How does a limiting reagent affect the products in a chemical reaction?

The presence of a limiting reagent will reduce the amount of products a particular reaction can form.

The reactant that acts as a limiting reagent will be consumed first by the reaction, in essence leaving the other reactant(s) in excess. This implies that the amounts of products the reaction forms will depend on the limiting reagent.

Here's an example of why that happens. The reaction between hydrogen gas and nitrogen produces ammonia according to the balanced chemical equation

#color(red)(3)H_(2(g)) + N_(2(g)) -> color(blue)(2)NH_(3(g))#

Notice that 1 mole of #N_2# requires #color(red)(3)# moles of hydrogen in order to produce #color(blue)(2)# moles of ammonia. These mole ratios will help you decide if you have an insufficient amount of one reactant.

Now take a look at the following image.

Notice that the left container has 9 molecules of #H_2# and 5 molecules of nitrogen. Since the balanced chemical equation tells you that you need 3 molecules of hydrogen for every 1 molecule of nitrogen, it appears that you have insufficient hydrogen present.

In order for all of the nitrogen molecules to react, you'd need

#5cancel("molecules "N_2) * (color(red)(3)"molecules "H_2)/(1cancel("molecule "N_2)) = color(blue)(15)" molecules "# #H_2#

Since you only have 9 molecules of #H_2# available, #H_2# will be the limiting reagent for this reaction. The 9 molecules of hydrogen will react with 3 molecules of nitrogen; at the same time, the excess nitrogen molecules will not participate in the reaction.

As you can see, the fact that not all of the nitrogen reacted influenced how many ammonia molecules were produced. Instead of 5 molecules, this reaction will only produce 3 molecules of ammonia.