States of matter
Contents: 6 sections
The ideal gas
An ideal gas is a model, and the model rests on a short list of assumptions:
- The molecules are in constant random motion.
- The volume of the molecules themselves is negligible compared with the volume of the container.
- There are no intermolecular forces between the molecules.
- Collisions between molecules are perfectly elastic, so no kinetic energy is lost.
- The average kinetic energy is proportional to the absolute temperature.
Two of those are approximations, and knowing which is what the deviation questions test.
When real gases deviate
A real gas behaves least like an ideal gas at high pressure and low temperature.
- At high pressure the molecules are squeezed close together, so their own volume is no longer negligible compared with the container.
- At low temperature the molecules move slowly, so the intermolecular forces have time to act and are no longer negligible.
It follows that a gas behaves most ideally at low pressure and high temperature, and that a gas with weak intermolecular forces and small molecules, such as helium or hydrogen, is closest to ideal. Ammonia, which hydrogen bonds, deviates strongly.
The ideal gas equation
pV = nRT
| Symbol | Quantity | Unit |
|---|---|---|
| p | Pressure | Pa |
| V | Volume | m³ |
| n | Amount | mol |
| R | Gas constant, 8.31 | J K⁻¹ mol⁻¹ |
| T | Temperature | K |
Almost every error here is a unit error, so convert before substituting:
- kPa to Pa: multiply by 1000
- cm³ to m³: divide by 1 000 000
- dm³ to m³: divide by 1000
- °C to K: add 273
Worked example
0.240 g of a gas occupies 200 cm³ at 100 kPa and 27 °C. Find its relative molecular mass.
Step 1: convert.
- V = 200 cm³ = 200 ÷ 1 000 000 = 2.00 × 10⁻⁴ m³
- p = 100 kPa = 1.00 × 10⁵ Pa
- T = 27 + 273 = 300 K
Step 2: find n. The top of the fraction is pV = 1.00 × 10⁵ × 2.00 × 10⁻⁴ = 20.0, and the bottom is RT = 8.31 × 300 = 2493.
Step 3: find Mᵣ. Writing n as 0.00802 mol keeps the division simple.
So the relative molecular mass is about 30.
Lattice structures
A lattice is a regular repeating arrangement of particles. Which particles, and what holds them together, decides every physical property.
Giant ionic
Oppositely charged ions in a regular three-dimensional array, held by strong electrostatic attraction in all directions. Sodium chloride has each Na⁺ surrounded by six Cl⁻ and each Cl⁻ by six Na⁺.
High melting point, because a great many strong attractions must be overcome. Brittle, because a blow that slides one layer over another brings like charges together and the crystal splits along the plane. Conducts only when molten or dissolved, when the ions are free to move.
Giant covalent
Atoms joined by covalent bonds throughout the structure.
Diamond has each carbon bonded to four others tetrahedrally. Very high melting point, extremely hard, and it does not conduct, because every outer electron is in a bond.
Graphite has each carbon bonded to three others in flat hexagonal layers, with weak forces between the layers. It is soft and slippery because the layers slide, and it conducts because the fourth electron of each carbon is delocalised.
Silicon dioxide is tetrahedral like diamond, with each silicon bonded to four oxygens, and behaves similarly: hard, high melting, non-conducting.
Simple molecular
Small molecules held in a lattice by weak intermolecular forces. Iodine and carbon dioxide are the usual examples. Low melting and boiling points, because only those weak forces are broken, and no conduction, because there are no free charges.
Giant metallic
A lattice of positive ions in a sea of delocalised electrons.
- Conducts electricity and heat in the solid state, because the delocalised electrons move.
- Malleable and ductile, because the layers of ions slide over one another without breaking the bonding, which is still there whatever the arrangement.
- Melting point rises with the charge on the ion and the number of delocalised electrons, which is why magnesium melts far higher than sodium.
Comparing the four
| Property | Giant ionic | Giant covalent | Simple molecular | Giant metallic |
|---|---|---|---|---|
| Melting point | High | Very high | Low | Usually high |
| Conducts as solid | No | No, except graphite | No | Yes |
| Conducts when molten | Yes | No | No | Yes |
| Soluble in water | Often | No | Usually not | No |
| Mechanical | Brittle | Hard | Soft | Malleable |
Common mistakes
- Substituting cm³ or kPa straight into pV = nRT. Convert to m³ and Pa first.
