Properties of Matter & Measurement

Physical and Chemical Properties

Every substance has unique or characteristic properties that help us identify it. These properties fall into two broad categories:

Physical Properties

Properties that can be measured or observed without changing the identity or composition of the substance.

Questions: colour, odour, melting point, boiling point, density, hardness, solubility, refractive index, electrical conductivity.

• Measuring the boiling point of water doesn't change water into something else — it's still $\text{H}_2\text{O}$.
• Observing that gold is yellow and shiny doesn't alter the gold.

Chemical Properties

Properties that describe how a substance interacts with other substances or how it changes into new substances. Observing chemical properties requires a chemical change to occur.

Questions: combustibility, reactivity with acids/bases, tendency to rust, acidity/basicity, electrochemical behaviour.

• Iron's tendency to rust is a chemical property — you can only observe it when iron actually reacts with oxygen and moisture.
• Hydrogen's combustibility is a chemical property — you need to burn it to observe this.

Key Point: Physical properties can be observed without a chemical change. Chemical properties can only be observed when a substance undergoes a chemical change.

[Exam Important] The distinction between physical and chemical properties is a very common Board exam question. Remember: if the substance's chemical identity is preserved, it's a physical property.

Measurement of Physical Properties

Science is quantitative — we don't just say "this room is big", we say "this room is 6 m long". Every quantitative measurement has two parts:

1. A number (magnitude) — tells us "how much"
2. A unit — tells us "of what"

For example: Length = 6 m (6 is the number, m is the unit)

Without units, a number is meaningless in science. "The mass is 50" tells us nothing. "The mass is 50 kg" is a complete measurement.

Systems of Measurement

Historically, two systems were used:

• English System — used in Britain and the US (pounds, feet, inches)
• Metric System — originated in France, based on the decimal system (kilograms, metres)

The need for a single, universal system led to the creation of the SI System in 1960.

Key Point: Every measurement = number + unit. The SI system is the internationally accepted system of units used in science.

The International System of Units (SI)

The SI System (Le Système International d'Unités) was established by the 11th General Conference on Weights and Measures (CGPM) in 1960. It is based on seven base units from which all other units are derived.

The 7 SI Base Units

Physical Quantity	Symbol	SI Unit	Unit Symbol
Length	$l$	metre	m
Mass	$m$	kilogram	kg
Time	$t$	second	s
Electric current	$I$	ampere	A
Temperature	$T$	kelvin	K
Amount of substance	$n$	mole	mol
Luminous intensity	$I_v$	candela	cd

[JEE Tip] Remember: the SI unit of mass is kilogram (kg), not gram. The mole is the SI unit for amount of substance, which you'll study in detail in Section 7.

Important SI Definitions

• Metre (m): Defined by fixing the speed of light in vacuum at exactly 299,792,458 m/s
• Kilogram (kg): Defined by fixing Planck's constant at exactly $6.62607015 \times 10^{-34}$ J·s
• Second (s): Defined by the caesium-133 atom's hyperfine transition frequency: 9,192,631,770 Hz
• Mole (mol): One mole contains exactly $6.02214076 \times 10^{23}$ elementary entities (Avogadro number)
• Kelvin (K): Defined by fixing Boltzmann constant at exactly $1.380649 \times 10^{-23}$ J/K

SI Prefixes

The SI system uses prefixes to express very large or very small quantities:

Prefix	Symbol	Multiplier	Question
tera	T	$10^{12}$	1 THz = $10^{12}$ Hz
giga	G	$10^{9}$	1 GB = $10^9$ bytes
mega	M	$10^{6}$	1 MHz = $10^6$ Hz
kilo	k	$10^{3}$	1 km = 1000 m
centi	c	$10^{-2}$	1 cm = 0.01 m
milli	m	$10^{-3}$	1 mm = 0.001 m
micro	µ	$10^{-6}$	1 µm = $10^{-6}$ m
nano	n	$10^{-9}$	1 nm = $10^{-9}$ m
pico	p	$10^{-12}$	1 pm = $10^{-12}$ m
femto	f	$10^{-15}$	1 fm = $10^{-15}$ m

[JEE Tip] You MUST know these prefixes. Interconversion problems (like converting nm to m, or µg to kg) appear frequently in competitive exams.

