Molar Volume of Gases — Revision Notes

⚡ 30-Second Revision

Molar Volume ($V_m$) — Volume of 1 mole of gas.
Old STP — $0^circ\text{C}$ ($273.15,\text{K}$), $1,\text{atm}$. $V_m = 22.4,\text{L/mol}$.
IUPAC STP — $0^circ\text{C}$ ($273.15,\text{K}$), $1,\text{bar}$. $V_m = 22.7,\text{L/mol}$.
NTP — $20^circ\text{C}$ ($293.15,\text{K}$), $1,\text{atm}$. $V_m approx 24.04,\text{L/mol}$.
Ideal Gas Law — $PV = nRT$.
Molar Volume from Ideal Gas Law — $V_m = \frac{RT}{P}$ (for $n=1$).
Gas Density — $ho = \frac{\text{Molar Mass}}{V_m} = \frac{PM}{RT}$.
Avogadro's Law — $V propto n$ (at constant $P, T$). Volume ratios = mole ratios for gases in reactions.

2-Minute Revision

Molar volume is the volume occupied by one mole of any gas. For ideal gases, this volume is constant under specific conditions of temperature and pressure, regardless of the gas's identity. The most crucial values to remember are for Standard Temperature and Pressure (STP).

Historically, old STP is $0^circ\text{C}$ and $1,\text{atm}$, where the molar volume is $22.4,\text{L/mol}$. The IUPAC standard STP is $0^circ\text{C}$ and $1,\text{bar}$, yielding $22.7,\text{L/mol}$. Always check which STP definition is implied in NEET problems, but $22.

4, ext{L}$ is most common.

When conditions are not standard, you must use the Ideal Gas Law, $PV=nRT$. To find molar volume ($V_m$) at any condition, simply set $n=1$ in the ideal gas equation, giving $V_m = RT/P$. Remember to convert temperature to Kelvin.

This concept is vital for stoichiometry involving gases, allowing direct conversion between volume and moles. Gas density can also be calculated using molar volume: $ho = \text{Molar Mass} / V_m$. Real gases deviate from ideal behavior, especially at high pressure and low temperature, so their actual molar volume may differ slightly from the ideal value.

5-Minute Revision

The molar volume of a gas is a fundamental concept in chemistry, representing the volume occupied by one mole ($6.022 \times 10^{23}$ molecules) of that gas. Its significance for ideal gases lies in its universality: one mole of *any* ideal gas occupies the same volume under identical conditions of temperature and pressure. This principle is a direct consequence of Avogadro's Law and the Ideal Gas Equation, $PV=nRT$.

For NEET, two sets of standard conditions are critical:

1
Old STP — $0^circ\text{C}$ ($273.15,\text{K}$) and $1,\text{atm}$ ($101.325,\text{kPa}$). At these conditions, the molar volume of an ideal gas is $22.4,\text{L/mol}$.
2
IUPAC STP — $0^circ\text{C}$ ($273.15,\text{K}$) and $1,\text{bar}$ ($100,\text{kPa}$). Here, the molar volume is $22.7,\text{L/mol}$.

If the conditions are not standard, you must use the Ideal Gas Law. To find the molar volume ($V_m$) for one mole of gas, rearrange $PV=nRT$ to $V_m = RT/P$. Always ensure temperature is in Kelvin ($T(\text{K}) = T(^circ\text{C}) + 273.15$) and units for $P$, $V$, and $R$ are consistent. For example, if $R = 0.0821,\text{L} cdot \text{atm} cdot \text{mol}^{-1} cdot \text{K}^{-1}$, then $P$ must be in atm and $V$ in L.

Example: Calculate the volume of $0.25,\text{mol}$ of $ext{CH}_4$ at $27^circ\text{C}$ and $1.5,\text{atm}$.

$T = 27^circ\text{C} + 273.15 = 300.15,\text{K}$
$P = 1.5,\text{atm}$
$n = 0.25,\text{mol}$
$R = 0.0821,\text{L} cdot \text{atm} cdot \text{mol}^{-1} cdot \text{K}^{-1}$
$V = \frac{nRT}{P} = \frac{0.25,\text{mol} \times 0.0821,\text{L} cdot \text{atm} cdot \text{mol}^{-1} cdot \text{K}^{-1} \times 300.15,\text{K}}{1.5,\text{atm}} approx 4.10,\text{L}$.

