Question

Look at the following hypothetical reaction: A + 4B - C + 3D. Assume that the equation is balanced. Which of the following mole ratios will produce the most product?
a) A/B

b) A/4B

c) 3A/4B

d) 4A/B

Answer 1

Answer is: b) A/4B.
Chemical reaction: A + 4B → C + 3D.
from chemical reaction: n(A) : n(B) = 1 : 4.
a) if 1A reacts with 1B, there is not enough B (need 3B more).
c) if 3A react with 4B, there is not enough B (need 8B more).
d) if 4A react with 1B, there is not enough B (need 15B more). 

Answer 2

The correct answer is b. Since the equation is balance we can establish that A and B react in the ration 1:4. So in order for the reactants to produce more product there must exist a limiting reactant that gets used up once the ratio of reactants is 1:4 or greater than this value. The first pair of reactants gives us a 1:1 ratio, which means

$a.mol A \times \frac{mol C}{mol A} = mol\ C\\\\mol B \times \frac{mol C}{4mol B} = 0.25 mol\ C$.

Here B is the limiting reactant and it get used up before we can go above our treshold ratio.

$b. mol A \times \frac{mol C}{mol A} = mol C\\\\4mol B \times \frac{mol C}{4mol\ B} = mol\ C$

The reactants react in the ratio 1:4 which gives 1 mol of C

$c. 3mol A \times \frac{mol C}{mol A} = 3mol\ C\\\\4mol B \times \frac{mol C}{4mol B} = 1 mol C$

The 3:4 ratio makes B be the limiting reactant which means even though we have 3 moles of A, after 1 mol A has reacted all the 4 moles of B will be used up.

$d, 4mol A \times \frac{molC }{mol A} = 4mol\ C\\\\mol\ B \times \frac{mol C}{ mol B} = 1 mol C$

Here there is not enough moles of B to get more product.