The decomposition of acetaldehyde is a second order reaction with a rate constant of \(4.71 \times 10^{-8} \mathrm{L} \mathrm{mol}^{-1} \mathrm{s}^{-1}\). What is the instantaneous rate of decomposition of acetaldehyde in a solution with a concentration of \(5.55 \times 10^{-4}\) \(M ?\)

Understanding the rate law is fundamental to studying the speed of chemical reactions. The rate law expresses the relationship between the reaction rate and the concentration of reactants. For a second-order reaction like the decomposition of acetaldehyde, the rate law tells us the reaction rate is directly proportional to the square of the concentration of the reactant. This is mathematically represented as \text{Rate} = k[A]^2,where \(k\) is the rate constant indicating the speed of the reaction and \([A]\) stands for the molar concentration of the reactant, acetaldehyde in this case. It’s crucial to know the order of the reaction to use the correct formula for the rate law, as each order of reaction has its unique rate law expression.

Reaction kinetics deals with studying the rates of chemical processes and determining the various factors that influence these rates. It's a branch of physical chemistry that seeks to understand and describe how quickly reactions proceed to completion. Factors that affect reaction rates include the chemical nature of the reactants, their concentration, the presence of catalysts, temperature, and the physical state or surface area of reactants. Kinetic analysis helps us to infer things like the reaction mechanism, energy barriers, called activation energies, and the stability of reaction intermediates.

The concentration of a substance refers to the amount of that substance in a given volume of solution. Chemical concentration plays a pivotal role in reaction kinetics as it can drastically affect the reaction rate. In the context of our second-order reaction, the instantaneous rate is highly sensitive to changes in the concentration of acetaldehyde. This sensitivity is captured in the rate law expression where the concentration term is squared, meaning that a small increase in concentration results in a much larger increase in the rate of the reaction. Students must ensure they correctly interpret and utilize concentration units to perform accurate calculations in reaction kinetics.

The instantaneous rate of reaction is the rate at which a reaction is proceeding at a particular moment in time, which can change over the course of the reaction. For instance, in our exercise, we calculate this rate based on the concentration of acetaldehyde at a specific time. Unlike average rate, which measures the rate over an interval of time, instantaneous rate provides us with a snapshot, offering insight into the reaction's progression at that exact moment. To find it for a second-order reaction, it's essential to raise the concentration to the power of two and multiply by the rate constant as shown in the mathematical relation given by the rate law. Calculating the instantaneous rate assists in understanding the dynamics of the reaction under current conditions.