What is van der waals equation

💨 Van der Waals Equation: A Realistic View of Gases

In physical chemistry, the ideal gas law works well for many gases under standard conditions. However, it begins to break down under high pressures or low temperatures, where real gases exhibit behaviors that deviate from ideality. To account for these deviations, Johannes Diderik van der Waals proposed a modified version of the ideal gas law, now known as the Van der Waals equation.

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⚙️ The Equation

(P+aVm2)(Vm−b)=RT\left( P + \frac{a}{V_m^2} \right)(V_m – b) = RT(P+Vm2​a​)(Vm​−b)=RT

Where:

• PPP: pressure of the gas
• VmV_mVm​: molar volume of the gas
• TTT: temperature in Kelvin
• RRR: gas constant
• aaa: Van der Waals constant for intermolecular attraction
• bbb: Van der Waals constant for finite molecular volume

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🧠 Understanding the Corrections

1. Pressure Correction aVm2\frac{a}{V_m^2}Vm2​a​:
   Real gas particles attract each other, slightly reducing the pressure they exert on the container walls. The term aVm2\frac{a}{V_m^2}Vm2​a​ accounts for this attractive force. The constant aaa reflects the strength of intermolecular attractions—larger for polar or easily condensable gases.
2. Volume Correction −b-b−b:
   Unlike ideal gas particles (assumed to have no volume), real molecules occupy space. The constant bbb corrects for the excluded volume due to finite particle size. It increases with molecular size.

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📊 Real-World Applications

• The Van der Waals equation gives a better approximation of gas behavior near liquefaction points.
• It explains why gases like CO₂ or NH₃ deviate from ideal behavior more significantly than He or Ne.
• Engineers use it in designing compressors, refrigeration systems, and in chemical process simulations.

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⚖️ Ideal vs. Real Gases

The ideal gas law assumes:

• No intermolecular forces
• No molecular volume

These assumptions fail under:

• High pressure (volume becomes very small → finite particle size matters)
• Low temperature (particles move slower → intermolecular attraction becomes significant)

The Van der Waals equation bridges this gap by acknowledging that gases are made of real particles with real interactions.

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🔬 Critical Constants

By manipulating the Van der Waals equation, you can derive expressions for the critical temperature (Tc), pressure (Pc), and volume (Vc)—important in phase transition studies. Tc=8a27Rb,Pc=a27b2,Vc=3bT_c = \frac{8a}{27Rb}, \quad P_c = \frac{a}{27b^2}, \quad V_c = 3bTc​=27Rb8a​,Pc​=27b2a​,Vc​=3b

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🧪 Quiz: Van der Waals Equation

1. What does the term aVm2\frac{a}{V_m^2}Vm2​a​ in the Van der Waals equation correct for?
   A. Temperature effects
   B. Molecular volume
   C. Intermolecular attractions
   D. External pressure
   Answer: C
2. Which of the following gases would likely have the highest Van der Waals ‘a’ constant?
   A. Helium (He)
   B. Argon (Ar)
   C. Water vapor (H₂O)
   D. Neon (Ne)
   Answer: C
3. Why is the volume term Vm−bV_m – bVm​−b used instead of VmV_mVm​?
   A. To include intermolecular repulsions
   B. To correct for high temperatures
   C. Because molecules have finite size
   D. To adjust for phase changes
   Answer: C
4. What happens to a real gas at very low pressures?
   A. It liquefies
   B. It behaves more ideally
   C. It breaks down into atoms
   D. Its volume increases to infinity
   Answer: B
5. In the Van der Waals equation, which constant is more related to molecular size?
   A. aaa
   B. bbb
   C. RRR
   D. TTT
   Answer: B