The question involves checking each diagram to see which one violates the Law of Mass Conservation in relation to the production of 'C' in the given reaction.
The Law of Mass Conservation states that the total amount of mass in a closed system remains constant, regardless of the internal processes. In other words, mass can neither be created nor destroyed.
Going by this law, for the reaction to hold true, the rate of production of 'C' (vC.prod) should always be equal to the rate of consumption of 'C' (vC.cons).
Let's evaluate each option:
a) The parameters are not given for this diagram, hence we cannot deduce anything about it.
b) In this diagram, the vC.prod value is 6 mM/s and the vC.cons value is also 6 mM/s. As both the production rate and the consumption rate are equal, this scenario aligns with the Law of Mass Conservation.
c) For this one, the vC.prod value is 12 mM/s, while vC.cons value is 4 mM/s. These are not equal. This means that more 'C' is being produced than is being consumed. Hence, this diagram violates the Law of Mass Conservation.
d) Here the vC.prod: 6 mM/s, and the vC.cons: 6 mM/s. The production and consumption rate are equal in this scenario, so it is in accordance with the Law of Mass Conservation.
In conclusion, option c is the diagram that violates the Law of Mass Conservation as it has different rates of production and consumption of C.