Part 1: Multiple choice
Brownian motion was first observed in 1827 for:
Brownian motion gives evidence that molecules of a gas:
The random motion of smoke particles is due to:
Ammonia and hydrogen chloride gases mix and form a white cloud of NH₄Cl. This experiment shows:
Gases are easily compressed because:
To study the relation between two variables of a gas (V, P, T), which must be kept constant?
Boyle's law relates the volume and pressure of a fixed mass of gas at constant:
When the pressure on a fixed mass of gas is increased to four times (constant temperature), its volume:
A gas occupies 200 cm³ at 1 atm. At constant temperature, its volume at 0.5 atm is:
In Boyle's experiment, the graph that is a straight line through the origin is:
A gas is slowly compressed to half its volume at constant temperature. Its pressure:
When a fixed mass of gas is compressed slowly to half its volume at constant temperature, its density:
In Boyle's apparatus, the pressure of the trapped air when the movable tube is raised so that its mercury level is h cm above that in the other tube is:
The coefficient of volume expansion of any gas at constant pressure is:
Charles's law: at constant pressure, the volume of a fixed mass of gas is directly proportional to its:
A gas at 0 °C has a volume of 300 cm³. At 91 °C (constant pressure) its volume is:
If the Kelvin temperature of a gas doubles at constant pressure, its volume:
2 litres of a gas at 27 °C are heated at constant pressure to 127 °C. The new volume is about:
At constant pressure, a gas at 273 K is heated until its volume doubles. The final temperature is:
In Charles's experiment, the length of the trapped air column is a measure of its volume because:
The pressure law states that, at constant volume, the pressure of a fixed mass of gas is directly proportional to its:
The coefficient of pressure increase at constant volume for all gases is:
A gas at 1 atm and 27 °C is heated to 127 °C at constant volume. The final pressure is about:
Jolly's apparatus is used to find the:
Mercury is placed in the bulb of Jolly's apparatus so as to fill about 1/7 of it in order to:
At constant volume, the pressure of a gas at 27 °C will double when it is heated to:
Absolute zero corresponds to:
The temperature of the human body (37 °C) on the Kelvin scale is about:
100 K corresponds to:
An ideal gas is one whose:
A graph of pressure against Kelvin temperature at constant volume is:
Real gases do not obey the gas laws near absolute zero because:
The general gas law for a fixed mass of gas is:
STP means:
A gas has P = 2 atm, V = 1 L, T = 300 K. If the pressure becomes 1 atm and V = 2 L, the temperature is:
An open flask is heated from 7 °C to 147 °C. The fraction of the original air that escapes is:
The value of the universal gas constant is about:
The mass of one mole of oxygen gas (O₂) is:
Two gases are mixed (constant temperature) in a container. The pressure of the mixture is equal to:
A helium balloon rises in the sky. Its volume:
Part 2: Written questions and problems
1. [Give reasons] Smoke particles seen under a microscope move randomly.
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They are bombarded unequally from different sides by the fast, randomly moving air molecules.
2. [Give reasons] Gases are compressible but liquids are almost incompressible.
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Gas molecules are far apart with large intermolecular spaces, which can be reduced by pressure; liquid molecules are nearly in contact.
3. [Give reasons] The white cloud of NH₄Cl forms in both beakers even though HCl is denser than NH₃.
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Gas molecules move randomly and diffuse through the spaces between other molecules irrespective of density.
4. [Give reasons] Readings in Boyle's experiment should be taken only after waiting for the temperature of the gas to return to room temperature.
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Boyle's law applies at constant temperature; compression or expansion can heat or cool the gas.
5. [Give reasons] Equal volumes of different gases expand by the same amount when heated through the same temperature rise at constant pressure.
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Experiment (two flasks) shows the mercury threads move equal distances: the coefficient of volume expansion is the same, 1/273 per °C, for all gases.
6. [Give reasons] Tyre pressure should be measured when the tyres are cold.
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Heating at nearly constant volume raises the pressure (P ∝ T), so a hot tyre shows a higher reading.
7. [Give reasons] Some mercury is put in the bulb of Jolly's apparatus.
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Mercury expands about seven times as much as glass, so about 1/7 of the bulb volume filled with mercury keeps the volume of the air constant.
8. [Give reasons] In Jolly's experiment the tube (C) is moved so that the mercury in the bulb arm returns to the same mark each time.
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To keep the volume of the gas constant while the pressure is measured.
9. [Give reasons] The Kelvin temperature is always positive.
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The lowest possible temperature is absolute zero (0 K); T = t + 273 is never negative.
10. [Give reasons] Real gases do not reach zero volume at absolute zero.
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Before reaching it they liquefy and solidify and no longer obey the gas laws.
11. [Give reasons] A sealed bottle of air may burst if left in the sun.
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At constant volume, heating raises the pressure (P ∝ T) until the walls cannot withstand it.
12. [Give reasons] A helium balloon expands as it rises high in the air.
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The external pressure falls, so the gas expands (V ∝ 1/P).
13. [Give reasons] A bubble expands as it rises from the bottom of a lake.
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The pressure on it decreases with decreasing depth, so by Boyle's law its volume increases.
14. [Give reasons] Some of the air escapes from an open flask when it is heated.
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The air expands, but the volume of the flask is fixed, so the excess goes out; the amount of gas left is proportional to 1/T.
15. [Give reasons] Celsius temperature cannot be used directly in the gas laws.
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V/T and P/T are constant only with temperature measured from absolute zero; Celsius readings can be zero or negative.
Part C — Define / compare
16. [Define] What is Brownian motion? Who discovered it?
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The continuous random motion of small particles (pollen, smoke) suspended in a fluid, due to collisions with the fluid molecules; discovered by Robert Brown in 1827.
