arrow.
- Combination reaction: Two or more substances combine to form a single product. Example: CaO + H2O → Ca(OH)2.
- Decomposition reaction: A single substance breaks down into two or more products. Types: thermal (heat), electrolytic (electricity), photolytic (light).
- Displacement reaction: A more reactive element displaces a less reactive one from its compound. Example: Fe + CuSO4 → FeSO4 + Cu.
- Double displacement reaction: Two compounds exchange ions. Often produces a precipitate. Example: Na2SO4 + BaCl2 → BaSO4 + 2NaCl.
- Oxidation: Gain of oxygen or loss of hydrogen. Reduction: Loss of oxygen or gain of hydrogen. When both occur together, it is a redox reaction.
- Exothermic reactions release heat; endothermic reactions absorb heat.
- Corrosion: Metals are slowly destroyed by reaction with air and moisture (e.g., rusting of iron). Prevented by painting, galvanising, alloying.
- Rancidity: Oxidation of fats/oils in food causes bad smell/taste. Prevented by antioxidants, nitrogen flushing, airtight storage, refrigeration.
Keywords
Chemical Reaction
Transformation of reactants into new products with different properties
Chemical Equation
Symbolic representation of a reaction using chemical formulae
Balanced Equation
Equation with equal atoms of each element on both sides
Reactants
Substances that undergo change (left side of arrow)
Products
New substances formed (right side of arrow)
Combination Reaction
Two or more substances → single product
Decomposition Reaction
Single substance → two or more products
Displacement Reaction
More reactive element replaces less reactive one
Double Displacement
Exchange of ions between two compounds
Precipitation Reaction
Reaction producing an insoluble solid (precipitate)
Exothermic Reaction
Releases heat energy to surroundings
Endothermic Reaction
Absorbs heat energy from surroundings
Oxidation
Gain of oxygen or loss of hydrogen
Reduction
Loss of oxygen or gain of hydrogen
Redox Reaction
Simultaneous oxidation and reduction
Corrosion
Gradual destruction of metals by environment
Rancidity
Oxidation of fats/oils causing spoilage
Galvanisation
Coating iron with zinc to prevent rusting
NCERT Exercises
Q1. L1 Remember
Which of the following statements about the observed characteristics of a chemical reaction is incorrect?
(a) Change in temperature (b) Change in colour (c) Change in the condition of pressure (d) Evolution of a gas
Answer: (c) Change in the condition of pressure.
While changes in temperature, colour, and gas evolution are commonly observed signs of a chemical reaction, a change in pressure is not typically listed as a characteristic sign. (Note: pressure changes may occur in gaseous reactions but are not a standard observation criterion at this level.)
While changes in temperature, colour, and gas evolution are commonly observed signs of a chemical reaction, a change in pressure is not typically listed as a characteristic sign. (Note: pressure changes may occur in gaseous reactions but are not a standard observation criterion at this level.)
Q2. L1 Remember
What are the observations that help us to determine whether a chemical reaction has taken place?
Answer: The following observations indicate that a chemical reaction has occurred:
(i) Change in colour -- e.g., blue CuSO4 turns green when iron is added.
(ii) Change in state -- e.g., a solid precipitate forms in a liquid.
(iii) Evolution of a gas -- e.g., bubbles form when zinc reacts with acid.
(iv) Change in temperature -- e.g., the beaker gets hot when quicklime reacts with water.
(i) Change in colour -- e.g., blue CuSO4 turns green when iron is added.
(ii) Change in state -- e.g., a solid precipitate forms in a liquid.
(iii) Evolution of a gas -- e.g., bubbles form when zinc reacts with acid.
(iv) Change in temperature -- e.g., the beaker gets hot when quicklime reacts with water.
Q3. L2 Understand
What happens when dilute hydrochloric acid is added to iron filings? Note down the observation and write the balanced chemical equation.
Observation: When dilute HCl is added to iron filings, hydrogen gas is evolved (bubbles are seen). The iron dissolves gradually and the solution turns greenish (due to ferrous chloride).
