Chemistry Q128 – AP-EAMCET 2026

Home Chemistry Chemical ThermodynamicsQuestion #293

Consider the following reaction

A_{2} B_{4} (g) \to 2 A B_{2} (g)

300 K

Δ_{r} H

for this reaction is

- x k J m o l^{- 1}

. What is its

Δ_{r} U

(in

k J m o l^{- 1}

) at the same temperature? (

R = 8.3 J m o l^{- 1} K^{- 1}

)

Clue 1 of 3: Enthalpy and Internal Energy

The relationship between enthalpy ( $Δ H$ ) and internal energy ( $Δ U$ ) depends on the change in the number of moles of gaseous substances in a reaction.

🧠 Full Solution Path

Step 1: Determine the change in moles of gas (

Δ n_{g}

)✦ Active

The given reaction is $A_{2} B_{4} (g) \to 2 A B_{2} (g)$ . From the balanced chemical equation, we can find the number of moles of gaseous products and reactants.

Moles of gaseous products = 2 (from 2 A B_{2} (g))

Moles of gaseous reactants = 1 (from A_{2} B_{4} (g))

Δ n_{g} = (moles of gaseous products) - (moles of gaseous reactants)

Δ n_{g} = 2 - 1 = 1 m o l

💡 Teacher's Secret Hint

Remember to only consider gaseous species when calculating $Δ n_{g}$ .

Step 2: State the relationship between

Δ H

and

Δ U

and identify given values○ Expand

The relationship between change in enthalpy ( $Δ H$ ) and change in internal energy ( $Δ U$ ) is given by:

Δ H = Δ U + Δ n_{g} R T

We are given: $Δ_{r} H = - x k J m o l^{- 1}$ $T = 300 K$ $R = 8.3 J m o l^{- 1} K^{- 1}$ And we found $Δ n_{g} = 1 m o l$ .

💡 Teacher's Secret Hint

Ensure all units are consistent. Since $Δ H$ is in $k J$ , it's usually best to convert $J$ to $k J$ for the $Δ n_{g} R T$ term.

Step 3: Calculate the

Δ n_{g} R T

term and convert units○ Expand

Now, calculate the product $Δ n_{g} R T$ :

Δ n_{g} R T = (1 m o l) \times (8.3 J m o l^{- 1} K^{- 1}) \times (300 K)

Δ n_{g} R T = 2490 J

Since $Δ H$ is given in $k J$ , convert $Δ n_{g} R T$ from Joules to kilojoules (1 $k J = 1000 J$ ):

Δ n_{g} R T = \frac{2490}{1000} k J = 2.49 k J

💡 Teacher's Secret Hint

A common mistake is forgetting to convert units, especially between Joules and kilojoules. Always double-check unit consistency before final calculations.

Step 4: Solve for

Δ_{r} U

○ Expand

Rearrange the formula $Δ H = Δ U + Δ n_{g} R T$ to solve for $Δ U$ :

Δ U = Δ H - Δ n_{g} R T

Substitute the given value of $Δ_{r} H = - x k J m o l^{- 1}$ and the calculated value of $Δ n_{g} R T = 2.49 k J m o l^{- 1}$ :

Δ_{r} U = (- x k J m o l^{- 1}) - (2.49 k J m o l^{- 1})

Δ_{r} U = - (x + 2.49) k J m o l^{- 1}

Comparing this result with the given options, it matches option 3.

💡 Teacher's Secret Hint

Pay close attention to the signs when substituting values. A negative $Δ H$ and a positive $Δ n_{g} R T$ can sometimes lead to different interpretations of the final sign.

✦ STEM Console utilizes AI models to generate step-by-step explanations and math clues. AI can make mistakes.

Chemistry Question 128 – AP-EAMCET 2026

Clue 1 of 3: Enthalpy and Internal Energy

🧠 Full Solution Path