please help me with the following:

Question

The methanol production process is operated at 250 - 300 ºC & @ pressures of 50 - 100 atmospheres in the presence of a copperbased catalyst.

Comment on whether these operating conditions, 250 - 300 ºC & 50 - 100 atmospheres, are consistent with the aims of achieving a high equilibrium yield of methanol & a high rate of production, noting any potential conflicts in realizing both these aims. Explain the role of the copper-based catalyst, noting how its presence helps to address
any conflicts you have identified and the impact this may have on the overall costs of the production process.

You need to know or be able to find the equilibrium constant for the production of methanol. Remember that rates increase with T and that increasing P favors the side of the reaction with fewer mols of gas.

Is this the equilibrium constant?
CO(g)+2H2(g)<-->CH3OH(g)delta H = -90kj

If so, where do i go from here?

No, but it's the reaction you need to answer the question. You need to read your text and/or notes about the effect of temperature on the rate of a reaction. From a knowledge that rate is increased with increasing T, you know T should be high in order to increase the rate. BUT, this is an exothermic reaction, meaning that heat is given off during the reaction (delta H = -90 kJ--- a negative number tells you that), so increasing T will drive the equilibrium conditions to the left. That will decrease the yield. That is what the problem means when it says "noting any potential conflicts" etc. Increasing pressure will drive the equilibrium to the right (for a gaseous reaction, increasing P will make the reaction shift to the side with fewer moles---there are 3 mols gas on the left and just 1 on the right; therefore, it will shift to the right which increases yield). So you need to raise T to increase rate but not get it too too high for the higher T goes the less the yield. Part of that can be offset by increasing P. You need to put this into your own words as well as address the effect of a catalyst. A catalyst will help increase the speed with which the reaction goes so that will offset, to some degree, the effect of T, also. I hope this helps