Balanced equation:
Balanced equation:
\(\text{Fe}(s) + 2\text{HCl}(aq) \rightarrow \text{FeCl}_2(aq) + \text{H}_2(g)\uparrow\)
Q4. L2 Understand
What is a balanced chemical equation? Why should chemical equations be balanced?
Answer: A balanced chemical equation is one in which the number of atoms of each element on the reactant side is equal to the number of atoms of that element on the product side.
Chemical equations must be balanced because they must obey the Law of Conservation of Mass, which states that matter can neither be created nor destroyed in a chemical reaction. The total mass of the reactants must equal the total mass of the products.
Chemical equations must be balanced because they must obey the Law of Conservation of Mass, which states that matter can neither be created nor destroyed in a chemical reaction. The total mass of the reactants must equal the total mass of the products.
Q5. L3 Apply
Translate the following statements into chemical equations and then balance them:
(a) Hydrogen gas combines with nitrogen to form ammonia.
(b) Hydrogen sulphide gas burns in air to give water and sulphur dioxide.
(c) Barium chloride reacts with aluminium sulphate to give aluminium chloride and a precipitate of barium sulphate.
(d) Potassium metal reacts with water to give potassium hydroxide and hydrogen gas.
(a)
\(3\text{H}_2(g) + \text{N}_2(g) \rightarrow 2\text{NH}_3(g)\)
(b)
\(2\text{H}_2\text{S}(g) + 3\text{O}_2(g) \rightarrow 2\text{H}_2\text{O}(l) + 2\text{SO}_2(g)\)
(c)
\(3\text{BaCl}_2(aq) + \text{Al}_2(\text{SO}_4)_3(aq) \rightarrow 2\text{AlCl}_3(aq) + 3\text{BaSO}_4(s)\downarrow\)
(d)
\(2\text{K}(s) + 2\text{H}_2\text{O}(l) \rightarrow 2\text{KOH}(aq) + \text{H}_2(g)\uparrow\)
Q6. L3 Apply
Balance the following chemical equations:
(a) HNO3 + Ca(OH)2 → Ca(NO3)2 + H2O
(b) NaOH + H2SO4 → Na2SO4 + H2O
(c) NaCl + AgNO3 → AgCl + NaNO3
(d) BaCl2 + H2SO4 → BaSO4 + HCl
(a)
\(2\text{HNO}_3 + \text{Ca(OH)}_2 \rightarrow \text{Ca(NO}_3)_2 + 2\text{H}_2\text{O}\)
(b)
\(2\text{NaOH} + \text{H}_2\text{SO}_4 \rightarrow \text{Na}_2\text{SO}_4 + 2\text{H}_2\text{O}\)
(c)
\(\text{NaCl} + \text{AgNO}_3 \rightarrow \text{AgCl} + \text{NaNO}_3\)
(Already balanced -- 1 atom of each element on both sides.)
(d)\(\text{BaCl}_2 + \text{H}_2\text{SO}_4 \rightarrow \text{BaSO}_4 + 2\text{HCl}\)
Q7. L3 Apply
Write the balanced chemical equations for the following reactions:
(a) Calcium hydroxide + Carbon dioxide → Calcium carbonate + Water
(b) Zinc + Silver nitrate → Zinc nitrate + Silver
(c) Aluminium + Copper chloride → Aluminium chloride + Copper
(d) Barium chloride + Potassium sulphate → Barium sulphate + Potassium chloride
(a)
\(\text{Ca(OH)}_2(aq) + \text{CO}_2(g) \rightarrow \text{CaCO}_3(s) + \text{H}_2\text{O}(l)\)
(b)
\(\text{Zn}(s) + 2\text{AgNO}_3(aq) \rightarrow \text{Zn(NO}_3)_2(aq) + 2\text{Ag}(s)\)
(c)
\(2\text{Al}(s) + 3\text{CuCl}_2(aq) \rightarrow 2\text{AlCl}_3(aq) + 3\text{Cu}(s)\)
(d)
\(\text{BaCl}_2(aq) + \text{K}_2\text{SO}_4(aq) \rightarrow \text{BaSO}_4(s)\downarrow + 2\text{KCl}(aq)\)
Q8. L4 Analyse
Write the balanced chemical equation for each and identify the type of reaction:
(a) Potassium bromide(aq) + Barium iodide(aq) → Potassium iodide(aq) + Barium bromide(aq)
(b) Zinc carbonate(s) → Zinc oxide(s) + Carbon dioxide(g)
(c) Hydrogen(g) + Chlorine(g) → Hydrogen chloride(g)
(d) Magnesium(s) + Hydrochloric acid(aq) → Magnesium chloride(aq) + Hydrogen(g)
(a)
\(2\text{KBr}(aq) + \text{BaI}_2(aq) \rightarrow 2\text{KI}(aq) + \text{BaBr}_2(aq)\)
Type: Double displacement reaction (exchange of ions between KBr and BaI2).