Key Point: The SI system has 7 base units. All other units (like m/s, kg/m³, N, J, etc.) are derived from these base units.

Mass and Weight

These two terms are often confused in everyday language, but in science, they are very different:

Mass

• The amount of matter present in a substance
• Constant everywhere — your mass is the same on Earth, Moon, or in space
• SI unit: kilogram (kg)
• Measured using an analytical balance
• In chemistry labs, gram (g) is commonly used since chemical quantities are small
• 1 kg = 1000 g

Weight

• The gravitational force acting on an object: $W = mg$
• Varies from place to place (depends on the value of $g$)
• SI unit: newton (N)
• Weight on the Moon is about $\frac{1}{6}$ of weight on Earth

Key Point: Mass is constant; weight varies with gravity. In chemistry, we almost always work with mass, not weight.

Volume

Volume is the amount of space occupied by a substance. Since volume = (length)³, its SI unit is m³ (cubic metre).

However, in chemistry labs, we work with much smaller volumes, so we commonly use:

Common Volume Units and Conversions

$$1 \text{ L} = 1000 \text{ mL} = 1000 \text{ cm}^3 = 1 \text{ dm}^3$$

$$1 \text{ m}^3 = 10^3 \text{ dm}^3 = 10^3 \text{ L} = 10^6 \text{ cm}^3 = 10^6 \text{ mL}$$

Note: The litre (L) is not an SI unit, but it is widely used in chemistry.

Volume Measuring Equipment

• Graduated cylinder — for approximate volume measurements
• Burette — for precise delivery of variable volumes (used in titrations)
• Pipette — for precise delivery of a fixed volume
• Volumetric flask — for preparing solutions of known volume and concentration

Density

Density relates mass and volume:

$$\text{Density} = \frac{\text{Mass}}{\text{Volume}}$$

$$d = \frac{m}{V}$$

• SI unit: $\text{kg m}^{-3}$ (or kg/m³)
• Commonly used: $\text{g cm}^{-3}$ (or g/mL)

Density tells us how closely the particles are packed. Higher density = more closely packed particles.

Useful conversion: $1 \text{ g cm}^{-3} = 1000 \text{ kg m}^{-3}$

For example: Density of water = 1 g/cm³ = 1000 kg/m³

Key Point: $1 \text{ L} = 1 \text{ dm}^3 = 1000 \text{ cm}^3 = 1000 \text{ mL}$. Density = Mass/Volume.

Temperature

Temperature is measured using three common scales:

The Three Temperature Scales

Scale	Symbol	Freezing Point of Water	Boiling Point of Water
Celsius	°C	0°C	100°C
Fahrenheit	°F	32°F	212°F
Kelvin	K	273.15 K	373.15 K

Note: Kelvin is the SI unit of temperature and does NOT use the degree symbol (°).

Conversion Formulas

Celsius to Fahrenheit: $$°F = \frac{9}{5}(°C) + 32$$

Fahrenheit to Celsius: $$°C = \frac{5}{9}(°F - 32)$$

Celsius to Kelvin: $$K = °C + 273.15$$

Important Points

• On the Celsius scale, negative temperatures are possible (e.g., $-10°\text{C}$)
• On the Kelvin scale, negative temperatures are NOT possible. The lowest possible temperature is 0 K (absolute zero = $-273.15°\text{C}$)
• The size of one degree is the same on both the Celsius and Kelvin scales — only the zero point is different
• For most chemistry calculations at this level, we use $K = °C + 273$ (dropping the 0.15)

[JEE Tip] Always convert temperatures to Kelvin when using gas law equations or thermodynamic formulas. Many students lose marks by forgetting this conversion.

Key Point: The Kelvin scale is the SI unit for temperature. $K = °C + 273.15$. Negative temperatures are not possible on the Kelvin scale.

Question and Answers

Question 1: SI Unit Conversions — Length

Convert 25.6 nm to metres.

