When the mixture is placed in hot water, a greater proportion of brown iodine monochloride is formed. What does this tell you about the energetics of the forward reaction in which brown iodine monochloride reacts with chlorine to form yellow iodine trichloride?

The reaction moves in the direction that absorbs energy. So the back reaction is endothermic, which means that the forward reaction must be exothermic.

What happens to the value of K_c for this equilibrium when it is heated?

The concentration of products decreases and the concentration of reactants increases at higher temperature. This means that the top of the fraction for K_c gets smaller and the bottom of the fraction gets bigger. So K_c becomes smaller at a higher temperature.

What is the advantage of moving the U-tube from hot water to cold water and back to hot water again?

To show that the changes that occur in the composition of the equilibrium mixture when the temperature is changed are reversible.

Why might it useful to video the demonstration using a webcam?

The video images can be displayed on a large screen so that all students can see what's happening. The video can be saved and replayed at a later date for students not present at the time or for independent student study.