What are your thoughts?

1) CO2 + 4H2 = CH4 + 2H2O + heat
Predict, using Le Chatelier's principle, the conditions required in a closed system to produce MAXIMUM amount of methane.

u have the correct idea, but you should say "low temperature" and not "decrease temperature". You are supposed to describe the condition, not what you are suppose to do.

5moles of gas reactants produce 3 moles of gas reactants (assuming the reaction condition is such that water is in vapour phase). This implies high pressure would favour the forward reaction. Incidentally, this would suggest an increase in concentration [partial pressure] of the reactants and a smaller volume for the reaction system to take place in. Since the forward reaction is exothermic, a low temperature environment would favour the forward reaction. All this are in accordance to Le Chatelier's Principle.

2) CaCO3 + 2H+ = Ca2+ + H2O + CO2
How would the hardness of the water [Ca2+] affect the growth of stalagmites and stalacites (ie CaCO3)?

the higher the hardness of water, the more aq. Ca²⁺ present. This should provide sufficient hint to your question here.

3)CuCl4(2-) + 4H2O = Cu(H2O)4(2+) + 4Cl-
Predict the shift and effects in the equilibrium after AgNO3 is added.

What happens when you add aq silver nitrate to a chloride solution?

The Cl- ion react with Ag+ from AgNO3 to form a white ppt.

LOL. In a chemical plant, the equilibrium mixture will be sent into a seperator whereby most water will be removed as effluent, methane as a pure stream, and the rest back into the reactor to recycle the reactants for better economy.

Upon addition of aq AgNO₃, the chloride in solution will be precipitated out as AgCl (s), thus reducing the amount of Cl^- present. This favours the forward reaction of the equillibrium below:

CuCl₄ ^2- (aq) <-> Cu²⁺(aq)  + 4Cl^-(aq)

Some green CuCl₄ ^2- (aq) complex will be converted to Cu ²⁺ (aq). Hence, the solution turns blue and white precipitate (AgCl) is formed.

this is because AgCl has a very low solubility product constant. a low concentration of chloride ions is sufficient to cause precipitation of AgCl in the presence of aq Ag⁺ ions

Given the equilibirum constant and the equilibrium expression, you should be able to manipulate the algebreic expression to get the required values. The table below should  help:

PCl₅ <=> PCl₃ + Cl₂

for a Fixed Volume 1-Litre Equilibrium Mixture,

		PCl5		PCl3		Cl2
initial amount:		1.00		0		0
change in amount:		-x		+x		+x
equilibrium amount:		(1.00 - x)		x		x

Note, the amount reacted agrees with the stoichiometric ratio, ie. X moles of PCl5 breaks down to form X moles of PCl3 and X moles of Cl2

the equilibrium expression is:

K = [PCl3][Cl2]/[PCl5] = x² / (1.00-x) where K is the equilibirium constant

This expression can be manupilated to the form of a quadratic equation which you should be able to solve

ask yourself 2 questions:

1. does nitrogen react with any equilibrium component?
2. does addition of nitrogen increase the volume of the system?