Answer:

1. Identify the prefix: nano (n) = $10^{-9}$
2. Apply the conversion: $$25.6 \text{ nm} = 25.6 \times 10^{-9} \text{ m}$$
3. Express in scientific notation: $$= 2.56 \times 10^{-8} \text{ m}$$

Final Answer: 25.6 nm = $2.56 \times 10^{-8}$ m

Takeaway: To convert from a smaller unit to a larger unit, multiply by the prefix value (which will be a power of 10 less than 1).

Question 2: Temperature Conversion — Celsius to Fahrenheit

Convert 37°C (normal body temperature) to Fahrenheit.

Answer:

1. Use the formula: $°F = \frac{9}{5}(°C) + 32$
2. Substitute: $°F = \frac{9}{5}(37) + 32$
3. Calculate: $°F = \frac{333}{5} + 32 = 66.6 + 32 = 98.6$

Final Answer: 37°C = 98.6°F

Takeaway: Normal body temperature is 37°C or 98.6°F — a useful reference point to remember.

Question 3: Temperature Conversion — Fahrenheit to Kelvin

At what temperature are the Celsius and Fahrenheit scales equal? Also express this temperature in Kelvin.

Answer:

1. Set °C = °F = x: $$x = \frac{9}{5}x + 32$$
2. Solve for x: $$x - \frac{9}{5}x = 32$$ $$\frac{5x - 9x}{5} = 32$$ $$\frac{-4x}{5} = 32$$ $$x = \frac{32 \times 5}{-4} = -40$$
3. So: $-40°\text{C} = -40°\text{F}$
4. Convert to Kelvin: $K = -40 + 273.15 = 233.15$ K

Final Answer: The Celsius and Fahrenheit scales read the same at $-40°$. In Kelvin, this is 233.15 K.

Takeaway: $-40°$ is the unique point where Celsius and Fahrenheit readings coincide. This is a classic exam question!

Question 4: Density Calculation

A piece of metal has a mass of 54.0 g and a volume of 20.0 cm³. Calculate its density in (a) g/cm³ and (b) kg/m³. Identify the metal.

Answer:

1. Calculate density in g/cm³: $$d = \frac{m}{V} = \frac{54.0 \text{ g}}{20.0 \text{ cm}^3} = 2.70 \text{ g/cm}^3$$

2. Convert to kg/m³: $$2.70 \text{ g/cm}^3 = 2.70 \times 1000 \text{ kg/m}^3 = 2700 \text{ kg/m}^3$$

   (Since $1 \text{ g/cm}^3 = 1000 \text{ kg/m}^3$)

3. Identify the metal: Density of 2.70 g/cm³ corresponds to aluminium (Al).

Final Answer: Density = 2.70 g/cm³ = 2700 kg/m³. The metal is aluminium.

Takeaway: To convert g/cm³ to kg/m³, multiply by 1000. Density values can help identify unknown substances.

Question 5: Volume Unit Conversions

Convert the following: (a) 5.2 L to mL (b) 750 cm³ to dm³ (c) 0.35 m³ to litres

Answer:

(a) 5.2 L to mL: $$5.2 \text{ L} = 5.2 \times 1000 \text{ mL} = 5200 \text{ mL}$$

(b) 750 cm³ to dm³: Since $1 \text{ dm}^3 = 1000 \text{ cm}^3$: $$750 \text{ cm}^3 = \frac{750}{1000} \text{ dm}^3 = 0.750 \text{ dm}^3$$

(c) 0.35 m³ to litres: Since $1 \text{ m}^3 = 1000 \text{ L}$: $$0.35 \text{ m}^3 = 0.35 \times 1000 \text{ L} = 350 \text{ L}$$

Takeaway: The key conversion chain is: $1 \text{ m}^3 = 10^3 \text{ L} = 10^3 \text{ dm}^3 = 10^6 \text{ mL} = 10^6 \text{ cm}^3$.

Question 6: Prefix Conversions — Mass

Convert: (a) 4.5 µg to g, (b) 0.025 kg to mg.

