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Zorluk: OrtaDeviations of Real Gases from Ideal Gas Behavior

At a specific temperature and pressure, 2.0 moles2.0\text{ moles} of a real gas occupy a volume of 18.0 dm318.0\text{ dm}^3. Under the exact same conditions, 2.0 moles2.0\text{ moles} of an ideal gas occupy a volume of 22.5 dm322.5\text{ dm}^3. What is the compressibility factor (ZZ) of the real gas under these conditions?

Cevap: 0.8

Cevap

0.8
The compressibility factor ZZ measures the deviation of a real gas from ideal gas behavior and is calculated as Z=VrealVidealZ = \frac{V_{\text{real}}}{V_{\text{ideal}}}. Substituting the given values yields Z=18.022.5=0.80Z = \frac{18.0}{22.5} = 0.80. A value of Z<1Z < 1 indicates that intermolecular attractive forces dominate, causing the real gas to occupy less volume than predicted by the ideal gas equation.

Adım Adım Çözüm

1
Identify the formula for compressibility factor
Z=VrealVidealZ = \frac{V_{\text{real}}}{V_{\text{ideal}}}
The compressibility factor ZZ quantifies deviation from ideality as the ratio of molar volume of a real gas to that of an ideal gas at the same temperature and pressure.
2
Substitute the given values into the equation
Z=18.0 dm322.5 dm3Z = \frac{18.0\text{ dm}^3}{22.5\text{ dm}^3}
Both volumes are measured under identical pressure, temperature, and mole count.
3
Calculate the numerical value
Z=0.80Z = 0.80
Dividing 18.0 by 22.5 gives 0.80, indicating Z<1Z < 1 due to predominant intermolecular attraction.

Anahtar Kavram

Compressibility factor (Z = V_real / V_ideal) measuring real gas deviation
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Konular

Deviations of Real Gases from Ideal Gas Behavior

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