Question

An ideal gaseous reaction (which is a hypothetical gaseous reaction that conforms to the laws governing gas behavior) occurs at a constant pressure of 45.0 atm and releases 63.9 kJ of heat. Before the reaction, the volume of the system was 9.00 L . After the reaction, the volume of the system was 2.00 L .

Calculate the total internal energy change, ΔU, in kilojoules.

Answer 1

The total internal energy change, ΔU, in kilojoules, given that after the reaction, the volume of the system was 2.00 L is -31.98 KJ

How to calculate the total internal energy change?

Step 1: Calculate the work done. This is shown below:

• Initial volume of system (V₁) = 9.00 L
• Final volume of system (V₂) = 2.00 Liter
• Change in volume of system (ΔV) = V₂ - V₁ = 2 - 9 = -7 L
• Pressure of system (P) = 45.0 atm
• Work done (W) = ?

W = -PΔV

= -45 × -7

= 315 L.atm

Multiply by 101.32 to express in J

= 315 × 101.32

= 31915.8 J

Divide by 1000 to express in KJ

= 31915.8 / 1000

= 31.9158 KJ

Step 2: Calculate the internal energy change, ΔU. Details below:

• Heat released (Q) = -63.9 KJ
• Work done (W) = 31.9158 KJ
• Internal energy change (ΔU) =?

ΔU = Q + W

= -63.9 + 31.9158

= -31.98 KJ