2 moles of a diatomic gas are enclosed in a vessel.when a certain amount of heat is supplied,50% of the gas molecules get dissociated,but there is no rise in temperature.what is the heat supplied,if temperature is T?

To solve this problem, we need to understand the process of dissociation of gas molecules and how heat is involved in this process. In this case, we have 2 moles of a diatomic gas, and when heat is supplied, 50% of the gas molecules dissociate without any change in temperature. Let's break this down step by step.

Understanding the Basics

A diatomic gas consists of molecules made up of two atoms. When we say that 50% of the gas molecules get dissociated, it means that half of the molecules break apart into individual atoms. For 2 moles of a diatomic gas, we have:

• Number of molecules = 2 moles × Avogadro's number (approximately 6.022 × 10²³ molecules/mole) = 1.2044 × 10²⁴ molecules.
• 50% dissociation means 1.2044 × 10²³ / 2 = 6.022 × 10²³ molecules dissociate.

Heat and Dissociation

The heat supplied to dissociate the gas molecules can be calculated using the concept of bond dissociation energy. Each diatomic molecule requires a certain amount of energy to break the bond between the two atoms. This energy is known as the bond dissociation energy.

Let’s denote the bond dissociation energy of the diatomic gas as \( D \) (in joules per mole). Therefore, the total energy required to dissociate 1 mole of the diatomic gas is \( D \) joules. Since we have 1 mole of molecules dissociating (as calculated earlier), the total heat \( Q \) supplied can be expressed as:

Calculating the Heat Supplied

The heat supplied to dissociate the gas can be calculated using the formula:

Q = n × D

Where:

• Q = heat supplied (in joules)
• n = number of moles of gas that dissociate (1 mole in this case)
• D = bond dissociation energy (in joules per mole)

Since we have 1 mole of gas dissociating, the heat supplied becomes:

Q = 1 × D = D

Final Expression

In summary, the heat supplied to dissociate 50% of the gas molecules in this scenario, while maintaining a constant temperature \( T \), is equal to the bond dissociation energy \( D \) of the diatomic gas. If you know the specific value of \( D \) for the gas in question, you can substitute it into the equation to find the exact amount of heat supplied.

Thus, the final answer is that the heat supplied is equal to the bond dissociation energy \( D \) of the diatomic gas. If you have any further questions or need clarification on any part of this explanation, feel free to ask!