What Does It Mean If the Compressibility Factor Z Is Greater or Less Than 1?
The compressibility factor Z is a crucial concept in gas physics, especially for competitive exams like JEE Main. It helps quantify how much a real gas deviates from ideal gas behaviour in various conditions such as changing pressure and temperature. Mastering compressibility factor Z allows you to correctly analyse real gas scenarios using simple formulas and graphs, boosting your score in both theory and numericals. Vedantu experts strongly recommend revising this topic along with related concepts like ideal gas law corrections.
Definition and Formula of Compressibility Factor Z
Compressibility factor Z is defined to measure the deviation of a real gas from ideal gas law. For any amount of gas,
Z = (pV)/(nRT), where:
- p = Pressure of the gas (in Pa)
- V = Volume of gas (in m3)
- n = Number of moles
- R = Universal gas constant (8.314 J·mol-1·K-1)
- T = Absolute temperature (in K)
An ideal gas always has Z = 1, while real gases may show Z ≠ 1. This correction factor helps in refining the ideal gas equation under non-ideal conditions. For practical applications and advanced numericals, understanding the meaning and formula of compressibility factor Z is essential. You can also compare this with the standard ideal gas law equation for clarity.
Physical Meaning and Interpretation of Compressibility Factor Z
The value of Z gives clear information about the behaviour of a gas in given conditions. Here's what different Z values indicate:
| Condition | Interpretation |
|---|---|
| Z = 1 | Gas behaves ideally (PV = nRT). |
| Z < 1 | Gas is more compressible than ideal. Intermolecular attraction dominates. |
| Z > 1 | Gas is less compressible than ideal. Repulsive forces dominate. |
When using compressibility factor Z in MCQs, carefully check the Z value given. For values like Z = 0.85, expect attractive forces, such as at moderate pressures. Z > 1 often appears at high pressures or very low temperatures.
Derivation and Calculation of Compressibility Factor Z
To derive compressibility factor Z, start from the ideal gas equation: PV = nRT. For real gases, deviations are adjusted by introducing Z:
- Real gas law: PV = ZnRT
- So, Z = PV/(nRT)
For an ideal gas, substituting real values returns Z = 1. In JEE/NEET problems, calculate Z by plugging in known values of pressure, volume, n, R, and temperature. Always check units before applying the formula.
Variation of Compressibility Factor Z with Pressure and Temperature
Compressibility factor Z varies with both pressure and temperature, especially for real gases. Graphical understanding is essential for MCQs. Recognize these trends:
- At low pressure, most gases approach Z = 1 (ideal behaviour).
- Z vs P graph for real gases shows dips (Z < 1) at moderate P and rise (Z > 1) at high P.
- Increase in temperature makes the gas more ideal (Z moves toward 1), even at some higher pressures.
These graphical trends are very useful with kinetic theory of gases or gaseous and liquid states questions.
Numerical Example Using Compressibility Factor Z
Let’s solve a simple numerical for compressibility factor Z. Suppose 2 moles of a real gas occupy 0.05 m3 at 5 × 105 Pa and 300 K. Find Z. Use R = 8.314 J·mol-1·K-1.
- Formula: Z = (pV)/(nRT)
- Here, p = 5 × 105 Pa, V = 0.05 m3, n = 2, R = 8.314, T = 300 K
- Calculate denominator: nRT = 2 × 8.314 × 300 = 4988.4
- Numerator: pV = 5 × 105 × 0.05 = 25000
- Z = 25000 / 4988.4 ≈ 5.01
Here, Z > 1 indicates significant repulsive forces, so real gas is less compressible than ideal. Always substitute SI units and cross-verify calculations during exams.
- Compare with values from the kinetic theory mock test for more practice.
- Further practice with properties of solids and liquids mock questions.
Common Mistakes and Tips for Compressibility Factor Z in Exams
- Forgetting to use absolute temperature (K) in the formula.
- Mistaking Z = 1 as always true for all gases at all conditions.
- Incorrect substitution of p or V units (use SI, not atm or cm3 unless converted).
