SCH3U · Unit 5 test review

Gases & Atmospheric Chemistry: Test Review

Everything for the Unit 5 test on one page: the key facts from all 8 lessons, the mistakes that cost the most marks, and a practice test that points you back to the lessons you need.

Key facts

States of Matter & the Kinetic Molecular Theory

KMT postulate: particles are in constant, random, straight-line motion.
KMT postulate: particle volume is negligible compared to the container's volume.
KMT postulate: no attractive/repulsive forces act between ideal gas particles.
KMT postulate: collisions are perfectly elastic (no net kinetic energy lost).
KMT postulate: average kinetic energy $\propto$ absolute (Kelvin) temperature.

Pressure, Temperature, and the Kelvin Scale

$1 atm = 101.325 kPa = 760 mmHg = 760 torr$
$T (K) = T (° C) + 273.15$ (or $+ 273$ for typical sig figs)
Gas pressure results from particle collisions with container walls: $P = F / A$ .
Kelvin is the only valid temperature scale for gas law ratios/proportions — 0 K corresponds to minimum particle motion, with no negative values.
Gauges read pressure above the atmosphere: $P_{absolute} = P_{gauge} + P_{atmosphere} .$ Gas laws always use absolute pressure.

Boyle's, Charles's, and Gay-Lussac's Laws

Boyle's law: $P_{1} V_{1} = P_{2} V_{2}$ at constant $T, n$ (inverse relationship).
Charles's law: $\frac{V _{1}}{T _{1}} = \frac{V _{2}}{T _{2}}$ at constant $P, n$ (direct relationship, $T$ in Kelvin).
Gay-Lussac's law: $\frac{P _{1}}{T _{1}} = \frac{P _{2}}{T _{2}}$ at constant $V, n$ (direct relationship, $T$ in Kelvin).
$P$ vs. $V$ graphs (Boyle's law) are hyperbolas; $P$ vs. $1/ V$ is linear.
$V$ vs. $T$ (K) and $P$ vs. $T$ (K) graphs are straight lines through the origin.

The Combined Gas Law

Combined gas law: $\frac{P _{1} V _{1}}{T _{1}} = \frac{P _{2} V _{2}}{T _{2}}$ (constant $n$ ).
Reduces to Boyle's law when $T$ is constant, Charles's law when $P$ is constant, Gay-Lussac's law when $V$ is constant.
Always convert temperature to Kelvin before substituting.
$P_{1}, P_{2}$ must share units; $V_{1}, V_{2}$ must share units (any consistent pair works).
Correction-factor check: $V_{2} = V_{1} \times \frac{P _{1}}{P _{2}} \times \frac{T _{2}}{T _{1}}$ . Each ratio should be above 1 if that change makes the gas expand and below 1 if it squeezes it.

The Ideal Gas Law

$P V = n RT$
$R = 8.314 kPa \cdot L / (mol \cdot K)$ (use with $P$ in kPa, $V$ in L, $T$ in K)
Rearranged forms: $P = n RT / V$ , $V = n RT / P$ , $n = P V / (RT)$ , $T = P V / (n R)$
Ideal behaviour is best approximated at low pressure and high temperature.
Real gases deviate from ideal at high pressure (particle volume matters) and low temperature (intermolecular forces matter).

Molar Volume: STP and SATP

STP: 0°C (273.15 K), 101.325 kPa, $V_{m} = 22.4$ L/mol.
SATP: 25°C (298.15 K), 100.0 kPa, $V_{m} = 24.8$ L/mol.
STP and SATP are different standards — do not interchange their molar volumes.
Avogadro's law: equal volumes of gas at the same $T, P$ contain equal moles, regardless of gas identity.
$n = V / V_{m}$ and $V = n \times V_{m}$ — valid only exactly at STP or SATP.

Gas Stoichiometry

Gas stoichiometry road map: given quantity → moles (molar mass, molar volume, or ideal gas law) → mole ratio → moles of target → target quantity.
Use $V_{m}$ = 22.4 L/mol (STP) or 24.8 L/mol (SATP) only when the gas is exactly at that standard condition.
Use $n = P V / (RT)$ for gases at non-standard conditions.
For two gases at the SAME $T, P$ , their volume ratio equals their mole ratio (from the balanced equation's coefficients), by Avogadro's law.
Dalton's law: $P_{total} = P_{1} + P_{2} + \dots$ ; for a gas collected over water, $P_{gas} = P_{atm} - P_{H_{2} O}$ .

