Matter in Our Surroundings – Numerical Problems with Stepwise Solutions
CBSE Class 9 • Science — Chemistry
Chapter 1: Matter in Our Surroundings — 20 Numerical Problems with Stepwise Solutions
Content Bank — Important Formulas & Conversions
Density (ρ) = Mass (m) / Volume (V)
m = ρ × V
V = m / ρ
Relative density = Density of substance / Density of water
1 cm³ = 1 mL ; 1 L = 1000 mL = 1000 cm³
Mass (g) ↔ Kilogram (kg): 1 kg = 1000 g
Volume (cm³) ↔ m³: 1 m³ = 1,000,000 cm³
Common reference: density of water ≈ 1.00 g cm-3 at 4°C. Use given values where specified.
Topic 1 — Mass, Volume & Density (Problems 1–6)
1
A cube of metal has side 4.0 cm and mass 512 g. Calculate the density of the metal in g cm-3 and kg m-3.
Use V = side³. Convert units to get kg m⁻³.
2
A wooden block has mass 450 g and density 0.75 g cm-3. Find its volume in cm3 and dimensions if it is a cuboid with base area 150 cm2.
V = m / ρ ; height = V / base area.
3
A liquid has density 0.86 g cm-3. What mass of this liquid will completely fill a container of volume 2.5 L?
Convert L to cm³ (1 L = 1000 cm³).
4
A metal piece of irregular shape weighs 250 g in air and 210 g when submerged in water. (a) Calculate the buoyant force exerted by water on the metal. (b) Find the volume of the metal piece. (Density of water = 1.00 g cm-3.)
Buoyant force = loss in weight in water. Use Archimedes principle: loss = weight of displaced water = mass of displaced water (in g).
5
A 250 mL sample of oil has mass 220 g. Calculate the density of oil in g cm-3 and relative density with respect to water.
1 mL = 1 cm³.
6
A solid sphere has density 2.5 g cm-3 and mass 490 g. Find its radius in cm. (Volume of sphere = (4/3)πr³.)
Find volume from m/ρ then solve for r.
Topic 2 — States of Matter & Compressibility (Problems 7–11)
7
A gas occupies a volume of 4.0 × 103 cm³ at a certain pressure. When compressed, its volume reduces to 1.6 × 103 cm³. Find the fractional decrease in volume and percentage decrease.
Fractional decrease = (initial − final)/initial.
8
A cylinder contains 2.0 L of a gas at a pressure where it weighs 2.4 g per L. If the gas is compressed to 800 mL without any loss, what is the new mass per L?
Total mass remains same. Find new density per L after compression.
9
Air in a balloon of volume 3.0 m³ has a mass of 3.6 kg. Calculate the average density of air in kg m-3 and g cm-3.
1 m³ = 10⁶ cm³; convert units carefully.
10
A sample of gas has density 0.9 g L-1 at a given pressure. What mass of the gas occupies 5.0 L?
Use mass = density × volume. Keep units consistent (g L⁻¹ × L gives g).
11
A block of metal floats in water with 2/5 of its volume above water. If density of water is 1.00 g cm-3, calculate the density of the metal.
From Archimedes principle: fraction submerged = density of object / density of fluid.
Topic 3 — Particle Nature & Diffusion (Problems 12–15)
12
Two liquids A and B are immiscible. A has density 0.85 g cm-3 and B has density 1.20 g cm-3. If 100 mL of each are carefully mixed (so they form two layers), what is the mass of each layer and total mass?
Mass = density × volume. Keep units: 100 mL = 100 cm³.
13
A perfume bottle releases molecules that spread across a cubical room of side 4.0 m. If the perfume mass that enters the air is 0.50 g and assumes uniform distribution, estimate the average mass of perfume per m³ of air in mg m-3.
Volume of room = side³. Convert grams to milligrams.
14
If a drop of dye spreads in water to form a cylinder of radius 1.5 cm and height 8.0 cm, what volume of water has been coloured? (Use V of cylinder = πr²h). If initial drop had mass 0.020 g, find concentration in g L-1.
Convert cm³ to L (1000 cm³ = 1 L).
15
A small pellet of iodine (mass 0.40 g) sublimes and spreads into gaseous iodine occupying 1.2 L of space inside a closed jar. Estimate the density of gaseous iodine in g L-1 and g cm-3.
Density = mass / volume. Convert L to cm³ if needed.
Topic 4 — Change of State & Evaporation (Problems 16–20)
16
A beaker contains 500 g of water at 25°C. Due to evaporation 15 g of water evaporates over the day. What fraction of water evaporated? Express as percentage.
Fraction = evaporated / initial × 100%.
17
A student places 200 g of water in a shallow pan and the surface area is 0.25 m². Another pan has same mass but area 0.50 m². If evaporation rate is proportional to surface area, what is the ratio of times taken for first pan to dry to the second pan (assume same conditions otherwise)?
If rate ∝ area, time ∝ 1/area for fixed mass.
18
During evaporation, high-energy molecules escape from liquid. If initial average kinetic energy per molecule corresponds to temperature T, explain qualitatively how removal of high-energy molecules affects temperature and compute new average if 1/10 of molecules (the highest-energy ones) leave and they carried away 20% of total energy. (Simple proportional estimate.)
If 20% of total energy is removed from system, remaining energy = 80% of initial. Average energy ∝ temperature for ideal approximation.
19
A 120 g sample of water is heated until 20 g evaporates. If latent heat data is not used, estimate the change in mass fraction of water remaining and comment on how evaporation preferentially removes higher-energy molecules but does not change mass calculations.
Mass fraction remaining = remaining mass / initial mass.
20
A metal cylinder of mass 300 g and density 7.5 g cm-3 is dropped into a graduated cylinder containing water (initial water level 200 cm³). What is the new water level? (Assume cylinder is fully submerged and does not dissolve.)
Volume of metal = mass / density. Add displaced volume to initial water level.
Tip: Try solving each problem yourself before opening the solution. These numericals focus on NCERT concepts — practice will strengthen conceptual clarity and calculation speed.