Molar volume is crucial for gas stoichiometry: for reactions involving gases at constant T and P, volume ratios are directly proportional to mole ratios. Also, gas density ($ho$) is related to molar mass ($M$) and molar volume by $ho = M/V_m$, which can be expanded to $ho = PM/RT$. Remember that these concepts apply primarily to ideal gases; real gases show deviations, especially at high pressures and low temperatures, due to intermolecular forces and finite molecular volume.

Prelims Revision Notes

Molar Volume of Gases: NEET Quick Recall

1. Definition: Volume occupied by one mole ($6.022 \times 10^{23}$ molecules) of any gas.

2. Key Principle (Avogadro's Law): Equal volumes of all gases, at the same temperature and pressure, contain the same number of moles/molecules. Conversely, one mole of any ideal gas occupies the same volume under identical T & P.

3. Standard Conditions & Molar Volume Values (for Ideal Gases):

* Old STP (Standard Temperature and Pressure): * Temperature ($T$) = $0^circ\text{C} = 273.15,\text{K}$ * Pressure ($P$) = $1,\text{atm} = 101.325,\text{kPa}$ * **Molar Volume ($V_m$) = $22.4,\text{L/mol}$** (Most common in NEET) * IUPAC STP: * Temperature ($T$) = $0^circ ext{C} = 273.

15, ext{K}$* Pressure ($P$) =$1, ext{bar} = 100, ext{kPa}$* **Molar Volume ($V_m$) =$22.7, ext{L/mol}$** * **NTP (Normal Temperature and Pressure):** * Temperature ($T$) =$20^circ ext{C} = 293.

15, ext{K}$* Pressure ($P$) =$1, ext{atm}$* **Molar Volume ($V_m$)$approx 24.

4. Ideal Gas Equation: $PV = nRT$ * $P$: Pressure (atm, Pa, bar) * $V$: Volume (L, $ext{m}^3$) * $n$: Moles * $R$: Ideal Gas Constant ($0.0821,\text{L} cdot \text{atm} cdot \text{mol}^{-1} cdot \text{K}^{-1}$ or $8.314,\text{J} cdot \text{mol}^{-1} cdot \text{K}^{-1}$) * $T$: Absolute Temperature (Kelvin, $T(\text{K}) = T(^circ\text{C}) + 273.15$)

5. Calculating Molar Volume at Non-Standard Conditions:

* Set $n=1$ in the Ideal Gas Equation: $V_m = \frac{RT}{P}$. * Crucial: Always convert $T$ to Kelvin. Ensure units of $P$ and $R$ are compatible.

6. Relationship with Gas Density ($ ho$):

* $ho = \frac{\text{Mass}}{\text{Volume}} = \frac{\text{Molar Mass} (M)}{\text{Molar Volume} (V_m)}$ * Substituting $V_m = \frac{RT}{P}$: $ho = \frac{PM}{RT}$

7. Stoichiometry of Gaseous Reactions:

* At constant $T$ and $P$, volume ratios of gaseous reactants and products are equal to their mole ratios (from balanced equation). * Example: $2\text{H}_2(g) + \text{O}_2(g) \rightarrow 2\text{H}_2\text{O}(g)$. $2,\text{L}$ of $ext{H}_2$ reacts with $1,\text{L}$ of $ext{O}_2$ to give $2,\text{L}$ of $ext{H}_2\text{O}$ vapor.

8. Common Misconceptions/Traps:

* **$22.4,\text{L}$ is NOT universal:** It's specific to ideal gases at old STP. Molar volume changes with T and P. * Not for Liquids/Solids: The $22.4,\text{L}$ rule does not apply to liquids or solids. Their molar volumes are substance-specific. * Real vs. Ideal Gases: Real gases deviate from ideal behavior (and thus from ideal molar volume) at high pressures and low temperatures due to intermolecular forces and finite molecular volume.

Vyyuha Quick Recall

To remember the molar volume at old STP: 'Twenty-Two Point Four' is the 'Volume' for 'One Mole' of 'Gas' at 'Standard' conditions. (22.4 L/mol at STP)