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State Board · Class 9 · Science and Technology

Lesson 4: Measurement of Matter

5 concepts · 40 practice questions with answers · Free to read

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Laws of chemical combination

From daily life

When you burn a candle, it seems to vanish. But if you collected all the smoke, gases and wax drops, their total mass would be the same as the candle plus the oxygen used. Matter changes form but is not lost.

Simple definition

The law of conservation of mass (वस्तुमान अक्षय्यतेचा नियम) says that total mass of reactants equals total mass of products. The law of constant proportion (स्थिर प्रमाणाचा नियम) says that a compound always has its elements in a fixed mass ratio.

12 g carbon and 32 g oxygen give 44 g carbon dioxideMass before = mass after (12 + 32 = 44)12 gcarbon+ 32 goxygen= 44 gcarbon dioxide

In the figure : In the figure nothing is lost in a reaction; the total mass stays the same.

Rule 1: Law of conservation of mass — Lavoisier stated this law in 1785. In a chemical reaction the total mass of the reactants equals the total mass of the products. For example, 56 g of calcium oxide and 18 g of water give 74 g of the product.

  • Easy : 12 g carbon + 32 g oxygen gives 44 g carbon dioxide (12 + 32 = 44).
  • Medium : 10 g of a gas is used in a reaction with 25 g of a solid and the product is a single compound. Its mass is 10 + 25 = 35 g.
  • Exam-type : 48 g of reactants give a solid product of 30 g and a gas. The gas has mass 48 − 30 = 18 g.

Rule 2: Law of constant proportion — Proust stated this law in 1794. The proportion by mass of the elements in a compound is fixed, whatever the source of the compound. Water: hydrogen to oxygen is 1 : 8, so 9 g of water has 1 g hydrogen and 8 g oxygen. Carbon dioxide: carbon to oxygen is 3 : 8. Copper oxide: copper to oxygen is about 4 : 1.

  • Easy : 18 g of water has 2 g hydrogen and 16 g oxygen (ratio 2 : 16 = 1 : 8).
  • Medium : 22 g of carbon dioxide: carbon = 22 × 3 ÷ 11 = 6 g and oxygen = 22 × 8 ÷ 11 = 16 g.
  • Exam-type : How much hydrogen and oxygen are in 27 g of water? Total parts 1 + 8 = 9. Hydrogen = 27 ÷ 9 = 3 g; oxygen = 27 − 3 = 24 g.
Remember

Mass is conserved. Water is always H : O = 1 : 8 by mass.

Common mistake

Using the 1 : 8 ratio for the number of atoms. It is the ratio of mass.

Shortcut

Memory clue: "Lavoisier 1785 = Lost nothing; Proust 1794 = Proportion fixed".

Spot the difference

PointConservation of massConstant proportion
ScientistLavoisierProust
Year17851794
IdeaMass before = afterFixed mass ratio

Practice questions

Easy
  1. 1State the law of conservation of mass.
  2. 2Who stated the law of constant proportion, and when?
  3. 3In which ratio by mass are hydrogen and oxygen in water?
Medium
  1. 4In carbon dioxide, what is the ratio by mass of carbon to oxygen?
  2. 556 g of calcium oxide reacts with 18 g of water. What is the mass of the product?
  3. 6Find the mass of oxygen in 45 g of water.
Challenging
  1. 740 g of copper oxide has copper to oxygen about 4 : 1. Find both masses.
  2. 8Does the law of constant proportion hold if water is taken from a river or a well? Explain.
Show answers (try them yourself first)
  1. 1In a chemical reaction the total mass of reactants equals the total mass of products.
  2. 2Proust, in 1794.
  3. 31 : 8.
  4. 43 : 8.
  5. 556 + 18 = 74 g.
  6. 6Oxygen = 45 × 8 ÷ 9 = 40 g.
  7. 7Copper = 40 × 4 ÷ 5 = 32 g; oxygen = 8 g.
  8. 8Yes. The ratio of mass H : O is 1 : 8 whatever the source of the water.

Atomic size, mass and symbols

From daily life

Dust looks tiny, but an atom is far smaller than a speck of dust. To talk about such tiny things we need small units and a standard to compare their masses.

