Shaking the container would result in N2 (g) dissolving into N2 (aq) (because gasses dissolve when shaken), decreasing the concentration of N2 (g).
the question is asking what would increase the "concentration of N2 (g) in the water." your explanation would explain why choice I is correct, while it isn't. or am i reading the question wrong?
anyway, the equilibrium concentration doesn't depend on how hard you shake the container because after the components of the container settle back down, the same equilibrium will be reestablished. temperature does affect the equilibrium position, but raising the temperature makes gases LESS soluble, so that's not what we're looking for. the third choice shifts the equilibrium to more N2 dissolved...by La Chatlier's principle or whatever, when you add a gas to the system, the water will attempt to dissolve the added gas to cancel out the added component.
edit: i just typed my response to 71 and it deleted. ***.
anyway, it's just stoichiometry. the molality is 0.05 m (meaning 0.05 moles of solute / kg solvent). the volume of water (the solvent) is 1 kg, so multiply them together and you get 0.05 moles of solute, that is, 0.05 moles XY2.
there are two components to the calculation:
1. 40% of XY2 dissolves into the three things on the right side of the reaction. (1 + 2 = 3)
so 40% of 0.05 moles XY2, then times 3 = .....
2. 60% of XY2 stays as it is. because XY2 is aqueous, it counts toward the number of dissolved particles.
so 60% of 0.05= ....
add up your answers for 1 and 2 and you get 0.09