A moles of Hydrogen reacts with B mol Iodine to give 2x mol of HI at equilibrium.Find the total no of moles at equilibrium.

To find the total number of moles at equilibrium when a certain amount of hydrogen reacts with iodine to form hydrogen iodide (HI), we can start by looking at the balanced chemical equation for the reaction:

The Reaction Equation

The reaction between hydrogen (H₂) and iodine (I₂) can be represented as:

H₂(g) + I₂(g) ⇌ 2 HI(g)

Understanding the Stoichiometry

From the balanced equation, we see that one mole of hydrogen reacts with one mole of iodine to produce two moles of hydrogen iodide. This stoichiometric relationship is crucial for determining the moles at equilibrium.

Setting Up the Initial Conditions

Let's denote:

• A = moles of hydrogen (H₂) initially present
• B = moles of iodine (I₂) initially present
• 2x = moles of hydrogen iodide (HI) produced at equilibrium

Calculating Changes in Moles

As the reaction proceeds, the following changes occur:

• Hydrogen decreases by x moles.
• Iodine decreases by x moles.
• Hydrogen iodide increases by 2x moles.

Equilibrium Moles

At equilibrium, the moles of each substance can be expressed as:

• Moles of H₂ at equilibrium = A - x
• Moles of I₂ at equilibrium = B - x
• Moles of HI at equilibrium = 2x

Total Moles at Equilibrium

To find the total number of moles at equilibrium, we simply add the moles of each substance:

Total moles at equilibrium = (A - x) + (B - x) + 2x

By simplifying this expression, we get:

Total moles at equilibrium = A + B + x

Conclusion

Thus, the total number of moles at equilibrium is the sum of the initial moles of hydrogen and iodine, plus the moles of hydrogen iodide formed, represented as:

Total moles at equilibrium = A + B + x

In this equation, x represents the amount of hydrogen and iodine that reacted, which can be determined based on the initial conditions and the extent of the reaction. This approach allows you to calculate the total moles at equilibrium effectively.