To determine the limiting reactant, we need to compare the number of moles of methanol produced by each reactant.
From the balanced chemical equation, we can see that 1 mole of CO reacts with 2 moles of H2 to produce 1 mole of CH3OH.
Using the given information, we have 3 moles of CO and 8 moles of H2.
For CO:
Number of moles of CH3OH produced = 3 moles of CO * (1 mole of CH3OH / 1 mole of CO) = 3 moles of CH3OH
For H2:
Number of moles of CH3OH produced = 8 moles of H2 * (1 mole of CH3OH / 2 moles of H2) = 4 moles of CH3OH
Comparing the number of moles of CH3OH produced, we can see that CO produces 3 moles of CH3OH while H2 produces 4 moles of CH3OH. Therefore, the limiting reactant is CO.
Therefore, the limiting reactant is CO.