- Using °C in the equation. The temperature must be absolute.
- Saying a gas is ideal at high pressure. It is closest to ideal at low pressure and high temperature.
- Saying covalent bonds break when iodine sublimes. Only the intermolecular forces break.
- Saying ionic solids conduct. They do not, until the ions are free to move.
- Explaining metallic malleability by saying the bonds break. They do not; the delocalised electrons keep the bonding intact as layers slide.
Check you have it
Question 1
In this question it should be assumed that nitrogen behaves as an ideal gas under the conditions stated.
Which volume is occupied by 1.00 g of nitrogen at 50.0 °C and at a pressure of 120 kPa?
Answer: B.
Nitrogen is diatomic, so M = 28.0 g mol⁻¹ and n = 1.00 / 28.0 = 0.0357 mol.
T = 50.0 °C = 323 K, and p = 120 kPa = 120 000 Pa.
V = (0.0357 × 8.31 × 323) / 120 000 = 95.8 / 120 000 = 7.99 × 10⁻⁴ m³ = 0.799 dm³
which is B.
C, 1.60 dm³, comes from using 14.0 as the molar mass. Nitrogen gas is N₂, not N, and that single slip doubles the answer.
D, 22.4 dm³, is the molar volume at standard temperature and pressure. It is the volume of a whole mole under different conditions, and neither applies here.
The pressure has to become pascals because R is 8.31 J K⁻¹ mol⁻¹, and leaving it as 120 makes the volume come out a thousand times too large.
Question 2
In this question you may assume that nitrogen behaves as an ideal gas. One atmosphere pressure = 101 kPa.
Which volume does 1.0 g of nitrogen occupy at 50 °C and a pressure of 2.0 atmospheres?
Answer: C.
Nitrogen is N₂, so n = 1.0 / 28.0 = 0.0357 mol.
T = 50 °C = 323 K.
p = 2.0 atmospheres = 2.0 × 101 kPa = 202 000 Pa.
V = nRT / p = (0.0357 × 8.31 × 323) / 202 000 = 95.8 / 202 000 = 4.74 × 10⁻⁴ m³
and 1 m³ = 10⁶ cm³, so that is 470 cm³, which is C.
D, 950 cm³, is the volume at one atmosphere. Doubling the pressure halves the volume, so forgetting the factor of two leaves you with exactly twice the right answer.
B, 150 cm³, comes from using 14.0 for the molar mass and doubling the pressure as well.
You can also start from the previous conditions if you have them: at 120 kPa the same mass took 0.799 dm³, so at 202 kPa it takes 0.799 × 120/202 = 0.475 dm³. Boyle's law does the second half of the work once the first calculation is done.
Question 3
When an evacuated tube of volume 400 cm³ is filled with gas at 300 K and 101kPa, the mass of the tube increases by 0.65 g. Assume the gas behaves as an ideal gas. What is the identity of the gas?
Answer: A.
n = pV / RT, with V = 400 cm³ = 400 × 10⁻⁶ m³ and p = 101 kPa = 101 000 Pa:
n = (101 000 × 400 × 10⁻⁶) / (8.31 × 300) = 40.4 / 2493 = 0.0162 mol
M = 0.65 / 0.0162 = 40 g mol⁻¹
which is argon, 39.9. That is A.
Helium is 4.0, neon 20.2 and krypton 83.8, and none of them is close.
A quick sense check before the arithmetic: 400 cm³ at room conditions is roughly 0.016 mol, about a sixtieth of a mole, so a mass of 0.65 g points to a molar mass around 40. That is enough to pick argon out even if the calculation goes astray.
The volume must be converted to cubic metres and the pressure to pascals, because R = 8.31 J K⁻¹ mol⁻¹ is in SI units throughout. The tube is evacuated first so the increase in mass is the mass of the gas by itself.
What the syllabus asks for on this topicSyllabus points
Syllabus points
- State the basic assumptions of the kinetic theory as applied to an ideal gas.
- Explain the conditions under which a real gas deviates from ideal behaviour.
- Use the ideal gas equation pV = nRT in calculations, including finding relative molecular mass.
- Describe and compare the lattice structures of giant ionic, giant covalent, simple molecular and giant metallic solids.
- Relate the structure of a solid to its physical properties.
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