I have 4 of the same type of question with different numbers. When X is increasing/decreasing, how fast is Y increasing/decreasing?

Question

Consider the reaction. 2D(g) + 3E(g) + F(g) => 2G(g) + H(g). When G is increasing at 0.39 mol/Ls, how quickly is D decreasing?

1. the answer is 0.39.
2. 2/2(0.39) = 0.39.

Consider the reaction, 2D(g) + 3E(g) + F(g) => 2G(g) + H(g). When F is decreasing at 0.26 mol/Ls, how quickly is G increasing?

1. the answer is 0.520.
2. 2G/1F (0.26) = 0.520
3. how do you know it's 2G/1F, and not 1F/2G?

Consider the reaction 2D(g) + 3E(g) + F(g) => 2G(g) + H(g). When H is increasing at 0.45 mol/Ls, how quickly is E decreasing?

1. the answer is 1.350.
2. 3E/1H (0.45) = 1.350
3. how do you know it's 3E/1H, not 1H/3E?

Consider the reaction 2D(g) + 3E(g) + F(g) => 2G(g) + H(g). When G is increasing at 0.57 mol/Ls, how quickly is H increasing?

1. the answer is 0.285
2. 1H/2G (0.57) = 0.285.
3. how do you know it's 1H/2G, not 2G/1H?

My question: I don't understand how to figure out if you're dividing the increasing by the decreasing, or the decreasing by the increasing.

1. in the second question if you divide the decreasing by the increasing, you get 1F/2G (.26) = 0.13 which is not the answer.
2. in the third question if you divide the decreasing by the increasing, you get 3E/1H (.45) = 1.35 which is the answer.
3. in the fourth one, none is decreasing, so how would you know whether to divide by 2/1 or 1/2 to get the answer without knowing the answer.

So how do you determine the necessary action without first knowing the answer?

Answer 1

You’ll notice that the reactant is always decreasing and the product is always increasing. The relationship of the rates is dictated by the stoichiometry of the balanced equation. So in #1 e.g., the stoichiometry is 1:1 for D and G so for every G formed 1 D will disappear. In #3 e.g, you have 1 H increasing so you will need 3E to disappear (decrease), so the rate of disappearance of E will be 3x the rate of appearance of H = 3x0.45.

Answer 2

You can use dimensional analysis if you like a mathematical approach. Pay attention to how the units cancel out:

First one:

0.39 mol G / Ls • (1 mol D / 1 mol G).

Mol G cancels out. Left with mol D/Ls

the conversion factor in parenthesis comes from the mole ratio in the balanced equation

Second one:

0.26 mol F / Ls • (2 mol G / 1 mol F) = 0.52 mol G/ Ls

Mol F cancels out. Left with mol G/ Ls

Third one:

0.45 mol H / Ls • (3 mol E / 1 mol H) = 1.35 mol E/ Ls

Mol H cancels out. Left with mol E /Ls

Fourth one:

0.57 mol G / Ls • (1 mol H / 2 mol G) = 0.285 mol H / Ls

Mol G cancels out. Left with mol H /Ls

Answer 3

I think it can be understood if you imagine each molecule as a piece of clay. You take two "D" pieces, 3 "E" pieces, and one "F" piece, combine them together in one big ball, and then divide it onto two "G" pieces and one "H" piece. You are repeating that operation with a constant speed, and you are making, e.g. 10 "G" pieces each second (assume you are kind of Maxwell's daemon). Obviously, two "D" pieces are needed to produce a single ball that will be converted into two "G" pieces (and one "H"), so the rate of disappearance of "D" will be equal to the rate of formation of "G", so if 10 "G" pieces are produced each second, 10 "D" pieces are disappearing during the same time. The same works for other cases. Thus, since one "H" is produced each time two "G" are made, then the rate of "H" formation will be two times smaller. In our case, if the rate of formation of "G" is 10 per second, the rate of formation of "H" is 5.

I understand that sounds like an explanation for little kids, however, it is sometimes is useful even when you are thinking about very complex concepts