PV nRT Formula and Applications in Gas

❓ Concept Question

What is the Ideal Gas Equation and how is it used in gas law problems?

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🖼 Concept Image

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✍️ Short Concept

This concept is based on:

👉 Ideal gas equation
👉 Mole concept in gases
👉 Unit conversions.

Main idea:

$$\boxed{ PV=nRT }$$

This equation connects:

✔ Pressure
✔ Volume
✔ Temperature
✔ Number of moles

for an ideal gas.

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🔷 Step 1 — Ideal Gas Equation 💯

The ideal gas equation is:

$$\boxed{ PV=nRT }$$

Where:

• $P$ = pressure
• $V$ = volume
• $n$ = number of moles
• $R$ = universal gas constant
• $T$ = temperature in Kelvin

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🔷 Step 2 — Value of Gas Constant

Common values of:

$$R$$

are:

$$R=0.0821\ \text{L-atm/mol-K}$$

and

$$R=8.314\ \text{J/mol-K}$$

Use:

$$8.314$$

when:

✔ Pressure in Pa

✔ Volume in m$^3$

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🔷 Step 3 — Important Unit Conversions

Very important for JEE:

$$1\text{ atm}=1.013\times10^5\text{ Pa}$$
$$1\text{ L}=10^{-3}\text{ m}^3$$

Always convert units properly before calculation.

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🔷 Step 4 — Rearranged Forms

From:

$$PV=nRT$$

we get:

Number of moles

$$\boxed{ n=\frac{PV}{RT} }$$

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Temperature

$$\boxed{ T=\frac{PV}{nR} }$$

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Pressure

$$\boxed{ P=\frac{nRT}{V} }$$

These forms are frequently used in numericals.

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🔷 Step 5 — Relation with Density

Combining:

$$PV=nRT$$

with:

$$n=\frac mM$$

gives:

$$\boxed{ PM=dRT }$$

or

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

Useful in molecular mass questions.

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🔷 Step 6 — JEE Trap Alert 🚨

❌ Celsius directly use kar lena instead of Kelvin

❌ Unit conversion bhool jaana

❌ Wrong value of $R$ use kar dena

Remember:

$$\boxed{ T(\text{Kelvin})=^\circ C+273 }$$

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✅ Final Takeaway

Ideal gas equation:

$$\boxed{ PV=nRT }$$

is the most important equation in gaseous state problems.

It connects:

✔ Pressure
✔ Volume
✔ Temperature
✔ Moles

in one relation.

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⭐ Golden JEE Insight

In most gas law questions:

✔ First convert units

✔ Choose correct value of $R$

✔ Convert temperature into Kelvin

before applying formula.

This avoids most calculation mistakes in JEE.

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📚 Related Topics

• Molar Conductance of Double Salt
• Ionisation Isomerism Using Precipitation Tests
• Coefficient of Friction on Inclined Plane