Gases — Hard Practice Quiz

A Chemistry cheat sheet for Gases — every key formula with its symbols defined — plus a hard-level practice quiz to test recall.

Formulas & key concepts

<table style="width:100%; border-collapse: collapse; font-size: 0.85em;"> <thead> <tr style="border-bottom: 2px solid #444;"> <th style="padding: 4px; text-align: left;">Formula</th> <th style="padding: 4px; text-align: left;">Name</th> <th style="padding: 4px; text-align: left;">Characteristics</th> </tr> </thead> <tbody> <tr><td style="padding: 2px;">HCN</td><td style="padding: 2px;">Hydrogen cyanide</td><td style="padding: 2px;">Very toxic, slight odor of bitter almonds</td></tr> <tr><td style="padding: 2px;">H₂S</td><td style="padding: 2px;">Hydrogen sulfide</td><td style="padding: 2px;">Very toxic, odor of rotten eggs</td></tr> <tr><td style="padding: 2px;">CO</td><td style="padding: 2px;">Carbon monoxide</td><td style="padding: 2px;">Toxic, colorless, odorless</td></tr> <tr><td style="padding: 2px;">CO₂</td><td style="padding: 2px;">Carbon dioxide</td><td style="padding: 2px;">Colorless, odorless</td></tr> <tr><td style="padding: 2px;">CH₄</td><td style="padding: 2px;">Methane</td><td style="padding: 2px;">Colorless, odorless, flammable</td></tr> <tr><td style="padding: 2px;">C₂H₄</td><td style="padding: 2px;">Ethene (Ethylene)</td><td style="padding: 2px;">Colorless, ripens fruit</td></tr> <tr><td style="padding: 2px;">C₃H₈</td><td style="padding: 2px;">Propane</td><td style="padding: 2px;">Colorless, odorless, bottled gas</td></tr> <tr><td style="padding: 2px;">N₂O</td><td style="padding: 2px;">Nitrous oxide</td><td style="padding: 2px;">Colorless, sweet odor, laughing gas</td></tr> <tr><td style="padding: 2px;">NO₂</td><td style="padding: 2px;">Nitrogen dioxide</td><td style="padding: 2px;">Toxic, red-brown, irritating odor</td></tr> <tr><td style="padding: 2px;">NH₃</td><td style="padding: 2px;">Ammonia</td><td style="padding: 2px;">Colorless, pungent odor</td></tr> <tr><td style="padding: 2px;">SO₂</td><td style="padding: 2px;">Sulfur dioxide</td><td style="padding: 2px;">Colorless, irritating odor</td></tr> </tbody> </table>

$$\text{Table 10.1: Common Gases}$$

<table style="width:100%; border-collapse: collapse; font-size: 0.85em;"> <thead> <tr style="border-bottom: 2px solid #444;"> <th style="padding: 4px; text-align: left;">Units</th> <th style="padding: 4px; text-align: left;">Numerical Value</th> </tr> </thead> <tbody> <tr><td style="padding: 2px;">L-atm/mol-K</td><td style="padding: 2px;">0.08206</td></tr> <tr><td style="padding: 2px;">J/mol-K (SI unit)</td><td style="padding: 2px;">8.314</td></tr> <tr><td style="padding: 2px;">cal/mol-K</td><td style="padding: 2px;">1.987</td></tr> <tr><td style="padding: 2px;">m³-Pa/mol-K (SI unit)</td><td style="padding: 2px;">8.314</td></tr> <tr><td style="padding: 2px;">L-torr/mol-K</td><td style="padding: 2px;">62.36</td></tr> </tbody> </table>

