According to the van der Waals equation, the constant '$a$' accounts for which of the following?

Attractive forces between gas molecules

Volume occupied by gas molecules

Kinetic energy of gas molecules

If the pressure of a fixed amount of gas is doubled at constant temperature, what happens to its volume?

The volume increases by a factor of four.

Gases — Practice Quiz

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

Formulas & key concepts

Formula	Name	Characteristics
HCN	Hydrogen cyanide	Very toxic, slight odor of bitter almonds
H₂S	Hydrogen sulfide	Very toxic, odor of rotten eggs
CO	Carbon monoxide	Toxic, colorless, odorless
CO₂	Carbon dioxide	Colorless, odorless
CH₄	Methane	Colorless, odorless, flammable
C₂H₄	Ethene (Ethylene)	Colorless, ripens fruit
C₃H₈	Propane	Colorless, odorless, bottled gas
N₂O	Nitrous oxide	Colorless, sweet odor, laughing gas
NO₂	Nitrogen dioxide	Toxic, red-brown, irritating odor
NH₃	Ammonia	Colorless, pungent odor
SO₂	Sulfur dioxide	Colorless, irritating odor

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

Units	Numerical Value
L-atm/mol-K	0.08206
J/mol-K (SI unit)	8.314
cal/mol-K	1.987
m³-Pa/mol-K (SI unit)	8.314
L-torr/mol-K	62.36

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

Substance	a (L²-atm/mol²)	b (L/mol)
He	0.0341	0.02370
Ne	0.211	0.0171
Ar	1.34	0.0322
Kr	2.32	0.0398
Xe	4.19	0.0510
H₂	0.244	0.0266
N₂	1.39	0.0391
O₂	1.36	0.0318
Cl₂	6.49	0.0562
H₂O	5.46	0.0305
CH₄	2.25	0.0428
CO₂	3.59	0.0427
CCl₄	20.4	0.1383

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

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

A sample of gas occupies $10.0 \text{ L}$ at $1.00 \text{ atm}$ and $273 \text{ K}$. How many moles of gas are present? (Use $R = 0.08206 \text{ L} \cdot \text{atm} / (\text{mol} \cdot \text{K})$)
- $0.446 \text{ mol}$
- $0.223 \text{ mol}$
- $0.892 \text{ mol}$
- $1.00 \text{ mol}$
Answer: $0.446 \text{ mol}$
A gas mixture contains $2.0 \text{ mol}$ of $N_2$ and $3.0 \text{ mol}$ of $O_2$. If the total pressure is $5.0 \text{ atm}$, what is the partial pressure of $N_2$?
- $2.0 \text{ atm}$
- $3.0 \text{ atm}$
- $2.5 \text{ atm}$
- $5.0 \text{ atm}$
Answer: $2.0 \text{ atm}$
Which gas would effuse faster, $CH_4$ or $SO_2$? And by what approximate factor?
- $CH_4$ by a factor of $2$
- $SO_2$ by a factor of $2$
- $CH_4$ by a factor of $4$
- $SO_2$ by a factor of $4$
Answer: $CH_4$ by a factor of $2$
Calculate the density of $CO_2$ gas at $1.00 \text{ atm}$ and $298 \text{ K}$. (Molar mass of $CO_2 = 44.01 \text{ g/mol}$, $R = 0.08206 \text{ L} \cdot \text{atm} / (\text{mol} \cdot \text{K})$)
- $1.80 \text{ g/L}$
- $0.90 \text{ g/L}$
- $2.20 \text{ g/L}$
- $44.01 \text{ g/L}$
Answer: $1.80 \text{ g/L}$
A gas sample has a volume of $5.0 \text{ L}$ at $2.0 \text{ atm}$ and $27^\circ C$. If the pressure is increased to $4.0 \text{ atm}$ and the temperature to $127^\circ C$, what is the new volume?
- $3.33 \text{ L}$
- $2.50 \text{ L}$
- $6.67 \text{ L}$
- $5.00 \text{ L}$
Answer: $3.33 \text{ L}$
According to the van der Waals equation, the constant '$a$' accounts for which of the following?
- Attractive forces between gas molecules
- Volume occupied by gas molecules
- Kinetic energy of gas molecules
- Temperature of the gas
Answer: Attractive forces between gas molecules
Which of the following gases has the highest root-mean-square (rms) speed at a given temperature?
- $H_2$
- $N_2$
- $O_2$
- $CO_2$
Answer: $H_2$
Based on Table 10.1, which gas is described as "very toxic" and having an "odor of rotten eggs"?
- Hydrogen cyanide ($HCN$)
- Hydrogen sulfide ($H_2S$)
- Carbon monoxide ($CO$)
- Sulfur dioxide ($SO_2$)
Answer: Hydrogen sulfide ($H_2S$)
According to Table 10.2, what is the numerical value of the gas constant $R$ when using SI units for pressure (Pascals) and volume (cubic meters)?
- $0.08206$
- $8.314$
- $1.987$
- $62.36$
Answer: $8.314$
If the pressure of a fixed amount of gas is doubled at constant temperature, what happens to its volume?
- The volume is halved.
- The volume is doubled.
- The volume remains unchanged.
- The volume increases by a factor of four.
Answer: The volume is halved.

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Gases — Practice Quiz

Formulas & key concepts

Pressure is the force acting on a given area.

Ideal-Gas Equation.

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

Density of a gas.

Calculating molar mass from gas density.

Dalton's Law of Partial Pressures.

Total pressure related to total moles.

Partial pressure of a single component in a mixture.

Mole fraction of component 1.

Decomposition of potassium chlorate (example reaction).

Pressure from kinetic-molecular theory.

Average kinetic energy of a molecule.

Ideal-gas equation derived from kinetic-molecular theory.

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

Most probable speed of gas molecules.

Graham's Law of Effusion.

Ratio of effusion rates equals ratio of rms speeds.

Compressibility factor for 1 mole of an ideal gas.

Van der Waals equation for real gases.

Practice quiz

Select a subject

Subjects

Print

Gases — Practice Quiz

Formulas & key concepts

Pressure is the force acting on a given area.

Ideal-Gas Equation.

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

Density of a gas.

Calculating molar mass from gas density.

Dalton's Law of Partial Pressures.

Total pressure related to total moles.

Partial pressure of a single component in a mixture.

Mole fraction of component 1.

Decomposition of potassium chlorate (example reaction).

Pressure from kinetic-molecular theory.

Average kinetic energy of a molecule.

Ideal-gas equation derived from kinetic-molecular theory.

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

Most probable speed of gas molecules.

Graham's Law of Effusion.

Ratio of effusion rates equals ratio of rms speeds.

Compressibility factor for 1 mole of an ideal gas.

Van der Waals equation for real gases.

Practice quiz

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