Atmospheric Chemistry

Dry air composition (by volume): $N_{2} \approx 78.08%$ , $O_{2} \approx 20.95%$ , Ar $\approx 0.93%$ , $CO_{2} \approx 0.04%$ (≈420 ppm, rising).
Greenhouse gases ( $CO_{2}$ , $CH_{4}$ , $H_{2} O$ (g)) absorb and re-radiate infrared energy, warming the lower atmosphere.
Stratospheric ozone ( $O_{3}$ ) absorbs harmful UV radiation; CFCs catalytically destroy this protective ozone layer.
Acid rain forms when $SO_{2}$ / $NO_{x}$ from fossil fuel combustion react with atmospheric water to form sulfuric/nitric acid.
Ground-level ozone and particulate matter (from vehicle/industrial emissions) cause smog; the AQHI summarizes public health risk from air pollution.

Where marks get lost

Saying gas particles "expand" or get bigger when a gas expands — it's the empty space between the fixed-size particles that increases, not the particles themselves. (States of Matter & the Kinetic Molecular Theory)
Thinking gas pressure means the gas is "pushing outward" as some continuous substance, rather than the cumulative effect of many discrete particle-wall collisions. (States of Matter & the Kinetic Molecular Theory)
Forgetting that KMT assumes zero attractive forces — real gases (especially polar ones like $H_{2} O$ ) do attract each other somewhat, which is why they deviate from ideal behaviour. (States of Matter & the Kinetic Molecular Theory)
Confusing "elastic collision" with "no collisions happen" — elastic just means kinetic energy is conserved overall, not that particles never collide. (States of Matter & the Kinetic Molecular Theory)
Comparing kinetic energies with Celsius temperatures (saying a gas at 20°C has twice the kinetic energy of one at 10°C), or claiming heavier particles have more kinetic energy at the same temperature. Only Kelvin ratios work, and at equal temperature all gases share the same average kinetic energy; heavier particles simply move more slowly. (States of Matter & the Kinetic Molecular Theory)
Plugging a Celsius temperature directly into a gas law equation without converting to Kelvin first. (Pressure, Temperature, and the Kelvin Scale)
Adding 273 to a temperature that's already in Kelvin (double-converting). (Pressure, Temperature, and the Kelvin Scale)
Mixing up mmHg and torr conversion factors with kPa — remember 760 mmHg = 760 torr = 101.325 kPa, not 100 kPa. (Pressure, Temperature, and the Kelvin Scale)
Treating a temperature CHANGE (like "increased by 15°C") as if it needed the +273 conversion — differences don't, only absolute temperatures do. (Pressure, Temperature, and the Kelvin Scale)
Rounding 273.15 to 273 inconsistently within the same problem, causing small but avoidable errors. (Pressure, Temperature, and the Kelvin Scale)
Using Celsius temperatures directly in Charles's or Gay-Lussac's law instead of converting to Kelvin first. (Boyle's, Charles's, and Gay-Lussac's Laws)
Applying Boyle's law to a problem where temperature actually changes (should use the combined gas law instead). (Boyle's, Charles's, and Gay-Lussac's Laws)
Mixing up which variable is held constant, and therefore picking the wrong law entirely. (Boyle's, Charles's, and Gay-Lussac's Laws)
Assuming pressure and volume are directly proportional (they're inversely proportional in Boyle's law) — a doubled pressure means a HALVED volume, not a doubled one. (Boyle's, Charles's, and Gay-Lussac's Laws)
Forgetting that these three laws all assume a fixed amount of gas ( $n$ constant) — if gas is added or removed, none of them apply directly. (Boyle's, Charles's, and Gay-Lussac's Laws)
Forgetting to convert temperature to Kelvin before substituting — this is even more critical here since Kelvin appears twice (once in each ratio). (The Combined Gas Law)
Using inconsistent pressure or volume units between state 1 and state 2 (e.g., $P_{1}$ in kPa but $P_{2}$ in atm). (The Combined Gas Law)