$$\text{Table 10.2: Gas Constant R}$$

<table style="width:100%; border-collapse: collapse; font-size: 0.85em;"> <thead> <tr style="border-bottom: 2px solid #444;"> <th style="padding: 4px; text-align: left;">Substance</th> <th style="padding: 4px; text-align: left;">a (L²-atm/mol²)</th> <th style="padding: 4px; text-align: left;">b (L/mol)</th> </tr> </thead> <tbody> <tr><td style="padding: 2px;">He</td><td style="padding: 2px;">0.0341</td><td style="padding: 2px;">0.02370</td></tr> <tr><td style="padding: 2px;">Ne</td><td style="padding: 2px;">0.211</td><td style="padding: 2px;">0.0171</td></tr> <tr><td style="padding: 2px;">Ar</td><td style="padding: 2px;">1.34</td><td style="padding: 2px;">0.0322</td></tr> <tr><td style="padding: 2px;">Kr</td><td style="padding: 2px;">2.32</td><td style="padding: 2px;">0.0398</td></tr> <tr><td style="padding: 2px;">Xe</td><td style="padding: 2px;">4.19</td><td style="padding: 2px;">0.0510</td></tr> <tr><td style="padding: 2px;">H₂</td><td style="padding: 2px;">0.244</td><td style="padding: 2px;">0.0266</td></tr> <tr><td style="padding: 2px;">N₂</td><td style="padding: 2px;">1.39</td><td style="padding: 2px;">0.0391</td></tr> <tr><td style="padding: 2px;">O₂</td><td style="padding: 2px;">1.36</td><td style="padding: 2px;">0.0318</td></tr> <tr><td style="padding: 2px;">Cl₂</td><td style="padding: 2px;">6.49</td><td style="padding: 2px;">0.0562</td></tr> <tr><td style="padding: 2px;">H₂O</td><td style="padding: 2px;">5.46</td><td style="padding: 2px;">0.0305</td></tr> <tr><td style="padding: 2px;">CH₄</td><td style="padding: 2px;">2.25</td><td style="padding: 2px;">0.0428</td></tr> <tr><td style="padding: 2px;">CO₂</td><td style="padding: 2px;">3.59</td><td style="padding: 2px;">0.0427</td></tr> <tr><td style="padding: 2px;">CCl₄</td><td style="padding: 2px;">20.4</td><td style="padding: 2px;">0.1383</td></tr> </tbody> </table>

$$\text{Table 10.3: Van der Waals Constants}$$

Pressure is the force acting on a given area.

$$P = \frac{F}{A}$$

Where: P = pressure, F = force, A = area

Boyle's Law states that for a fixed quantity of gas at constant temperature, volume is inversely proportional to pressure.

$$PV = \text{constant}$$

Where: P = pressure, V = volume

Charles's Law states that for a fixed quantity of gas at constant pressure, volume is directly proportional to absolute temperature.

$$\frac{V}{T} = \text{constant}$$

Where: V = volume, T = absolute temperature (K)

Avogadro's Law states that the volume of a gas at constant temperature and pressure is directly proportional to the number of moles.

$$V = \text{constant} \times n$$

Where: V = volume, n = number of moles

Ideal-Gas Equation.

$$PV = nRT$$

Where: P = pressure, V = volume, n = moles, R = gas constant, T = temperature (K)

The ideal-gas equation rearranged to show the gas constant R.

$$\frac{PV}{nT} = R$$

Where: R = gas constant

Boyle's Law relates initial and final states at constant n and T.

$$P_1V_1 = P_2V_2$$

Where: 1 = initial state, 2 = final state

Combined Gas Law for a fixed amount of gas (constant n).

$$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$$

Where: 1 = initial state, 2 = final state

Moles per unit volume (concentration) derived from ideal-gas equation.

$$\frac{n}{V} = \frac{P}{RT}$$

Where: n/V = molar concentration

Density of a gas.

$$d = \frac{PM}{RT}$$

Where: d = density, M = molar mass

Calculating molar mass from gas density.

$$M = \frac{dRT}{P}$$

Where: M = molar mass, d = density

Dalton's Law of Partial Pressures.