Simple definition

Relative atomic mass (सापेक्ष अणुवस्तुमान) compares the mass of an atom with a standard; the standard is carbon = 12. Its unit is the Dalton (u).

Rule 1: Atomic size — Atomic radius is measured in nanometres (1 m = 109 nm). A hydrogen atom is about 10-10 m. Size increases with the number of orbits, so K is bigger than Na. With the same number of outer orbits, more electrons make the atom smaller, so Mg is smaller than Na.

  • Easy : Li has 2 orbits and Na has 3, so Na is bigger.
  • Medium : Compare Na and Cl (both have 3 orbits): Cl has 17 electrons and Na has 11, so Cl is smaller.
  • Exam-type : Arrange Na, K and Mg from largest to smallest: K (4 orbits) is largest; Na (3 orbits, 11 electrons) is bigger than Mg (3 orbits, 12 electrons). So K, Na, Mg.

Rule 2: Atomic mass and symbols — Earlier hydrogen was taken as 1. Since 1961 the standard is carbon = 12. The unit is the Dalton (u); 1 u = 1.66 × 10-27 kg. Symbols follow IUPAC and the Berzelius method: the first letter is capital and the second is small. Helium and neon are mono-atomic; oxygen and nitrogen are diatomic (O2, N2).

  • Easy : Calcium is written Ca, not CA or ca.
  • Medium : O2 has two atoms: its mass is 2 × 16 = 32 u.
  • Exam-type : Mass of 5 atoms of carbon = 5 × 12 = 60 u.
Remember

Carbon = 12 is the standard. Symbol: first capital, second small.

Common mistake

Writing CO for cobalt (it is Co).

Shortcut

Memory clue: "Carbon 12, Capital then small".

Spot the difference

PointValue
StandardCarbon = 12 (since 1961)
1 u1.66 × 10-27 kg
Mono-atomicHe, Ne
DiatomicO2, N2

Practice questions

Easy
  1. 1In which unit is atomic radius expressed?
  2. 2What is the standard for relative atomic mass now?
  3. 3What is 1 u in kg?
Medium
  1. 4Which is bigger, K or Na?
  2. 5Give two examples each of mono-atomic and diatomic elements.
  3. 6Find the mass of N2 in u (N = 14).
Challenging
  1. 7Why is Mg smaller than Na although both have 3 orbits?
  2. 8Write the correct symbols: sodium, silicon and chlorine as per the rule of capital and small letters.
Show answers (try them yourself first)
  1. 1Nanometre.
  2. 2Carbon = 12.
  3. 31.66 × 10-27 kg.
  4. 4K, because it has more orbits.
  5. 5Mono-atomic: He, Ne. Diatomic: O2, N2.
  6. 62 × 14 = 28 u.
  7. 7Mg has more electrons and a larger nuclear charge, which pulls the orbits closer.
  8. 8Na, Si, Cl.

Molecular mass, mole and Avogadro's number

From daily life

A shopkeeper does not count rice grains; he sells it by the kilogram. Chemists also cannot count atoms one by one, so they count them in a big packet called a mole.

Simple definition

A mole (मोल) is the amount of substance whose mass in grams equals its molecular mass in u. It has 6.022 × 1023 molecules.

18 g of water, 44 g of carbon dioxide and 58.5 g of salt are one mole eachOne mole = 6.022 × 10²³ particles💧Water H₂O18 g= 1 mole🫧CO₂44 g= 1 mole🧂NaCl58.5 g= 1 mole

In the figure : In the figure the mass of one mole in grams equals the molecular mass in u.

Rule 1: Molecular mass — Molecular mass is the sum of the atomic masses of all the atoms in the molecule. H2O is 18 u, CO2 is 44 u and NaCl is 58.5 u.

  • Easy : O2 = 2 × 16 = 32 u.
  • Medium : CH4 = 12 + (4 × 1) = 16 u.
  • Exam-type : H2SO4 = (2 × 1) + 32 + (4 × 16) = 2 + 32 + 64 = 98 u.