Treating a combined gas law problem as a simple Boyle's or Charles's law problem when, in fact, more than one variable changes. (The Combined Gas Law)
Algebra slip when cross-multiplying/rearranging the double ratio — it helps to isolate the unknown symbolically first, then substitute numbers. (The Combined Gas Law)
Not sanity-checking the final answer's direction (e.g., pressure should intuitively rise if volume shrinks and temperature rises, as in a compression + heating scenario). (The Combined Gas Law)
Using $R$ 's value without matching units for $P$ and $V$ — if pressure is given in atm or mmHg, it must be converted to kPa first to use $R = 8.314$ . (The Ideal Gas Law)
Forgetting to convert temperature to Kelvin before substituting into $P V = n RT$ . (The Ideal Gas Law)
Mixing up which variable to isolate when rearranging (a common slip: writing $T = n R / P V$ instead of $T = P V / (n R)$ ). (The Ideal Gas Law)
Forgetting units entirely on the final answer (moles, litres, kPa, or Kelvin, depending on what was solved for). (The Ideal Gas Law)
Assuming the ideal gas law works equally well at very high pressures or very low temperatures, where real-gas deviations become significant. (The Ideal Gas Law)
Using 22.4 L/mol for a problem that actually specifies SATP conditions (or 24.8 L/mol for an STP problem). (Molar Volume: STP and SATP)
Applying molar volume (22.4 or 24.8) to a gas sample that is NOT at STP or SATP — in that case the full ideal gas law is required instead. (Molar Volume: STP and SATP)
Forgetting that molar volume is the same for any ideal gas, and incorrectly thinking it depends on molar mass or identity. (Molar Volume: STP and SATP)
Rounding STP's 273.15 K to "273" but then still expecting the molar volume to come out to exactly 22.4 without minor rounding differences — small rounding is expected and fine. (Molar Volume: STP and SATP)
Using molar volume for a substance that is not a gas under the stated conditions, such as liquid water or a solid reactant. 22.4 L/mol and 24.8 L/mol only describe gases. (Molar Volume: STP and SATP)
Using STP's 22.4 L/mol for a gas that is actually described at SATP or at other non-standard conditions. (Gas Stoichiometry)
Forgetting the mole-ratio step entirely — converting given volume straight to moles and then straight back to a volume of a DIFFERENT substance without applying the balanced equation's coefficients. (Gas Stoichiometry)
Trying to directly compare volumes of two gases at DIFFERENT temperatures/pressures as if they were in the same ratio as moles — the volume-ratio shortcut only works when both gases are at the SAME conditions. (Gas Stoichiometry)
Forgetting to balance the chemical equation first, which throws off every mole ratio downstream. (Gas Stoichiometry)
Using the wrong molar mass or arithmetic slip when converting grams to moles as the first step. (Gas Stoichiometry)
Confusing the protective stratospheric ozone layer ("good" ozone, blocks UV) with ground-level ozone in smog ("bad" ozone, a lung irritant) — they're the same molecule but very different in terms of location and effect. (Atmospheric Chemistry)
Thinking the greenhouse effect itself is entirely bad — the natural greenhouse effect is essential for life; the concern is the human-ENHANCED (excess) portion of it. (Atmospheric Chemistry)
Mixing up the causes of acid rain (sulfur/nitrogen oxides) with the causes of ozone depletion (CFCs) — these are two separate atmospheric issues with separate chemical causes. (Atmospheric Chemistry)
Assuming $CO_{2}$ 's small percentage in the atmosphere (~0.04%) means it can't have a large chemical/climate effect — concentration and chemical potency are not the same thing. (Atmospheric Chemistry)
Believing smog is just "fog" or water vapour, rather than a chemical mixture of ground-level ozone and particulate matter from combustion emissions. (Atmospheric Chemistry)

Practice test

24 questions from across the unit. Each one shows the lesson it comes from.