$$P_{total} = P_1 + P_2 + P_3 + \dots$$

Where: P_{total} = total pressure, P_i = partial pressure of component i

Total pressure related to total moles.

$$P_{total} = (n_1 + n_2 + \dots)\frac{RT}{V} = n_t \frac{RT}{V}$$

Where: n_t = total moles

Partial pressure of a single component in a mixture.

$$P_1 = n_1 \frac{RT}{V}$$

Where: P_1 = partial pressure, n_1 = moles of component 1

Mole fraction of component 1.

$$X_1 = \frac{n_1}{n_t}$$

Where: X_1 = mole fraction

Partial pressure related to mole fraction and total pressure.

$$P_1 = X_1 P_{total}$$

Where: P_1 = partial pressure, X_1 = mole fraction, P_{total} = total pressure

Decomposition of potassium chlorate (example reaction).

$$2\text{KClO}_3(s) \rightarrow 2\text{KCl}(s) + 3\text{O}_2(g)$$

Collecting gas over water. Total pressure includes water vapor pressure.

$$P_{total} = P_{gas} + P_{H_2O}$$

Where: P_{H_2O} = vapor pressure of water

Pressure from kinetic-molecular theory.

$$P \propto \frac{n m (u_{rms})^2}{V}$$

Where: m = mass of molecule, u_{rms} = rms speed

Average kinetic energy of a molecule.

$$\epsilon = \frac{1}{2} m u^2$$

Where: \epsilon = kinetic energy, u = speed

Ideal-gas equation derived from kinetic-molecular theory.

$$PV = nRT$$

Root-mean-square (rms) speed of gas molecules.

$$u_{rms} = \sqrt{\frac{3RT}{M}}$$

Where: M = molar mass (kg/mol for SI units)

Most probable speed of gas molecules.

$$u_{mp} = \sqrt{\frac{2RT}{M}}$$

Where: u_{mp} = most probable speed

Graham's Law of Effusion.

$$\frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}}$$

Where: r = rate of effusion, M = molar mass

Ratio of effusion rates equals ratio of rms speeds.

$$\frac{r_1}{r_2} = \frac{u_{rms1}}{u_{rms2}}$$

Where: r = effusion rate, u_{rms} = rms speed

Compressibility factor for 1 mole of an ideal gas.

$$\frac{PV}{RT} = 1$$

Where: Z = compressibility factor (1 for ideal gas)

Van der Waals equation for real gases.

$$\left(P + \frac{n^2a}{V^2}\right)(V - nb) = nRT$$

Where: a, b = van der Waals constants

Practice quiz

  1. A $0.500 \text{ g}$ sample of an unknown gas is collected over water at $25 \text{ \textdegree C}$ in a $2.00 \text{ L}$ flask. The total pressure in the flask is $603 \text{ torr}$. If the vapor pressure of water at $25 \text{ \textdegree C}$ is $23.8 \text{ torr}$, identify the gas from Table 10.1.

    • Methane ($CH_4$)
    • Carbon dioxide ($CO_2$)
    • Nitrous oxide ($N_2O$)
    • Hydrogen sulfide ($H_2S$)

    Answer: Methane ($CH_4$)

  2. Calculate the pressure exerted by $1.00 \text{ mol}$ of $CO_2$ gas in a $0.500 \text{ L}$ container at $273 \text{ K}$ using both the ideal gas law and the Van der Waals equation. What is the percentage difference between the two calculated pressures? Use $a = 3.59 \text{ L}^2 \cdot \text{atm/mol}^2$ and $b = 0.0427 \text{ L/mol}$ for $CO_2$.

    • $10.5\%$
    • $15.2\%$
    • $22.7\%$
    • $30.1\%$

    Answer: $22.7\%$

  3. At $0 \text{ \textdegree C}$ and $1.00 \text{ atm}$, an unknown gas A has a density of $1.96 \text{ g/L}$. If this gas A effuses through a pinhole at a rate that is $1.50$ times faster than another unknown gas B, what is the molar mass of gas B?