Rule 2: Mole and Avogadro's number — Avogadro's number NA = 6.022 × 1023 molecules per mole. Moles = mass in g ÷ molecular mass. For example, 66 g of CO2 is 66 ÷ 44 = 1.5 mol, which has 1.5 × 6.022 × 1023 = 9.033 × 1023 molecules.

  • Easy : 18 g of water is 18 ÷ 18 = 1 mol, which has 6.022 × 1023 molecules.
  • Medium : 9 g of water is 9 ÷ 18 = 0.5 mol, so molecules = 0.5 × 6.022 × 1023 = 3.011 × 1023.
  • Exam-type : Find the mass of 2 mol of NaCl: mass = moles × molecular mass = 2 × 58.5 = 117 g.
Live figure

Molecular mass, mole and Avogadro's number

In the app you can move this figure with your finger.

Open in the app
Remember

n = mass ÷ molecular mass. 1 mol = 6.022 × 1023 molecules.

Common mistake

Dividing mass by atomic mass of one atom when the substance is a molecule. Use the molecular mass.

Shortcut

Memory clue: "Mole = Mass ÷ Molecular mass".

Spot the difference

PointFormula
Molesmass ÷ molecular mass
Massmoles × molecular mass
Moleculesmoles × 6.022 × 1023

Practice questions

Easy
  1. 1What is the molecular mass of water?
  2. 2What is Avogadro's number?
  3. 3What is the SI unit of the amount of substance?
Medium
  1. 4Find the molecular mass of CO2 (C = 12, O = 16).
  2. 5How many moles are in 36 g of water?
  3. 6Find the number of molecules in 22 g of CO2.
Challenging
  1. 7Find the mass of 3 mol of H2SO4.
  2. 8Explain why 18 g of water and 44 g of CO2 have the same number of molecules.
Show answers (try them yourself first)
  1. 118 u.
  2. 26.022 × 1023.
  3. 3mol.
  4. 412 + 2 × 16 = 44 u.
  5. 536 ÷ 18 = 2 mol.
  6. 622 ÷ 44 = 0.5 mol; 0.5 × 6.022 × 1023 = 3.011 × 1023.
  7. 798 × 3 = 294 g.
  8. 8Each is one mole (18 ÷ 18 = 1 and 44 ÷ 44 = 1), and one mole has 6.022 × 1023 molecules.

Valency and variable valency

From daily life

A two-rupee coin does not buy five things; it gives one and takes one. Atoms also "trade" in whole electrons: an atom gives away or takes up a whole number of them, never half. That number is its valency.

Simple definition

Valency (संयुजा) is the number of electrons an atom gives away or takes up while forming an ionic bond.

A sodium atom with 2, 8, 1 electrons gives one electron to a chlorine atom with 2, 8, 7 and they become Na plus and Cl minusSodium gives one electron to chlorineNaClNa+Cl−2, 8, 12, 8, 72, 82, 8, 8Valency of Na = 1 (gives 1), Cl = 1 (takes 1)

In the figure : In the figure valency is the number of electrons given or taken.

Rule 1: Valency — Na gives 1 electron to become Na+ (2, 8). Cl takes 1 electron to become Cl- (2, 8, 8). The valency of both is 1. Valency is always a whole number.

  • Easy : Mg gives 2 electrons, so its valency is 2.
  • Medium : Oxygen takes 2 electrons to become O2-, so its valency is 2.
  • Exam-type : Al (2, 8, 3) has 3 outer electrons. It gives 3 electrons to become Al3+ (2, 8), so its valency is 3.

Rule 2: Variable valency — Some elements show more than one valency. Fe has 2 and 3 (ferrous and ferric). Cu has 1 and 2 (cuprous and cupric). Hg has 1 and 2 (mercurous and mercuric).

  • Easy : FeCl2 has Fe with valency 2 (ferrous chloride).
  • Medium : FeCl3 has Fe with valency 3 (ferric chloride), because 3 Cl- need Fe3+.
  • Exam-type : Cu2O has two Cu+ for one O2-: cuprous oxide. CuO has Cu2+ for O2-: cupric oxide.
Remember

Valency = electrons given or taken (a whole number). Fe: 2, 3; Cu: 1, 2; Hg: 1, 2.

Common mistake

Giving a fraction as valency. Valency is always a whole number.