17. [Define] State Boyle's law and its mathematical form.
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At constant temperature the volume of a fixed mass of gas is inversely proportional to its pressure; PV = constant.
18. [Define] State Charles's law (two forms).
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At constant pressure the volume of a fixed mass of gas increases by 1/273 of its volume at 0 °C for each 1 °C rise; or V is directly proportional to the Kelvin temperature (V/T = constant).
19. [Define] State the pressure law (Gay-Lussac) in two forms.
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At constant volume the pressure of a fixed mass of gas increases by 1/273 of its pressure at 0 °C for each 1 °C rise; or P is directly proportional to the Kelvin temperature (P/T = constant).
20. [Define] Define the coefficient of volume expansion of a gas at constant pressure.
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The increase in volume of unit volume of the gas at 0 °C for a rise of 1 °C at constant pressure (= 1/273 K⁻¹).
21. [Define] Define the coefficient of pressure increase of a gas at constant volume.
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The increase in unit pressure of the gas measured at 0 °C for a rise of 1 °C at constant volume (= 1/273 K⁻¹).
22. [Define] What is meant by absolute zero? How is it deduced from Charles's law?
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- The lowest theoretically attainable temperature, −273 °C (0 K), at which an ideal gas would have zero volume (or pressure).
- Extending the straight V–t graph backwards, it cuts the temperature axis at −273 °C.
23. [Compare] Compare the three gas laws (constant quantity, relation, equation).
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Boyle: T constant, V ∝ 1/P, PV = const. Charles: P constant, V ∝ T, V/T = const. Pressure law: V constant, P ∝ T, P/T = const.
24. [Compare] Compare the Celsius and Kelvin scales.
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Celsius: −273 °C is the lowest, values can be negative, ice point 0 °C. Kelvin: starts at absolute zero, always positive, ice point 273 K; T = t + 273.
25. [Define] State the general gas law and derive it from Boyle's and Charles's laws.
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PV/T = constant. Boyle: V ∝ 1/P (T constant); Charles: V ∝ T (P constant); combined V ∝ T/P, so PV/T = const and P₁V₁/T₁ = P₂V₂/T₂.
Part D — Problems
26. [Problem] A gas has volume 600 cm³ at 76 cm Hg. Find its pressure when its volume is compressed to 400 cm³ at constant temperature.
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114 cm Hg
P₂ = 76 × 600/400.
27. [Problem] An air bubble of volume 8 cm³ is at a depth of 20.26 m in fresh water. Find its volume just below the surface if the temperature is the same. (ρ = 1000 kg/m³, g = 10 m/s², Pa = 1.013 × 10⁵ N/m²)
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24 cm³
P₁ = Pa + ρgh = 1.013 × 10⁵ + 2.026 × 10⁵ = 3 atm; V₂ = 3 × 8.
28. [Problem] A gas of volume 500 cm³ at 7 °C is heated at constant pressure until its volume is 750 cm³. Find the final temperature in °C.
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147 °C
T₂ = 280 × 750/500 = 420 K.
29. [Problem] A gas has 200 cm³ at 0 °C and 273.2 cm³ at 100 °C at constant pressure. Find the coefficient of volume expansion.
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3.66 × 10⁻³ per °C (≈ 1/273)
(273.2 − 200)/(200 × 100).
30. [Problem] The volume of a gas at 0 °C is 300 cm³. Find its volume at 273 °C at constant pressure.
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600 cm³
V = 300 × 546/273.
31. [Problem] The pressure of a gas is 45 cm Hg at 27 °C. Find its pressure at 127 °C at constant volume.
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60 cm Hg
P₂ = 45 × 400/300.
32. [Problem] A closed container of air at 0 °C has its pressure 80 cm Hg. It is cooled to −91 °C. Find the new pressure.
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53.3 cm Hg
80 × 182/273.
33. [Problem] A tyre has air at 2.0 atm at 7 °C. After a journey the temperature of the air is 47 °C. Find the pressure assuming constant volume.
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2.29 atm
2.0 × 320/280.
34. [Problem] A fixed volume of gas at 1 atm and 27 °C is heated until its pressure is 1.5 atm. Find the temperature in °C.
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177 °C
T₂ = 300 × 1.5 = 450 K.
35. [Problem] A gas has a volume of 450 cm³ at 27 °C and 60 cm Hg. Find its volume at STP.
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≈ 323 cm³
V₂ = 60 × 450 × 273/(300 × 76).
36. [Problem] A fixed mass of gas at 76 cm Hg, 300 K and 500 cm³ is compressed to 250 cm³ and heated to 360 K. Find its new pressure.
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182.4 cm Hg
P₂ = 76 × 500 × 360/(300 × 250).
37. [Problem] 3 L of gas at 2 atm and 27 °C changes to 6 L at 1.5 atm. Find the final temperature in °C.
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177 °C
T₂ = 300 × (1.5 × 6)/(2 × 3) = 450 K.
38. [Problem] An open flask of air is heated from 7 °C to 147 °C. What percentage of the original air escapes?
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33.3 %
Remaining fraction = 280/420 = 2/3.
39. [Problem] Gas A (6 L at 20 cm Hg) and gas B (4 L at 30 cm Hg) are transferred to a 3 L container at constant temperature. Find the pressure of the mixture.
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80 cm Hg
PA = 20 × 6/3 = 40; PB = 30 × 4/3 = 40; sum 80.
40. [Problem] Two moles of a gas at 300 K occupy 0.01 m³. Find the pressure. (R = 8.31 J/(mol·K))
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4.99 × 10⁵ Pa
P = nRT/V = 2 × 8.31 × 300/0.01.