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Ideal Gas Law Calculator Description

Understanding the Ideal Gas Law

The Ideal Gas Law combines several individual gas laws into one equation:

PV = nRT

• P = Pressure (atm, Pa)
• V = Volume (L, m³)
• n = Moles of gas
• R = Gas constant (0.0821 L·atm/mol·K or 8.314 J/mol·K)
• T = Temperature (Kelvin)

How It Works

This law assumes ideal behavior—molecules do not attract or repel and occupy no space. It is accurate under:

• Low pressure conditions
• High temperature ranges
• Monoatomic and light gases (e.g., He, H₂)

Formula Derivation

From kinetic theory:
PV = NkT
Since N = n × Avogadro's number,
⇒ PV = nRT

This connects microscopic particle motion to macroscopic properties.

Edge Cases & Corrections

• Extremely Low Temperatures: Volume shrinks dramatically; gases may liquefy.
• High Pressures: Deviations occur; use Van der Waals correction.
• Incorrect Units: Always match units to the R value selected.
• Gas Mixtures: Apply Dalton’s Law; total pressure equals the sum of partial pressures.
• Changing Conditions: Use the Combined Gas Law:

  (P₁ × V₁)/T₁ = (P₂ × V₂)/T₂

Real-World Case Studies

1. Inflating a Balloon

• Given: n = 0.5 mol, T = 298 K, P = 1 atm
• Find: Volume

V = (nRT)/P = (0.5 × 0.0821 × 298)/1 ≈ 12.24 L

2. Tire Pressure Rise

• Given: V = 25 L, n = 2.1 mol, T = 320 K
• Find: Pressure

P = (nRT)/V = (2.1 × 0.0821 × 320)/25 ≈ 2.21 atm

For more details, visit: Wikipedia: Ideal Gas Law or EPA: Gas Calculations.

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