Shortcut

Memory clue: "Ferrous = lower valency (2); Ferric = higher (3)".

Spot the difference

ElementLower valencyHigher valency
Iron2 (ferrous)3 (ferric)
Copper1 (cuprous)2 (cupric)
Mercury1 (mercurous)2 (mercuric)

Practice questions

Easy
  1. 1Define valency.
  2. 2What is the valency of Na and Cl?
  3. 3Can valency be a fraction?
Medium
  1. 4What is variable valency? Give an example.
  2. 5What are the valencies of copper?
  3. 6Find the valency of Mg from its electron arrangement 2, 8, 2.
Challenging
  1. 7Name FeCl2 and FeCl3 and state the valency of iron in each.
  2. 8Why does S (2, 8, 6) have valency 2 and not 6 when forming S2-?
Show answers (try them yourself first)
  1. 1The number of electrons an atom gives or takes while forming an ionic bond.
  2. 21 each.
  3. 3No, it is always a whole number.
  4. 4When an element shows more than one valency, e.g. Fe (2 and 3).
  5. 51 (cuprous) and 2 (cupric).
  6. 6It gives 2 outer electrons, so valency is 2.
  7. 7Ferrous chloride (2) and ferric chloride (3).
  8. 8It is easier to take 2 electrons to fill the outer orbit (8) than to give away 6.

Radicals and ions

From daily life

In a school, each student keeps their own identity, but a team of four students is one group. Similarly, an ion can act alone or as a group. These acting units in compounds are called radicals.

Simple definition

A positive ion is a cation (धनायन); a negative ion is an anion (ऋणायन). In ionic compounds these act independently as radicals (मूलके).

Rule 1: Basic and acidic radicals — Cationic radicals are basic radicals, for example Na+ and NH4+. Anionic radicals are acidic radicals, for example Cl- and MnO4-.

  • Easy : In NaCl, Na+ is the basic radical and Cl- is the acidic radical.
  • Medium : In NH4Cl the basic radical is NH4+ and the acidic radical is Cl-.
  • Exam-type : K+ is a cation, so it is a basic radical; Br- is an anion, so it is an acidic radical.

Rule 2: Simple and composite radicals — A single charged atom is a simple radical. A charged group of atoms is a composite radical, for example SO42- and NH4+. The charge on a radical is its valency.

  • Easy : Mg2+ is a simple radical with valency 2.
  • Medium : SO42- is a composite radical (S and four O atoms together) with valency 2.
  • Exam-type : In Na2SO4: two Na+ (simple, basic) and one SO42- (composite, acidic); total charge +2 − 2 = 0.
Remember

Cation = basic radical; anion = acidic radical. Charge = valency.

Common mistake

Calling NH4+ an acidic radical. It is positive, so it is basic.

Shortcut

Memory clue: "Cation = Plus = Basic".

Spot the difference

PointBasic radicalAcidic radical
ChargePositiveNegative
IonCationAnion
ExampleNa+, NH4+Cl-, MnO4-

Practice questions

Easy
  1. 1What is a cation?
  2. 2What is an anion?
  3. 3Which radicals are basic?
Medium
  1. 4Give two examples of acidic radicals.
  2. 5What is a composite radical? Give an example.
  3. 6Name the basic and the acidic radical in KCl.
Challenging
  1. 7Classify as simple or composite: Ca2+, NH4+, F-, SO42-.
  2. 8In (NH4)2SO4, how many NH4+ are needed for one SO42-?
Show answers (try them yourself first)
  1. 1A positively charged ion.
  2. 2A negatively charged ion.
  3. 3Cationic (positive) radicals, e.g. Na+.
  4. 4Cl- and MnO4-.
  5. 5A charged group of atoms, e.g. SO42-.
  6. 6Basic: K+; acidic: Cl-.
  7. 7Simple: Ca2+, F-. Composite: NH4+, SO42-.
  8. 82, so that +2 balances −2.

Quick revision

  • Conservation of mass (1785); constant proportion (1794).
  • Mole: 6.022 × 1023 particles; n = mass / molecular mass.
  • Valency = electrons given or taken in an ionic bond.