(b)\(\text{ZnCO}_3(s) \xrightarrow{\Delta} \text{ZnO}(s) + \text{CO}_2(g)\)
Type: Decomposition reaction (thermal decomposition -- single compound breaks into two).
(c)\(\text{H}_2(g) + \text{Cl}_2(g) \rightarrow 2\text{HCl}(g)\)
Type: Combination reaction (two elements combine to form a single compound).
(d)\(\text{Mg}(s) + 2\text{HCl}(aq) \rightarrow \text{MgCl}_2(aq) + \text{H}_2(g)\uparrow\)
Type: Displacement reaction (Mg displaces H from HCl).
Q9. L2 Understand
What does one mean by exothermic and endothermic reactions? Give examples.
Exothermic reactions: Reactions that release energy in the form of heat to the surroundings. The products have less energy than the reactants.
Examples:
(i) Burning of natural gas: \(\text{CH}_4(g) + 2\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(g) + \text{heat}\)
(ii) Respiration: \(\text{C}_6\text{H}_{12}\text{O}_6 + 6\text{O}_2 \rightarrow 6\text{CO}_2 + 6\text{H}_2\text{O} + \text{energy}\)
Endothermic reactions: Reactions that absorb energy from the surroundings. The products have more energy than the reactants.
Examples:
(i) Decomposition of CaCO3: \(\text{CaCO}_3(s) \xrightarrow{\Delta} \text{CaO}(s) + \text{CO}_2(g)\)
(ii) Electrolysis of water requires electrical energy input.
Examples:
(i) Burning of natural gas: \(\text{CH}_4(g) + 2\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(g) + \text{heat}\)
(ii) Respiration: \(\text{C}_6\text{H}_{12}\text{O}_6 + 6\text{O}_2 \rightarrow 6\text{CO}_2 + 6\text{H}_2\text{O} + \text{energy}\)
Endothermic reactions: Reactions that absorb energy from the surroundings. The products have more energy than the reactants.
Examples:
(i) Decomposition of CaCO3: \(\text{CaCO}_3(s) \xrightarrow{\Delta} \text{CaO}(s) + \text{CO}_2(g)\)
(ii) Electrolysis of water requires electrical energy input.
Q10. L2 Understand
Why is respiration considered an exothermic reaction? Explain.
Answer: Respiration is considered an exothermic reaction because during this process, glucose (food) is broken down using oxygen, and energy is released in the form of heat. This released energy is used by the body for various life processes.
\(\text{C}_6\text{H}_{12}\text{O}_6(aq) + 6\text{O}_2(g) \rightarrow 6\text{CO}_2(g) + 6\text{H}_2\text{O}(l) + \text{energy}\)
Since energy (heat) is produced, it is an exothermic process. This is why our body stays warm.Q11. L2 Understand
Why are decomposition reactions called the opposite of combination reactions? Write equations for these reactions.
Answer: In a combination reaction, two or more substances combine to form a single product (A + B → AB). In a decomposition reaction, a single compound breaks down into two or more simpler substances (AB → A + B). These are exact opposites of each other.
