Question

# An ideal gaseous reaction (which is a hypothetical gaseous reaction that conforms to the laws governing...

An ideal gaseous reaction (which is a hypothetical gaseous reaction that conforms to the laws governing gas behavior) occurs at a constant pressure of 50.0 atm and releases 62.9 kJ of heat. Before the reaction, the volume of the system was 6.60 L . After the reaction, the volume of the system was 3.00 L .

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

According to the First law of Themodynamics

Delta H = Delta U + w

Δ H =Δ U + w

ΔH = Enthalpy change

ΔU = Internal energy change

w = work done at constant pressure

Given

ΔH = - 62. 9 kJ ( energy is released)

ΔU = ?

w = - P( Final volume - Initial volume) = - 50.0 atm x (3.00 - 6.60) L = 180 L atm

0.082 L atm = 8.314 J (Recall the values of the gas constant R)

1 L atm = 8.314 J/ 0.082 = 101.4 J

Hence,

180 L atm = 180 x 101.4 J = 18252 J = 18.3 kJ

work done w = 18.3 kJ

The volume decreases from 6.6 L to 3.00 L .

Work is done on the system .Therefore workdone is positve.

-----------------------------------------------------------------------------------------------

ΔH = ΔU + w

ΔU = ΔH - w = - 62.9 kJ - 18.3kJ = - 81.2 kJ

The total internal energy change, ΔU = - 81.2 kJ

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