Final answer:
The question requires additional information to calculate the time for complete decomposition of the CaCO₃ sample. It involves understanding first-order reaction kinetics and could also consider equilibrium constants for reactions at a given temperature.
Step-by-step explanation:
The question is asking how long it will take for the entire sample of CaCO₃ to decompose given a constant rate of decomposition. However, to precisely answer how many minutes it would take for the decomposition of the entire sample, additional information is required, such as the initial amount of the sample and the rate of decomposition at the given temperature or conditions. The decomposition of CaCO₃, which is typically represented by the equation CaCO₃(s) → CaO(s) + CO₂(g), is temperature-dependent and can follow a first-order kinetics process.
In a first-order reaction, the rate of decomposition is directly proportional to the concentration of the reactant. The relationship between the decomposition rate, the half-life, and the initial concentration can be described using integrated rate laws for first-order reactions.
Examples provided related to the decomposition rate include the rate of decay of C-14 as a function of the radioactive decay constant, which is a similar process of decay but involves different constants and conditions compared to CaCO₃ decomposition. Equilibrium considerations, such as the equilibrium constant (Kc), also play a role in determining the amount of product and reactant present in a system at a given temperature but don't directly answer the question about time for complete decomposition.