## Question 8.101 [ENDORSED]

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### Question 8.101

A technician carries out the reaction 2SO2(g) + O2(g)  2SO3(g) at 25°C
and 1.00 atm in a constant-pressure cylinder fitted with a piston. Initially,
0.0300 mol SO2 and 0.0300 mol O2 are present in the cylinder. The
technician then adds a catalyst to initiate the reaction.
a. calculate the volume of the cylinder containing the reactant gases before the reactions begin
b. what is the limiting reactant
c. assuming that the reaction goes to completion and that the temperature and pressure of the reaction remain constant, what is the final volume of the cylinder
d. how much work takes place and is it done by the system or on the system
e. how much enthalpy is exchanged and does it leave or enter the system
f. calculate the change in internal energy for the reaction

Ive worked through parts a-c and specifically need help?/and explanation for the last three parts

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### Re: Question 8.101  [ENDORSED]

D. Because this is a constant external pressure problem, you will use the equation
$w=-P\Delta V$.
The problem says it occurs at 1 atm of pressure, and our change in volume was determined in parts a and c.
$\Delta V=$=1.1L - 1.5 L = -0.4L.
Plugging it into the equation, you get:
$w=-P\Delta V=-(1.00 \textup{atm})(-0.4\textup{L})(101.325 J\cdot L^{-1}\cdot atm^{-1})=40J$
Work here is positive because it is done on the system.

E. The enthalpy of the reaction requires you to use the standard enthalpies of formation, which can be found in the back of the textbook, and the balanced equation. When you calculate it, you'll find it is -197.78 kJ/mole.
The problem states that we are using 0.030 mol of SO2, so you would use the enthalpy of the reaction (remember, the balanced equation says that we use 2 moles of SO2, meaning 2 moles produces -197.78 kJ) to determine the enthalpy exchanged.

F. To calculate the internal energy, you would use the equation:
$\Delta U=q+w$
where q is calculated in part E and w is calculated in part D.