States of Matter & the Kinetic Molecular Theory
1
According to KMT, why do gases have much lower density than solids or liquids?
States of Matter & the Kinetic Molecular Theory
2
Which of the following is NOT one of the KMT postulates for an ideal gas?
States of Matter & the Kinetic Molecular Theory
3
A sealed syringe of air is pushed in, halving its volume at constant temperature. Which KMT description is correct?
Pressure, Temperature, and the Kelvin Scale
4
Convert 405 kPa to atm. Give your answer to 3 significant figures.
atm
Pressure, Temperature, and the Kelvin Scale
5
Order these temperatures from LOWEST to HIGHEST: 0 K, 0°C, 100°C, 300 K.
1. 10°C
2. 2100°C
3. 3300 K
4. 40 K
Pressure, Temperature, and the Kelvin Scale
6
Match each temperature to its Kelvin value.
Freezing point of water
Boiling point of water at 101.325 kPa
SATP temperature (25°C)
Absolute zero (−273.15°C)
Boyle's, Charles's, and Gay-Lussac's Laws
7
A gas has volume 6.00 L at 200.0 kPa. At constant temperature, the pressure drops to 120.0 kPa. Find the new volume.
L
Boyle's, Charles's, and Gay-Lussac's Laws
8
Match each gas law to its graph shape.
P vs. V (Boyle's law)
P vs. 1/V (Boyle's law)
V vs. T in Kelvin (Charles's law)
P vs. T in Kelvin (Gay-Lussac's law)
Boyle's, Charles's, and Gay-Lussac's Laws
9
A student plots volume against temperature in °C for a gas at constant pressure and gets a straight line that does NOT pass through the origin. Where does the line cross the temperature axis, and what does that tell you?
The Combined Gas Law
10
A gas at 150.0 kPa, 3.00 L, 280.0 K is changed to 200.0 kPa and 320.0 K. Find the new volume.
L
The Combined Gas Law
11
Match the variable held constant to the law the combined gas law reduces to.
Temperature constant
Pressure constant
Volume constant
Only the amount of gas constant
The Combined Gas Law
12
A weather balloon rises from the ground into air where both the pressure and the temperature are much lower. What happens to its volume, and why?
The Ideal Gas Law
13
Find the pressure exerted by 0.750 mol of gas in a 12.0 L container at 295.0 K. Round to one decimal place.
kPa
The Ideal Gas Law
14
What temperature (in K) is needed for 1.20 mol of gas to occupy 30.0 L at 110.0 kPa? Round to one decimal place.
K
The Ideal Gas Law
15
Using the kinetic molecular theory, explain why doubling the number of moles of gas at constant temperature and pressure doubles the volume.
Molar Volume: STP and SATP
16
How many moles of $N_{2}$ are in 11.2 L at STP?
mol
Molar Volume: STP and SATP
17
Match each standard condition to its correct temperature and pressure.
STP
SATP
Molar Volume: STP and SATP
18
A student uses 22.4 L/mol for a gas at 25°C and 101.3 kPa. Explain what is wrong and what they should do instead.
Gas Stoichiometry
19
For $2H_{2} + O_{2} \to 2H_{2} O$ , what volume of $H_{2}$ gas at STP is needed to react completely with 3.00 mol of $O_{2}$ ?
L
Gas Stoichiometry
20
Propane burns as $C_{3} H_{8} (g) + 5O_{2} (g) \to 3CO_{2} (g) + 4H_{2} O (g) .$ What volume of $O_{2}$ is needed to burn 2.00 L of propane, both at the same temperature and pressure?
L
Gas Stoichiometry
21
At the same temperature and pressure, 10.0 L of $N_{2}$ reacts completely with $H_{2}$ to form $NH_{3}$ ( $N_{2} + 3H_{2} \to 2NH_{3}$ ). What is the total volume of gas before and after the reaction?
Atmospheric Chemistry
22
Which gas makes up the LARGEST percentage of dry air by volume?
Atmospheric Chemistry
23
Match each atmospheric issue to its primary chemical cause.
Enhanced greenhouse effect
Stratospheric ozone depletion
Acid rain
Smog
Atmospheric Chemistry
24
Why were lakes on the Canadian Shield in Ontario especially vulnerable to acid rain?

Endless drill

Fresh numbers every time, for the calculation questions in this unit.

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Gases & Atmospheric Chemistry: Test Review

Key facts

Where marks get lost

Practice test

Endless drill

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