Combination example:
Combination example:
\(\text{CaO}(s) + \text{H}_2\text{O}(l) \rightarrow \text{Ca(OH)}_2(aq)\)
Decomposition example:\(\text{Ca(OH)}_2(s) \xrightarrow{\Delta} \text{CaO}(s) + \text{H}_2\text{O}(g)\)
The second reaction is the reverse of the first -- the product of combination becomes the reactant of decomposition.Q12. L3 Apply
Write one equation each for decomposition reactions where energy is supplied in the form of heat, light, and electricity.
Heat (Thermal decomposition):
\(2\text{Pb(NO}_3)_2(s) \xrightarrow{\Delta} 2\text{PbO}(s) + 4\text{NO}_2(g) + \text{O}_2(g)\)
Light (Photolytic decomposition):
\(2\text{AgCl}(s) \xrightarrow{\text{Sunlight}} 2\text{Ag}(s) + \text{Cl}_2(g)\)
Electricity (Electrolytic decomposition):
\(2\text{H}_2\text{O}(l) \xrightarrow{\text{Electricity}} 2\text{H}_2(g) + \text{O}_2(g)\)
Q13. L2 Understand
What is the difference between displacement and double displacement reactions? Write equations to illustrate your answer.
Displacement reaction: A more reactive element displaces a less reactive element from its compound. Only one element is displaced.
Double displacement reaction: Two compounds exchange their ions. Both compounds swap partners simultaneously.
\(\text{Fe}(s) + \text{CuSO}_4(aq) \rightarrow \text{FeSO}_4(aq) + \text{Cu}(s)\)
(Iron displaces copper.)Double displacement reaction: Two compounds exchange their ions. Both compounds swap partners simultaneously.
\(\text{Na}_2\text{SO}_4(aq) + \text{BaCl}_2(aq) \rightarrow \text{BaSO}_4(s) + 2\text{NaCl}(aq)\)
(Na+ pairs with Cl-, and Ba2+ pairs with SO42-.)Q14. L1 Remember
In the refining of silver, the recovery of silver from silver nitrate solution involved displacement by copper metal. Write down the reaction involved.
Answer:
\(\text{Cu}(s) + 2\text{AgNO}_3(aq) \rightarrow \text{Cu(NO}_3)_2(aq) + 2\text{Ag}(s)\)
Copper is more reactive than silver. It displaces silver from silver nitrate solution. The silver metal is deposited and the solution turns blue-green due to copper nitrate formation.Q15. L2 Understand
What do you mean by a precipitation reaction? Explain by giving examples.
Answer: A precipitation reaction is a chemical reaction in which two soluble compounds react in solution to form an insoluble product called a precipitate. The precipitate separates out as a solid from the solution.
Example 1:
Example 2:
Example 1:
\(\text{Na}_2\text{SO}_4(aq) + \text{BaCl}_2(aq) \rightarrow \text{BaSO}_4(s)\downarrow + 2\text{NaCl}(aq)\)
White precipitate of BaSO4 forms.Example 2:
\(\text{AgNO}_3(aq) + \text{NaCl}(aq) \rightarrow \text{AgCl}(s)\downarrow + \text{NaNO}_3(aq)\)
White curdy precipitate of AgCl forms.Q16. L4 Analyse
Explain the following in terms of gain or loss of oxygen with two examples each:
(a) Oxidation (b) Reduction
(a) Oxidation (gain of oxygen):
Example 1: \(2\text{Cu}(s) + \text{O}_2(g) \xrightarrow{\Delta} 2\text{CuO}(s)\) -- Copper gains oxygen, it is oxidised.
Example 2: \(\text{C}(s) + \text{O}_2(g) \rightarrow \text{CO}_2(g)\) -- Carbon gains oxygen, it is oxidised.
(b) Reduction (loss of oxygen):
Example 1: \(\text{CuO}(s) + \text{H}_2(g) \xrightarrow{\Delta} \text{Cu}(s) + \text{H}_2\text{O}(l)\) -- CuO loses oxygen, it is reduced.
Example 2: \(\text{ZnO}(s) + \text{C}(s) \rightarrow \text{Zn}(s) + \text{CO}(g)\) -- ZnO loses oxygen, it is reduced.
