Given the following balanced equation, determine the rate of reaction with respect to [HCl].

H2(g) + Cl2(g) → 2 HCl(g)

Question

Given the following balanced equation, determine the rate of reaction with respect to [HCl].

H2(g) + Cl2(g) → 2 HCl(g)

BlackTom AI · Accepted Answer

First, let's restate the problem: we have the balanced reaction H2(g) + Cl2(g) → 2 HCl(g), and we want the rate of reaction with respect to [HCl].

To relate rates, remember the general definition for aA + bB → cC: rate = -(1/a) d[A]/dt = -(1/b) d[B]/dt = (1/c) d[C]/dt. When focusing on a product, the rate expression becomes rate = (1/c) d[C]/dt, where c is the stoichiometric coefficient of the product.

For HCl, the product is HCl with coefficient c = 2. Therefore, the rate with respect to [HCl] is rate = (1/2) d[HCl]/dt. Since product concentrations increase as the reaction proceeds, d[HCl]/dt is positive, so the rate is a positive quantity.

Now, evaluate each answer option:
- Option: 'Rate = +' — This option correctly indicates that the rate with respect to HCl has a positive sign, reflecting that [HCl] increases over time. While it omits the explicit division by 2 and the differential form, the positive sign aligns with the correct direction of change for a product.
- Option: 'Rate = -' — This is incorrect because a negative rate would imply [HCl] is decreasing with time, which contradicts product formation in this forward reaction.
- Option: 'Rate = +' — This duplicate option also denotes a positive rate, sharing the same correct sign issue as the first. Without the explicit 1/2 factor and dt, it remains incomplete but sign-wise correct.
- Option: 'It is not possible to determine without more information.' — This is incorrect. The stoichiometry alone determines the relation between the rates, and the sign follows from product formation; no extra data are required.
- Option: 'Rate = -' — This is a repeated incorrect choice for the same reason: the rate with respect to a product should be positive since the product concentration increases in the forward reaction.

In summary, the correct conceptual conclusion is that the rate with respect to [HCl] is positive and equal to (1/2) d[HCl]/dt. The provided choices emphasize the sign, with the positive options correctly indicating a positive rate, while the negative options misrepresent the direction of change. The option asserting that more information is needed is unfounded given the stoichiometry of a straightforward elementary-like reaction.

CHM-1020-LD01.2025SU PS 1-Part I (Kinetics)

Given the following balanced equation, determine the rate of reaction with respect to [HCl]. H2(g) + Cl2(g) → 2 HCl(g)

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