Which of the following equations correctly describes the relationship between the rate at which NO2 and Cl2 are consumed in the following reaction?

2 NO2(g) + Cl2(g) → 2 NO2Cl(g)

A. -d(NO2)/dt = 1/2 [d(Cl2)/dt]
B. -d(NO2)/dt = 2 [d(Cl2)/dt]
C. -d(NO2)/dt = 2 [-d(Cl2)/dt]
D. -d(NO2)/dt = 1/2 [-d(Cl2)/dt]
E. -d(NO2)/dt = -d(Cl2)/dt

The correct equation that describes the relationship between the rate at which NO2 and Cl2 are consumed in the given reaction is option A:

-d(NO2)/dt = 1/2 [d(Cl2)/dt]

In the balanced chemical equation, the stoichiometric coefficient in front of Cl2 is 1, while the stoichiometric coefficient in front of NO2 is 2.

Therefore, for every 1 molecule of Cl2 consumed, 2 molecules of NO2 are consumed.

To relate the rates of consumption, we need to account for the stoichiometric coefficients. The rate at which NO2 is consumed (-d(NO2)/dt) will be half of the rate at which Cl2 is consumed (1/2 [d(Cl2)/dt]).

Hence, the correct equation is -d(NO2)/dt = 1/2 [d(Cl2)/dt], which is option A.

To determine the relationship between the rates at which NO2 and Cl2 are consumed in the given reaction, we need to consider the stoichiometry of the balanced chemical equation.

The balanced equation shows that in order to react, 2 moles of NO2 must react with 1 mole of Cl2, resulting in the formation of 2 moles of NO2Cl.

Looking at the coefficients in the balanced equation, we can determine the ratio between the rates of consumption of NO2 and Cl2. Since 2 moles of NO2 react with 1 mole of Cl2, the rate at which NO2 is consumed should be half the rate at which Cl2 is consumed.

Now let's analyze the answer choices:

A. -d(NO2)/dt = 1/2 [d(Cl2)/dt]
This answer choice correctly represents the relationship between the rates of consumption of NO2 and Cl2. It states that the rate of change of NO2 concentration is equal to half the rate of change of Cl2 concentration.

B. -d(NO2)/dt = 2 [d(Cl2)/dt]
This answer choice incorrectly indicates that the rate of change of NO2 concentration is equal to twice the rate of change of Cl2 concentration, which contradicts the stoichiometry of the balanced equation.

C. -d(NO2)/dt = 2 [-d(Cl2)/dt]
This answer choice incorrectly includes a negative sign and an additional factor of 2, which deviates from the correct relationship stated in option A.

D. -d(NO2)/dt = 1/2 [-d(Cl2)/dt]
This answer choice is incorrect as it incorrectly includes a negative sign and an additional factor of 2, which deviates from the correct relationship stated in option A.

E. -d(NO2)/dt = -d(Cl2)/dt
This answer choice incorrectly neglects the stoichiometric ratio between the rates of consumption of NO2 and Cl2, as it implies that the rates are equal.

Therefore, the correct answer is A. -d(NO2)/dt = 1/2 [d(Cl2)/dt].