Example 1: \(2\text{Cu}(s) + \text{O}_2(g) \xrightarrow{\Delta} 2\text{CuO}(s)\) -- Copper gains oxygen, it is oxidised.
Example 2: \(\text{C}(s) + \text{O}_2(g) \rightarrow \text{CO}_2(g)\) -- Carbon gains oxygen, it is oxidised.
(b) Reduction (loss of oxygen):
Example 1: \(\text{CuO}(s) + \text{H}_2(g) \xrightarrow{\Delta} \text{Cu}(s) + \text{H}_2\text{O}(l)\) -- CuO loses oxygen, it is reduced.
Example 2: \(\text{ZnO}(s) + \text{C}(s) \rightarrow \text{Zn}(s) + \text{CO}(g)\) -- ZnO loses oxygen, it is reduced.
Q17. L4 Analyse
A shiny brown coloured element 'X' on heating in air becomes black in colour. Name the element 'X' and the black coloured compound formed.
Answer: The element 'X' is copper (Cu). Copper is a shiny brown-coloured metal. When heated in air, it reacts with oxygen to form copper oxide (CuO), which is black in colour.
\(2\text{Cu}(s) + \text{O}_2(g) \xrightarrow{\Delta} 2\text{CuO}(s)\)
This is an example of oxidation (copper gains oxygen).Q18. L2 Understand
Why do we apply paint on iron articles?
Answer: We apply paint on iron articles to prevent rusting (corrosion). Paint forms a protective barrier between the iron surface and the atmospheric moisture and oxygen. Since air and water cannot reach the iron surface, oxidation does not occur and the iron is protected from forming rust (Fe2O3.xH2O).
Q19. L2 Understand
Oil and fat containing food items are flushed with nitrogen. Why?
Answer: Food items containing oils and fats are flushed with nitrogen gas to prevent rancidity. Rancidity occurs when fats and oils are oxidised by the oxygen in air, producing unpleasant smell and taste. Nitrogen is an inert gas (it does not react with fats). By replacing the air inside the packet with nitrogen, the oxidation of fats is prevented, and the food stays fresh for a longer period.
Q20. L2 Understand
Explain the following terms with one example each:
(a) Corrosion (b) Rancidity
(a) Corrosion: The process by which metals are gradually eaten away (destroyed) due to their reaction with oxygen, moisture, acids, or other chemicals in the environment.
Example: Rusting of iron -- When iron is exposed to moist air for a long time, it forms a reddish-brown flaky coating of hydrated iron oxide (rust, Fe2O3.xH2O). This weakens the iron and eventually destroys it.
(b) Rancidity: The condition in which food items containing fats and oils develop an unpleasant smell and taste when exposed to air for a long time, due to oxidation of fats.
Example: Butter or ghee left exposed to air for several days develops a bad smell and sour taste because the fats in it get oxidised. This can be prevented by storing food in airtight containers, adding antioxidants, or flushing packets with nitrogen gas.
Example: Rusting of iron -- When iron is exposed to moist air for a long time, it forms a reddish-brown flaky coating of hydrated iron oxide (rust, Fe2O3.xH2O). This weakens the iron and eventually destroys it.
(b) Rancidity: The condition in which food items containing fats and oils develop an unpleasant smell and taste when exposed to air for a long time, due to oxidation of fats.
Example: Butter or ghee left exposed to air for several days develops a bad smell and sour taste because the fats in it get oxidised. This can be prevented by storing food in airtight containers, adding antioxidants, or flushing packets with nitrogen gas.
Group Activity: Exothermic and Endothermic Processes
Try This at Home (with adult supervision):
Exothermic: Dissolve some washing soda (Na2CO3) in water in a beaker. Touch the beaker -- it feels warm! The dissolution releases heat.
Endothermic: Dissolve some ammonium chloride (NH4Cl) in water in a beaker. Touch the beaker -- it feels cold! The dissolution absorbs heat from the surroundings.
Discussion: Which of the following processes are exothermic and which are endothermic?