    • $29.3 \text{ g/mol}$
    • $43.9 \text{ g/mol}$
    • $65.9 \text{ g/mol}$
    • $98.8 \text{ g/mol}$

    Answer: $98.8 \text{ g/mol}$

  4. A $10.0 \text{ L}$ container at $298 \text{ K}$ holds a mixture of $5.00 \text{ g}$ of $N_2$ and an unknown mass of $O_2$. The total pressure in the container is $2.50 \text{ atm}$. What is the partial pressure of $O_2$?

    • $0.436 \text{ atm}$
    • $1.25 \text{ atm}$
    • $2.06 \text{ atm}$
    • $2.50 \text{ atm}$

    Answer: $2.06 \text{ atm}$

  5. At what temperature (in Kelvin) would $H_2$ gas have the same root-mean-square (rms) speed as $O_2$ gas at $300 \text{ K}$?

    • $18.9 \text{ K}$
    • $300 \text{ K}$
    • $1500 \text{ K}$
    • $4800 \text{ K}$

    Answer: $18.9 \text{ K}$

  6. Consider a real gas described by the Van der Waals equation. Under which conditions would the term $n^2a/V^2$ (related to intermolecular attractions) be most significant relative to the term $nb$ (related to molecular volume), causing the real gas pressure to be significantly lower than the ideal gas pressure?

    • High temperature and high pressure.
    • Low temperature and low pressure.
    • Low temperature and moderate pressure.
    • High temperature and low pressure.

    Answer: Low temperature and moderate pressure.

  7. A fixed amount of an ideal gas initially occupies a volume $V_1$ at pressure $P_1$ and temperature $T_1$, with a density $d_1$. If the pressure is doubled ($P_2 = 2P_1$) and the absolute temperature is halved ($T_2 = T_1/2$), what is the new density $d_2$ in terms of $d_1$?

    • $d_2 = d_1/4$
    • $d_2 = d_1/2$
    • $d_2 = 2d_1$
    • $d_2 = 4d_1$

    Answer: $d_2 = 4d_1$

  8. A $10.0 \text{ g}$ sample of solid potassium chlorate ($KClO_3$) is completely decomposed in a $5.00 \text{ L}$ container at $200 \text{ \textdegree C}$. The reaction is $2KClO_3(s) \rightarrow 2KCl(s) + 3O_2(g)$. What is the total pressure of oxygen gas produced in the container?

    • $0.475 \text{ atm}$
    • $0.950 \text{ atm}$
    • $1.42 \text{ atm}$
    • $1.90 \text{ atm}$

    Answer: $0.950 \text{ atm}$

  9. It takes $45.0 \text{ s}$ for $1.00 \text{ mol}$ of $CH_4$ gas to effuse through a porous barrier. How long would it take for $1.00 \text{ mol}$ of $SO_2$ gas to effuse through the same barrier under identical conditions?

    • $22.5 \text{ s}$
    • $45.0 \text{ s}$
    • $89.9 \text{ s}$
    • $180 \text{ s}$

    Answer: $89.9 \text{ s}$

  10. For a fixed amount of an ideal gas in a rigid container, if the absolute temperature is doubled, what happens to the average kinetic energy of the molecules, the root-mean-square (rms) speed, and the pressure exerted by the gas?

    • Average kinetic energy doubles, rms speed increases by a factor of $\sqrt{2}$, pressure doubles.
    • Average kinetic energy doubles, rms speed doubles, pressure doubles.
    • Average kinetic energy increases by a factor of $\sqrt{2}$, rms speed doubles, pressure increases by a factor of $\sqrt{2}$.
    • Average kinetic energy doubles, rms speed increases by a factor of $\sqrt{2}$, pressure increases by a factor of $\sqrt{2}$.

    Answer: Average kinetic energy doubles, rms speed increases by a factor of $\sqrt{2}$, pressure doubles.

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