Gaseous State flash cards

1. 1.State the three common measurable properties used to describe a gas sample.

   Pressure $P$, Volume $V$, Temperature $T$ (and amount of gas $n$). Gases have no fixed shape or volume, are highly compressible, exert equal pressure in all directions, and mix completely (diffuse) with one another.

   Hint: Four variables in $PV=nRT$.

2. 2.State Boyle's law and give its mathematical form.

   At constant $T$ and $n$, the volume of a fixed mass of gas is inversely proportional to its pressure: $V\propto \dfrac{1}{P}$, i.e. $PV=\text{constant}$, so $P_1V_1=P_2V_2$.

   Hint: Squeeze harder, volume shrinks — $T$ fixed.

3. 3.On a graph, what does a plot of $P$ vs $\dfrac{1}{V}$ look like for a gas obeying Boyle's law?

   A straight line passing through the origin with slope $=$ constant $=nRT$. A plot of $P$ vs $V$ is a rectangular hyperbola (an isotherm).

   Hint: Linearise the inverse relation.

4. 4.State Charles's law and its mathematical form.

   At constant $P$ and $n$, volume is directly proportional to absolute temperature: $V\propto T$, so $\dfrac{V_1}{T_1}=\dfrac{V_2}{T_2}$ (with $T$ in kelvin).

   Hint: Heat it, it expands — $P$ fixed.

5. 5.State the volume-per-degree form of Charles's law and its significance for absolute zero.

   $V_t=V_0\left(1+\dfrac{t}{273.15}\right)$. Extrapolating $V$ to zero gives $t=-273.15\,^\circ\text{C}=0\,\text{K}$, absolute zero, the temperature at which an ideal gas would have zero volume.

   Hint: Coefficient $1/273.15$ per $^\circ$C.

6. 6.State Gay-Lussac's (Amontons') law of pressure–temperature.

   At constant $V$ and $n$, pressure is directly proportional to absolute temperature: $P\propto T$, so $\dfrac{P_1}{T_1}=\dfrac{P_2}{T_2}$.

   Hint: Sealed rigid container heated.

7. 7.State Avogadro's law.

   At the same $T$ and $P$, equal volumes of all gases contain equal numbers of molecules: $V\propto n$ (at constant $T,P$). Equivalently $\dfrac{V_1}{n_1}=\dfrac{V_2}{n_2}$.

   Hint: Equal volumes ⇒ equal molecules.

8. 8.What is the molar volume of an ideal gas at STP, and what are the current STP conditions?

   At STP ($273.15\,\text{K}$, $10^5\,\text{Pa}=1\,\text{bar}$, IUPAC) molar volume $=22.7\,\text{L mol}^{-1}$. At the older STP ($1\,\text{atm}$) it is $22.414\,\text{L mol}^{-1}$.

   Hint: 22.7 L at 1 bar; 22.4 L at 1 atm.

9. 9.Write the ideal gas equation and identify each term.

   $PV=nRT$, where $P$ = pressure, $V$ = volume, $n$ = moles, $T$ = absolute temperature, $R$ = universal gas constant. It combines Boyle's, Charles's and Avogadro's laws.

   Hint: The master equation.

10. 10.Give the value of the gas constant $R$ in three common sets of units.

    $R=0.0821\,\text{L atm K}^{-1}\text{mol}^{-1}=8.314\,\text{J K}^{-1}\text{mol}^{-1}=2\,\text{cal K}^{-1}\text{mol}^{-1}$ (approx). Also $8.314\times10^{7}\,\text{erg K}^{-1}\text{mol}^{-1}$.

    Hint: 0.0821, 8.314, ~2.

11. 11.How is the ideal gas equation rewritten in terms of density $d$ and molar mass $M$?

    Since $n=\dfrac{w}{M}$ and $d=\dfrac{w}{V}$: $PM=dRT$, so $M=\dfrac{dRT}{P}$. Density is directly proportional to pressure and molar mass, inversely to temperature.

    Hint: Replace $n$ with $w/M$.

12. 12.What is the combined gas law?

    For a fixed amount of gas: $\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}$. It merges Boyle's, Charles's and Gay-Lussac's laws for changes in state.

    Hint: $PV/T$ constant.

13. 13.Distinguish an ideal gas from a real gas conceptually.

    An ideal gas obeys $PV=nRT$ at all $P,T$; its molecules have negligible volume and no intermolecular forces. Real gases have finite molecular size and attractive/repulsive forces, so they obey the ideal law only at low pressure and high temperature.

    Hint: No size, no forces = ideal.

14. 14.State Dalton's law of partial pressures.

    The total pressure of a mixture of non-reacting gases equals the sum of the partial pressures of the components: $P_\text{total}=P_1+P_2+P_3+\cdots$. Each partial pressure is the pressure the gas would exert alone in the same volume.

    Hint: Pressures add up.

15. 15.Relate the partial pressure of a component to its mole fraction.

    $P_i=x_i\,P_\text{total}$, where $x_i=\dfrac{n_i}{n_\text{total}}$ is the mole fraction of component $i$. Partial pressure is total pressure times mole fraction.

    Hint: $P_i = x_i P_T$.

16. 16.How is the pressure of a gas collected over water corrected?

    $P_\text{dry gas}=P_\text{total}-p_{\text{H}_2\text{O}}$, where $p_{\text{H}_2\text{O}}$ (aqueous tension) is the saturated vapour pressure of water at that temperature. Subtract the water vapour pressure.

    Hint: Subtract aqueous tension.

17. 17.State Graham's law of diffusion/effusion.

    At the same $T$ and $P$, the rate of diffusion (or effusion) is inversely proportional to the square root of the density (or molar mass): $r\propto\dfrac{1}{\sqrt{d}}\propto\dfrac{1}{\sqrt{M}}$, so $\dfrac{r_1}{r_2}=\sqrt{\dfrac{M_2}{M_1}}$.

    Hint: Lighter gas diffuses faster.

18. 18.Distinguish diffusion from effusion.

    Diffusion is the spontaneous intermingling of gases due to random molecular motion. Effusion is the escape of gas molecules through a tiny hole into vacuum/low pressure. Both follow Graham's law dependence on $\sqrt{M}$.

    Hint: Mixing vs escaping through a pinhole.

19. 19.State the fundamental postulates of the kinetic theory of gases.

    Gas consists of tiny particles in constant random motion; the volume of particles is negligible vs container volume; there are no intermolecular forces; collisions are perfectly elastic (no KE loss); average kinetic energy is directly proportional to absolute temperature.

    Hint: Point masses, elastic, KE ∝ T.

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