(i) Burning of candle -- Exothermic (releases heat and light)
(ii) Photosynthesis -- Endothermic (absorbs sunlight energy)
(iii) Dissolving sugar in water -- Endothermic (absorbs a small amount of heat)
(iv) Setting of cement -- Exothermic (releases heat during hardening)
Exothermic: Dissolve some washing soda (Na2CO3) in water in a beaker. Touch the beaker -- it feels warm! The dissolution releases heat.
Endothermic: Dissolve some ammonium chloride (NH4Cl) in water in a beaker. Touch the beaker -- it feels cold! The dissolution absorbs heat from the surroundings.
Discussion: Which of the following processes are exothermic and which are endothermic?
(i) Burning of candle -- Exothermic (releases heat and light)
(ii) Photosynthesis -- Endothermic (absorbs sunlight energy)
(iii) Dissolving sugar in water -- Endothermic (absorbs a small amount of heat)
(iv) Setting of cement -- Exothermic (releases heat during hardening)
Frequently Asked Questions — NCERT Exercises & Intext Questions
How do I solve NCERT Class 10 Science Chapter 1 (Chemical Reactions and Equations) exercise questions for the CBSE board exam?
Solve NCERT Chapter 1 — Chemical Reactions and Equations — exercise questions by first reading the question carefully, writing down the given data, recalling the relevant concepts like balancing equations, types of reactions, oxidation, and applying them step by step. This Part 4 covers every intext and end-of-chapter exercise from the NCERT textbook. Write balanced equations, label diagrams clearly and show each step — CBSE Class 10 board examiners award step marks even if the final answer has a small slip. Practising these solutions strengthens conceptual clarity and builds speed for the board exam.
Are the NCERT intext questions from Chemical Reactions and Equations important for the Class 10 board exam?
Yes, NCERT intext questions for Chapter 1 Chemical Reactions and Equations are highly important for the CBSE Class 10 Science board exam. Many board questions are directly lifted or only slightly modified from these intext questions, and they test the foundational concepts — balancing equations, types of reactions, oxidation — that chapter-end questions build on. Attempt every intext question first, then move on to the exercises. This practice ensures complete NCERT coverage, which is the CBSE exam's primary source.
What types of questions from Chemical Reactions and Equations are asked in the CBSE Class 10 Science board exam?
The CBSE Class 10 board paper asks a mix of question types from Chemical Reactions and Equations: 1-mark MCQ and assertion-reason, 2-mark short answers, 3-mark explanations, 5-mark long answers with diagrams or derivations, and 4-mark competency-based / case-study questions. These test understanding of balancing equations, types of reactions, oxidation, reduction. Practising every NCERT exercise and intext question prepares you to answer all of these formats with confidence.
How many marks does Chapter 1 — Chemical Reactions and Equations — carry in the Class 10 Science CBSE paper?
Chapter 1 — Chemical Reactions and Equations — is part of the Class 10 Science syllabus and typically contributes 5–9 marks in the CBSE board paper, depending on the annual weightage. Questions are drawn from definitions, reasoning, numerical/descriptive problems and diagrams on topics like balancing equations, types of reactions, oxidation. Solving the NCERT exercises in this part is essential because CBSE directly references NCERT for question design.
Where can I find step-by-step NCERT solutions for Chapter 1 Chemical Reactions and Equations Class 10 Science?
You can find complete, step-by-step NCERT solutions for Chapter 1 Chemical Reactions and Equations Class 10 Science on MyAiSchool. Every intext and end-of-chapter exercise question is solved with full working, labelled diagrams and CBSE-aligned mark distribution. Solutions highlight key points about balancing equations, types of reactions, oxidation that examiners look for. This makes revision quick and exam-focused for Class 10 CBSE board students.
What is the best way to revise Chemical Reactions and Equations before the Class 10 Science board exam?
The best way to revise Chemical Reactions and Equations for the CBSE Class 10 Science board exam is a three-pass approach. First pass: skim the chapter and note down key terms like balancing equations, types of reactions, oxidation in a one-page mind map. Second pass: solve every NCERT intext and exercise question without looking at the solution, then self-check. Third pass: attempt previous CBSE board questions and competency-based questions under timed conditions. This structured revision secures full marks for this chapter.
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