# Gases, Kinetic Theory and Intermolecular Forces Chemistry I · Atoms, Bonds and Reaction Rates · https://tryals.app/learn/chemistry-i/gases-kinetic-theory-and-intermolecular-forces ## From Free Particles to Condensed Matter Three experimental laws combine into the **ideal gas equation**: $$PV = nRT$$ with $R = 0.0821$ L atm mol$^{-1}$ K$^{-1}$. Boyle found $P \propto 1/V$ at fixed $T$, Charles found $V \propto T$ at fixed $P$, and Avogadro found $V \propto n$. For a fixed sample the combined law $P_1V_1/T_1 = P_2V_2/T_2$ handles most problems, and temperature must always be in kelvin. The **kinetic molecular model** explains why. Gas particles are treated as points in constant random motion, with negligible volume, no intermolecular forces, and perfectly elastic collisions. Average kinetic energy depends only on temperature, which gives the root-mean-square speed $$u_{\text{rms}} = \sqrt{\frac{3RT}{M}}$$ so at a given temperature light molecules move faster, hence Graham's law of effusion, $r_1/r_2 = \sqrt{M_2/M_1}$. The Maxwell distribution broadens and flattens as temperature rises. Real gases deviate at **high pressure** (molecular volume is no longer negligible) and **low temperature** (attractions matter, and eventually the gas liquefies). Van der Waals corrects both: $$\left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT$$ **Intermolecular forces** are what the ideal model throws away, and they set boiling points. In rising order: **London dispersion** forces, present in everything and growing with molecular size and polarisability; **dipole-dipole** attractions between permanent dipoles; and **hydrogen bonding**, a strong special case when H is bonded to N, O or F. Water's anomalously high boiling point is hydrogen bonding, and the same open hydrogen-bonded lattice makes ice less dense than liquid water. Solids are classified by what holds them: metallic, ionic, molecular (weak intermolecular forces, low melting), and covalent-network such as diamond, where the whole crystal is one molecule. > **Common pitfall:** using degrees Celsius in a gas law. Every relation here is proportional to *absolute* temperature; doubling from 20 °C to 40 °C is a rise of only about 7 %, not 100 %. ## Practice questions 7 of this lesson's 12 practice questions, with answers. The full set is in the app. ### 1. A sample of gas occupies 3.0 L at 300 K. If the pressure is held constant and the temperature is raised to 400 K, what is the new volume in litres, to one decimal place? **Answer:** 4 (within ±0.1) **Why:** Charles’s law gives $V_2 = V_1 T_2/T_1 = 3.0 \times 400/300 = 4.0$ L. Note that both temperatures are already in kelvin, as every gas law requires. Page: https://tryals.app/practice/chemistry-i/gases-kinetic-theory-and-intermolecular-forces/a-sample-of-gas-occupies-3-0-l-at-300-k-if-the-pressure-is-held ### 2. Helium has molar mass 4 g/mol and oxygen 32 g/mol. At the same temperature, set how many times faster the root-mean-square speed of helium is than that of oxygen. **Answer:** 2.83 (within ±0.25) **Why:** Both gases share the same average kinetic energy, so $u \propto 1/\sqrt{M}$ and the ratio is $\sqrt{32/4} = \sqrt{8} = 2.83$. Helium is not eight times faster, the square root matters, and getting it wrong is the standard error here. Page: https://tryals.app/practice/chemistry-i/gases-kinetic-theory-and-intermolecular-forces/helium-has-molar-mass-4-g-mol-and-oxygen-32-g-mol-at-the-same ### 3. Arrange these intermolecular forces from weakest to strongest. **Answer:** 1. London dispersion between small nonpolar molecules 2. Dipole-dipole between polar molecules 3. Hydrogen bonding involving O-H 4. Ionic attraction within a crystal lattice **Why:** London forces are weakest in small molecules, permanent dipoles are stronger, hydrogen bonding is the strongest intermolecular force, and full ionic attraction between charges exceeds all of them. Page: https://tryals.app/practice/chemistry-i/gases-kinetic-theory-and-intermolecular-forces/arrange-these-intermolecular-forces-from-weakest-to-strongest ### 4. How many moles of an ideal gas occupy 22.4 L at 273 K and 1.00 atm? Use $R = 0.0821$ L atm mol$^{-1}$ K$^{-1}$ and give the answer to one decimal place. **Answer:** 1 (within ±0.05) **Why:** $n = PV/RT = (1.00 \times 22.4)/(0.0821 \times 273) = 22.4/22.41 = 1.0$ mol. This is the molar volume at STP, and it is the same for every ideal gas. Page: https://tryals.app/practice/chemistry-i/gases-kinetic-theory-and-intermolecular-forces/how-many-moles-of-an-ideal-gas-occupy-22-4-l-at-273-k-and-1-00-atm ### 5. Sort each solid by the type of bonding that holds the crystal together. **Answer:** - Metallic: Copper - Ionic: Potassium bromide - Molecular: Solid carbon dioxide - Covalent network: Diamond **Why:** Copper has cations in an electron sea, KBr alternating ions, dry ice discrete CO2 molecules held by weak London forces, and diamond a continuous covalent network, which is why their melting points differ so enormously. Page: https://tryals.app/practice/chemistry-i/gases-kinetic-theory-and-intermolecular-forces/sort-each-solid-by-the-type-of-bonding-that-holds-the-crystal ### 6. An ideal gas model assumes particles possess zero volume and exert no attractions. Why do real gases deviate from this model precisely at low temperatures rather than high temperatures? A. Slower particles undergo inelastic collisions with container walls B. Molecules expand at lower temperatures and occupy more space C. Low thermal energy lets weak particle attractions dominate D. The universal gas constant decreases as absolute temperature falls **Answer:** C. Low thermal energy lets weak particle attractions dominate **Why:** At high speeds, kinetic energy dwarfs intermolecular attractions during collisions. When a gas cools, particles move slowly enough for those transient attractive forces to alter trajectories, eventually prompting condensation into a liquid. Page: https://tryals.app/practice/chemistry-i/gases-kinetic-theory-and-intermolecular-forces/an-ideal-gas-model-assumes-particles-possess-zero-volume-and-exert-no ### 7. Which assumptions does the kinetic molecular model make about an ideal gas? A. There are no attractive forces between particles B. Particles have negligible volume compared to the container C. Collisions are perfectly elastic D. All particles travel at the same speed at a given temperature **Answer:** A. There are no attractive forces between particles; B. Particles have negligible volume compared to the container; C. Collisions are perfectly elastic **Why:** The model assumes point particles, no intermolecular forces and elastic collisions. It does *not* assume a single speed, the Maxwell distribution gives a wide spread about the average. Page: https://tryals.app/practice/chemistry-i/gases-kinetic-theory-and-intermolecular-forces/which-assumptions-does-the-kinetic-molecular-model-make-about-an