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#pressure effect

5 public questions tagged with this topic.

Molecular Mass Density and Ideal Gas Equation

The mean free path of a gas molecule is 3.0 × 10⁻⁶ m at 0.25 atm. What will it be at 1 atm if temperature remains consta

**Ideal gas equation** P V = n R T = (m/M) R T, density ρ = m/V = P M/(R T), molecular mass M (kg/mol), P pressure (Pa), T temperature (K). At given P,T density proportional to M, heavier gases denser, e.g., at 1.5 atm 300 K V=24 L n= P V/(R T)=1.5×1.013×10⁵×0.024/(8.314×300)≈1.46 mol. l ∝ (1)/(n), n ∝ P. If P increases by 4 times (0.25 to 1), n increases 4 times, l reduces to (1)/(4).New l = 3.0 × 10⁻⁶/4 = 7.5 × 10⁻⁷ m. Substituting values gives 7.5 × 10⁻⁷ m, which matches expected kinetic theory result, confirming mean free path λ

Ref: NCERT > Physics Book > Behaviour of Perfect Gas and Kinetic Theory > Molecular Mass Density and Ideal Gas Equation

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Internal Energy of Ideal Gases

The mean free path of a gas molecule is 1.5 × 10⁻⁶ m at 0.2 atm. What will it be at 0.8 atm if temperature remains const

**Internal energy of ideal gas** U = f/2 n R T depends only on temperature, f degrees of freedom, n moles, R=8.314 J/mol·K, for monatomic f=3 U=3/2 n R T, diatomic f=5 at moderate T U=5/2 n R T, independent of pressure or volume, only T matters for ideal gas. l ∝ (1)/(n), n ∝ P. If P increases by 4 times (0.2 to 0.8), n increases 4 times, l reduces to (1)/(4).New l = 1.5 × 10⁻⁶/4 = 3.75 × 10⁻⁷ m. Substituting values gives 3.75 × 10⁻⁷ m, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2 n π

Ref: NCERT > Physics Book > Behaviour of Perfect Gas and Kinetic Theory > Internal Energy of Ideal Gases

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Mean Free Path and Molecular Diameter

The mean free path of a gas molecule is 4 × 10⁻⁷ m at 2 atm. What will it be at 4 atm if temperature remains constant?

**Kinetic theory mean free path** λ = 1/(√2 π d² n) quantifies collision frequency. With n =1.0×10²⁵ m⁻³, λ=9×10⁻⁷ m, d² =1/(1.414×10²⁵×3.14×9×10⁻⁷)=2.5×10⁻²⁰ m², d≈1.58×10⁻¹⁰ m, typical molecular size ~10⁻¹⁰ m, consistent with gas kinetic theory. l ∝ (1)/(n), n ∝ P. If P doubles, n doubles, l halves.New l = 4 × 10⁻⁷/2 = 2 × 10⁻⁷ m. Substituting values gives 2 × 10⁻⁷ m, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2 n π d²), ideal gas law P V = n R T and v_rms = √(3 R T/M) relations.

Ref: NCERT > Physics Book > Behaviour of Perfect Gas and Kinetic Theory > Mean Free Path and Molecular Diameter

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Relationship Between Kp Kc and Factors Affecting Equilibrium - Le Chatelier

In the equilibrium N₂(g) + 3H₂(g) 2NH₃(g) , increasing the pressure shifts the equilibrium towards which direction?

According to Le Chatelier’s principle, increasing pressure favors the side with fewer moles of gas. Here, 4 moles (reactants) become 2 moles (products), so it shifts right.

Ref: NCERT Class 11 Chemistry > Chapter 6: Equilibrium > Topic: Relationship Between Kp Kc and Factors Affecting Equilibrium - Le Chatelier

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