Compressibility Factor

The Gas Compressibility Factor calculator computes the compressibility factor (Z), also known as the compression factor. This is the ratio of the molar volume of a gas to the molar volume of an ideal gas at the same temperature and pressure.

INSTRUCTIONS: Choose units and enter the following:

• (p)  Pressure of the gas
• (V_m) Molar Volume of Gas
• (T)  Temperature of Gas

Compression Factor (Z): The calculator returns the compressibility factor (Z) as a real number.

The Math / Science

The formula for compressibility factor is: 

             `Z = (P*V_m)/(R*T)`
where:

• Z = Gas Compressibility Factor
• p = Pressure of the gas
• V_m = Volume of one mole of the gas
• T = Temperature of the gas
• R = Ideal Gas Constant.

The compressibility factor is a useful thermodynamic property for modifying the ideal gas law to account for the real gas behavior.^[1] In general, deviation from ideal behavior becomes more significant the closer a gas is to a phase change, the lower the temperature or the larger the pressure. Compressibility factor values are usually obtained by calculation from equations of state (EOS), such as the virial equation which take compound specific empirical constants as input. For a gas that is a mixture of two or more pure gases (air or natural gas, for example), the gas composition must be known before compressibility can be calculated.
 Alternatively, the compressibility factor for specific gases can be read from generalized compressibility charts^[1] that plot  as a function of pressure at constant temperature.

Chemistry Calculators

• R - Gas Constant: 8.3144626181532 J/(K⋅mol)
• Boyle's Law Calculator:  P₁ • V₁ = P₂ • V₂
• Charles Law Calculator: V₁• T₂ = V₂ • T₁
• Combined Gas Law Calculator:   P•V / T= k
• Gay-Lussac Law:  T₁•P₂ =T₂•P₁ 
• Ideal Gas Law: P•V = n•R•T
• Bragg's Law:   n·λ = 2d·sinθ
• Hess' Law:  ΔH⁰_rxn=ΔH⁰_a+ΔH⁰_b+ΔH⁰_c+ΔH⁰_d
• Internal Energy: ΔU = q + ω 
• Activation Energy:  E_a = (R*T₁⋅T₂)/(T₁ - T₂) ⋅  ln(k₁/k₂)
• Arrhenius Equation:  k = Ae^E_a/(RT)
• Clausius-Clapeyron Equation:  ln(P₂/P₁) = (ΔH_vap)/R * (1/T₁ - 1/T₂)
• Compressibility Factor: Z = (p*V_m)/(R*T)
• Peng-Robinson Equation of State:  p = (R*T)/(V_m - b) - (a*α)/(V_m² + 2*b*V_m - b²)
• Reduced Specific Volume:  v_r = v/(R* T_cr / P_c)
• Van't Hoff Equation:  ΔH⁰ = R * ( -ln(K₂/K₁))/ (1/T₁ - 1/T₂)

REFERENCE

[1] Compressibility factor Source: Wikipedia URL: https://en.wikipedia.org/wiki/Compressibility_factor
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