Question

Positive deviation from ideal behaviour takes place because of (a) molecular interaction between atoms and \(\frac{\mathrm{PV}}{\mathrm{nRT}}>1\) (b) molecular interaction between atoms and \(\frac{\mathrm{PV}}{\mathrm{nRT}}<1\) (c) finite size of atoms and \(\frac{\mathrm{PV}}{\mathrm{nRT}}>1\) (d) finite size of atoms and \(\frac{\mathrm{PV}}{\mathrm{nRT}}<1\)

Short answer

Option (c) is correct: finite size of atoms and \( \frac{\mathrm{PV}}{\mathrm{nRT}} > 1 \).

Step-by-step solution

Identify the Condition for Positive Deviation

Positive deviation from ideal behavior occurs when the observed volume is greater than the ideal volume. Mathematically, this is expressed as \( \frac{\mathrm{PV}}{\mathrm{nRT}} > 1 \).

Analyze the Reason for Positive Deviation

The deviation arises because of the finite size of gas molecules. In gases, if the size of the molecules is significant, it leads to an actual molar volume that is larger than predicted by the ideal gas law.

Match the Description with the Correct Option

In the options given, we must find the pair that combines both the reason (finite size of atoms) and the mathematical condition (\( \frac{\mathrm{PV}}{\mathrm{nRT}} >1 \)).

Key concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental principle in chemistry and physics that describes how an "ideal" gas behaves under various conditions of temperature, pressure, and volume. It is expressed by the equation \( PV = nRT \), where \( P \) is the pressure of the gas, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin. This law assumes that gas molecules are point particles that do not interact with each other and occupy no volume.

• **Pressure (64;P)**: The force that the gas molecules exert per unit area.
• **Volume (64;V)**: The amount of space the gas occupies.
• **Moles (64;n)**: The quantity of gas in terms of the standard unit of chemical amount.
• **Ideal Gas Constant (64;R)**: A constant that makes the equation work for ideal gases, approximately 8.31 J/mol K.
• **Temperature (64;T)**: Measured in Kelvin, affects the speed and movement of the molecules.

However, no real gases perfectly obey this law because real gases have volume and interactions which are not considered in the Ideal Gas Law. This law works best under low pressure and high temperature conditions, where these factors are minimized.

Molecular Volume

Molecular volume is the volume occupied by one mole of gas particles, accounting for their finite size. In an ideal gas approximation, we often assume particles are point-like with no volume. But in reality, gas molecules have size, and their volume can impact the gas's behavior.

When computing the behavior of real gases, molecular volume becomes crucial because it affects how closely molecules can pack together. As molecules take up space, the actual volume they occupy may be larger than what is predicted by the Ideal Gas Law.

By comparing the actual molar volume (the volume per mole) with the predicted volume from the Ideal Gas Law, scientists understand how much space the molecules are occupying. This understanding leads to the Bettered approach for explaining aspects such as how dense or compressible a gas can be under certain conditions.

This deviation from ideal behavior is what leads us to concepts such as positive deviation.

Finite Size of Atoms

The finite size of atoms means that the atoms or molecules of a gas occupy physical space and are not just point particles as assumed in the Ideal Gas Law. This real size of molecules leads to certain behavioral deviations in gases.

When we consider real gases, the positivity of deviation is often attributed to this finite size. As these molecules occupy more space, the actual pressure exerted by the gas becomes higher than what is predicted.

• **Higher pressure:** Due to space taken by the gas molecules.
• **More repulsive interactions:** Since molecules are of finite size, they impede one another more frequently, thus increasing the observed volume.

This can be critical when predicting the behavior of gases under non-ideal conditions, such as in high-pressure scenarios, where these deviations become more pronounced. The real world product is often larger than the ideal calculated value, making \( \frac{\mathrm{PV}}{\mathrm{nRT}} > 1 \). This indicates that the actual space occupied by the gas is more than that predicted due to the molecule's finite size.