
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

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system
In the contact process for the production of sulfuric acid, the main reaction occurs at 450°C in the presence of a catalyst: $2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g);\ \Delta H = -190\ \text{kJ/mol}$  
(1) The expression for the equilibrium constant for this reaction is ______________, the equilibrium constant at 450°C is ______________ than the equilibrium constant at 500°C.  
(2) Indicate which of the following indicates that the reaction has reached equilibrium:  
a. $V(O_2)_{forward} = 2V(SO_3)_{reverse}$  
b. $\Delta(SO_2)_{forward} \times \Delta(O_2)_{reverse} = 2:1$  
c. The density of the gases in the container does not change over time.  
d. The total number of gas molecules in the container does not change over time.  
e. The average molecular weight of the gases in the container does not change over time.  
(3) In a sealed container with a fixed volume of 5L, 0.20 mol of $SO_2$ and 0.10 mol of $O_2$ are introduced. Half a minute later, equilibrium is reached, and it is found that there is 0.18 mol of $SO_3$ in the container. Then, $V(O_2)$ = ______________ mol·L<sup>-1</sup>·min<sup>-1</sup>. If an additional 0.30 mol of $SO_2$ and 0.15 mol of $O_2$ are introduced, the equilibrium ______________ (moves towards the forward reaction, moves towards the reverse reaction, or does not move). Once equilibrium is reached again, ______________ mol < $n(SO_3)$ < ______________ mol.

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