Answer:

(a) 4.5 µg to g:

• micro (µ) = $10^{-6}$ $$4.5 \text{ µg} = 4.5 \times 10^{-6} \text{ g}$$

(b) 0.025 kg to mg:

• Step 1: Convert kg to g: $0.025 \text{ kg} = 0.025 \times 10^3 \text{ g} = 25 \text{ g}$
• Step 2: Convert g to mg: $25 \text{ g} = 25 \times 10^3 \text{ mg} = 25000 \text{ mg}$
• Or directly: $0.025 \text{ kg} = 0.025 \times 10^6 \text{ mg} = 2.5 \times 10^4 \text{ mg}$

Final Answer: (a) $4.5 \times 10^{-6}$ g, (b) 25,000 mg or $2.5 \times 10^4$ mg

Takeaway: When converting between prefixes, identify each prefix's power of 10 and use multiplication/division accordingly.

Question 7: Density Application — Finding Volume

The density of mercury is 13.6 g/cm³. What volume would 500 g of mercury occupy?

Answer:

1. Use the density formula rearranged for volume: $$V = \frac{m}{d}$$
2. Substitute values: $$V = \frac{500 \text{ g}}{13.6 \text{ g/cm}^3}$$
3. Calculate: $$V = 36.76 \text{ cm}^3 \approx 36.8 \text{ cm}^3$$
4. Convert to mL: Since 1 cm³ = 1 mL, $V = 36.8$ mL

Final Answer: 500 g of mercury occupies approximately 36.8 cm³ (or 36.8 mL).

Takeaway: Mercury is extremely dense (13.6 g/cm³ — about 13.6 times denser than water), so even 500 g occupies a relatively small volume.

Question 8: Temperature Conversion — Clinical Scenario

A patient's body temperature is recorded as 104°F. Convert this to Celsius and Kelvin. Is this a fever?

Answer:

1. Convert to Celsius: $$°C = \frac{5}{9}(°F - 32) = \frac{5}{9}(104 - 32) = \frac{5}{9} \times 72 = 40°\text{C}$$

2. Convert to Kelvin: $$K = °C + 273.15 = 40 + 273.15 = 313.15 \text{ K}$$

3. Clinical significance: Normal body temperature is 37°C (98.6°F). A temperature of 40°C (104°F) is a high fever and requires medical attention.

Final Answer: 104°F = 40°C = 313.15 K. Yes, this is a significant fever.

Takeaway: $°C = \frac{5}{9}(°F - 32)$ is the key formula. Always check if your answer makes physical sense.

Question 9: Derived SI Units

Express the SI unit of density in terms of base SI units.

Answer:

1. Density = Mass / Volume = Mass / (Length)³
2. SI unit of mass = kg
3. SI unit of length = m
4. Therefore, SI unit of volume = m³
5. SI unit of density: $$\frac{\text{kg}}{\text{m}^3} = \text{kg} \cdot \text{m}^{-3}$$

Similarly, some other derived units:

• Speed = distance/time → m/s = m·s⁻¹
• Force = mass × acceleration → kg·m·s⁻² = Newton (N)
• Pressure = force/area → kg·m⁻¹·s⁻² = Pascal (Pa)
• Energy = force × distance → kg·m²·s⁻² = Joule (J)

Takeaway: All derived units can be expressed in terms of the 7 SI base units. Understanding this helps in dimensional analysis.

Question 10: Mass vs Weight — Conceptual

An astronaut has a mass of 75 kg on Earth. What would be their mass and weight on (a) Earth and (b) the Moon? (Take $g_{\text{Earth}} = 9.8$ m/s², $g_{\text{Moon}} = 1.63$ m/s²)

Answer:

(a) On Earth:

• Mass = 75 kg (constant everywhere)
• Weight = $mg = 75 \times 9.8 = 735$ N

(b) On the Moon:

• Mass = 75 kg (unchanged — mass doesn't depend on location)
• Weight = $mg_{\text{Moon}} = 75 \times 1.63 = 122.25$ N

Comparison: The astronaut's weight on the Moon is about $\frac{122.25}{735} \approx \frac{1}{6}$ of their weight on Earth, but their mass remains exactly the same.

Takeaway: Mass is an intrinsic property (depends on amount of matter) while weight is an extrinsic property (depends on gravitational field). In chemistry, we always measure and report mass.