Gas Laws — Revision Notes

⚡ 30-Second Revision

Boyle's Law — $P_1V_1 = P_2V_2$ (Constant T, n)
Charles's Law — $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ (Constant P, n; T in Kelvin)
Gay-Lussac's Law — $\frac{P_1}{T_1} = \frac{P_2}{T_2}$ (Constant V, n; T in Kelvin)
Avogadro's Law — $\frac{V_1}{n_1} = \frac{V_2}{n_2}$ (Constant P, T)
Combined Gas Law — $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$ (Constant n; T in Kelvin)
Ideal Gas Equation — $PV = nRT$ (T in Kelvin)
Dalton's Law — $P_{total} = P_A + P_B + ...$
Graham's Law — $\frac{\text{Rate}_1}{\text{Rate}_2} = \sqrt{\frac{M_2}{M_1}}$
STP — $0^circ C$ (273.15 K), $1,\text{atm}$. Molar volume = 22.4 L.
R values — $0.0821,\text{L atm mol}^{-1}\text{K}^{-1}$, $8.314,\text{J mol}^{-1}\text{K}^{-1}$, $8.314,\text{kPa L mol}^{-1}\text{K}^{-1}$.
Key conversion — $T(\text{K}) = T(^circ C) + 273.15$.

2-Minute Revision

Gas laws describe how pressure (P), volume (V), temperature (T), and moles (n) of a gas are related. Boyle's Law ($PV=k$) shows P and V are inversely related at constant T and n. Charles's Law ($V/T=k$) states V is directly proportional to absolute T at constant P and n.

Gay-Lussac's Law ($P/T=k$) states P is directly proportional to absolute T at constant V and n. Always convert Celsius to Kelvin for T. Avogadro's Law ($V/n=k$) links V and n directly at constant P and T.

These combine into the Ideal Gas Equation, $PV=nRT$, where R is the universal gas constant. Remember its different values based on units. Dalton's Law of Partial Pressures ($P_{total} = sum P_i$) says total pressure in a mixture is the sum of individual partial pressures; crucial for gases collected over water.

Graham's Law of Diffusion/Effusion ($ext{Rate} propto 1/sqrt{M}$) explains that lighter gases move faster. Real gases deviate from ideal behavior at high pressure and low temperature due to molecular volume and intermolecular forces.

5-Minute Revision

Mastering gas laws for NEET involves understanding the individual laws, their combined forms, and their applications. Start with Boyle's Law ($P_1V_1 = P_2V_2$), which describes the inverse relationship between pressure and volume at constant temperature and moles.

Visualize this with a syringe. Next, Charles's Law ($rac{V_1}{T_1} = \frac{V_2}{T_2}$) and Gay-Lussac's Law ($rac{P_1}{T_1} = \frac{P_2}{T_2}$) highlight the direct proportionality of volume/pressure with absolute temperature (always Kelvin!

). Remember, $0^circ C$ is $273.15,\text{K}$. Avogadro's Law ($rac{V_1}{n_1} = \frac{V_2}{n_2}$) connects volume to the number of moles. These laws culminate in the Ideal Gas Equation, $PV=nRT$, a powerful tool.

Be fluent with the different values of R ($0.0821,\text{L atm mol}^{-1}\text{K}^{-1}$, $8.314,\text{J mol}^{-1}\text{K}^{-1}$) and ensure unit consistency. Dalton's Law of Partial Pressures ($P_{total} = P_A + P_B + ...

$) is vital for gas mixtures, especially when gases are collected over water (remember to subtract water vapor pressure). Finally, Graham's Law of Diffusion/Effusion ($rac{ ext{Rate}_1}{ ext{Rate}_2} = sqrt{rac{M_2}{M_1}}$) explains why lighter gases effuse/diffuse faster.

Practice numerical problems extensively, paying close attention to unit conversions and identifying the correct law for each scenario. Conceptual questions often revolve around ideal vs. real gas behavior (real gases deviate at high P, low T) and graphical interpretations.

Prelims Revision Notes

1
Boyle's Law — $P propto 1/V$ (constant T, n). $P_1V_1 = P_2V_2$. Graph P vs V is hyperbola; P vs 1/V is straight line through origin.
2
Charles's Law — $V propto T$ (constant P, n). $\frac{V_1}{T_1} = \frac{V_2}{T_2}$. T must be in Kelvin ($T(K) = T(^circ C) + 273.15$). Graph V vs T is straight line through origin.
3
Gay-Lussac's Law — $P propto T$ (constant V, n). $\frac{P_1}{T_1} = \frac{P_2}{T_2}$. T must be in Kelvin. Graph P vs T is straight line through origin.
4
Avogadro's Law — $V propto n$ (constant P, T). $\frac{V_1}{n_1} = \frac{V_2}{n_2}$. At STP ($0^circ C$, 1 atm), 1 mole of any ideal gas occupies 22.4 L.
5
Combined Gas Law — $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$ (constant n). Use when P, V, T all change.
6
Ideal Gas Equation — $PV = nRT$. R is Universal Gas Constant.

* $R = 0.0821,\text{L atm mol}^{-1}\text{K}^{-1}$ (P in atm, V in L) * $R = 8.314,\text{J mol}^{-1}\text{K}^{-1}$ (P in Pa, V in $m^3$) * $R = 8.314,\text{kPa L mol}^{-1}\text{K}^{-1}$ (P in kPa, V in L)

1
Density and Molar Mass from Ideal Gas Eq — $PV = \frac{m}{M}RT \implies PM = \frac{m}{V}RT \implies PM = dRT \implies M = \frac{dRT}{P}$.
2
Dalton's Law of Partial Pressures — $P_{total} = P_A + P_B + ...$. Partial pressure $P_A = X_A P_{total}$ (where $X_A$ is mole fraction).

* For gas collected over water: $P_{dry gas} = P_{total} - P_{water vapor}$ (aqueous tension).

1
Graham's Law of Diffusion/Effusion — Rate $propto \frac{1}{\sqrt{M}}$. $\frac{\text{Rate}_1}{\text{Rate}_2} = \sqrt{\frac{M_2}{M_1}} = \sqrt{\frac{d_2}{d_1}}$. Lighter gases diffuse/effuse faster.
2
Ideal vs. Real Gases — Real gases deviate from ideal behavior at high pressure and low temperature. Reasons: finite molecular volume, intermolecular forces.
3
Units — Always check and convert units to be consistent with R. $1,\text{atm} = 760,\text{mmHg} = 760,\text{torr} = 1.01325 \times 10^5,\text{Pa} = 101.325,\text{kPa}$.

Vyyuha Quick Recall

For the main gas laws (Boyle, Charles, Gay-Lussac, Avogadro) and their variables: "Boys Can Get All Volumes Perfectly Together Now."

Boyle: Volume, Pressure (T, n constant)
Charles: Volume, Temperature (P, n constant)
Gay-Lussac: Pressure, Temperature (V, n constant)
Avogadro: Volume, Number of moles (P, T constant)

For Ideal Gas Law: "Perfect Volume Never Reaches Temperature" ($PV=nRT$)