- Overlooking that Z < 1 means attractive, Z > 1 means repulsive forces.
- Not linking graphs to physical meaning in graphical MCQ questions.
- Missing out on links to related topics like thermodynamics and gas theory mock papers.
- Revise conceptual differences using the real gas and ideal gas page.
- Connect with derivations in first law of thermodynamics discussions for holistic understanding.
- Find graphical explanations via solids and liquids revision notes for visual learners.
- Link practice to laws of gases and revision notes.
- More applications are explored in solid and liquid state important questions.
- Cement concepts for JEE Main preparation using key examples on this topic.
Compressibility factor Z helps in understanding the deviation from ideal gas behaviour and solving advanced real gas physics questions. Practical use includes identifying the correct law, applying the formula, and interpreting values for MCQs. Take time to practise these numericals and graphical applications using Vedantu’s curated resources for a competitive edge in exams.
FAQs on Compressibility Factor Z: Concept, Formula, and Uses
1. What is compressibility factor Z?
Compressibility factor Z is a dimensionless quantity that measures how much a real gas deviates from ideal gas behavior.
- It is defined as Z = (pV) / (nRT), where p is pressure, V is volume, n is the number of moles, R is the universal gas constant, and T is temperature.
- If Z = 1, the gas behaves ideally; if Z ≠ 1, the gas exhibits non-ideal or real-gas properties.
2. What is the compressibility factor (Z) for an ideal gas?
For an ideal gas, the compressibility factor Z is always equal to 1.
- This means ideal gases follow the equation pV = nRT precisely, without any deviation.
- Thus, Z = 1 serves as a reference to identify deviations for real gases.
3. How is Z calculated for a real gas?
To calculate the compressibility factor Z for a real gas, use the formula:
- Z = (pV) / (nRT)
- Measure the actual pressure, volume, moles, and temperature of the gas sample.
- Substitute the values in the equation to find Z.
4. What does it mean if Z is greater than 1?
If Z > 1, it means the gas is less compressible than an ideal gas under the same conditions.
- This usually occurs at high pressures where repulsive forces dominate.
- The molecules experience repulsion, leading to a larger volume than predicted by the ideal gas law.
5. What does it mean if Z is less than 1?
If Z < 1, the gas is more compressible than an ideal gas at those conditions.
- Occurs mainly at moderate pressures and lower temperatures.
- Indicates that attractive intermolecular forces dominate, reducing the actual volume below the ideal prediction.
6. What is the formula of Z in terms of PV = nRT?
The compressibility factor Z formula based on the ideal gas law is:
- Z = (pV)/(nRT)
- If the gas obeys the ideal gas equation perfectly, then Z = 1.
- This formula is widely used to analyze gas behavior in exam questions.
7. What are the main factors affecting the compressibility factor?
The value of Z depends mainly on:
- Pressure (p): Z changes as pressure changes, often increasing at high pressure due to repulsive forces.
- Temperature (T): Z approaches 1 at high temperatures, reflecting more ideal behavior.
- Type of gas: Molecular size and nature of intermolecular forces also affect Z.
8. Why is Z used in physical chemistry and physics calculations?
The compressibility factor Z is crucial because it accounts for real gas deviations from ideality.
- Helps solve numerical problems where the ideal gas law is inaccurate.
- Supports understanding of real gas behavior in JEE, NEET, and competitive exams.
- Links theoretical knowledge to experimental gas measurements through practical Z values.
9. How does Z change with pressure and temperature for real gases?
The behavior of the compressibility factor Z with changing conditions is:
- At low pressures, most gases approach Z = 1 (ideal behavior).
- At high pressures, Z often becomes greater than 1 due to repulsion.
- With lower temperatures, Z can drop below 1 due to attractive forces.
10. Can Z be negative or stay constant for a gas under all conditions?
The compressibility factor Z is always a positive real number for real gases under physical conditions.
- Z may approach but never become negative as volume and pressure are always positive in physical scenarios.
- Z varies with pressure, temperature, and the nature of the gas—it does not remain constant under all conditions except for an ideal gas.
