Question

For a zero order reaction, the plot of conc. \((a-x)\) vs time is linear with (a) \(+\) ve slope and zero intercept (b) - ve slope and zero intercept (c) \(+\) ve slope and non-zero intercept (d) - ve slope and non-zero intercept

Short answer

(b) - ve slope and zero intercept

Step-by-step solution

Understanding Zero Order Reactions

In a zero order reaction, the rate of reaction is constant and does not depend on the concentration of the reactants. The rate law for a zero order reaction can be written as rate = k[Reactant]^0, which simplifies to rate = k, where k is the rate constant.

Determine the Plot Characteristics

For a zero order reaction, the concentration of reactant decreases linearly with time. Therefore, when plotting concentration \(a-x\) versus time, the graph should be a straight line with a constant negative slope, since the concentration of the reactant is decreasing.

Identify the Correct Option

Since the concentration decreases linearly with time, the slope of the plot should be negative. The intercept will be zero if we start measuring from the initial concentration \(a\). Therefore, the plot will have a negative slope and a zero intercept.

Key concepts

Understanding Reaction Kinetics

Reaction kinetics is a fundamental topic in chemistry that deals with the rates at which chemical reactions occur and the factors that affect these rates. It's essential for determining how quickly reactants are converted into products in a chemical process.

Within this field, different types of reactions are categorized by their order, which refers to the power to which the concentration of the reactant is raised in the rate law. A zero order reaction is particular because its rate does not depend on the concentration of the reactant; it remains constant over time. This happens when the reaction is limited by a factor other than the concentration of reactants, such as surface area or catalyst availability.

A deeper understanding of reaction kinetics allows chemists to manipulate conditions to control reaction rates. This is crucial for many industrial applications such as the synthesis of pharmaceuticals or in catalysis, where reactions must occur at a specific rate for desired outcomes.

Chemical Reaction Rate

The chemical reaction rate indicates how fast a reactant is consumed or a product is formed over time. In a zero order reaction, the rate is constant and is represented by the rate constant, denoted as 'k'. Unlike reactions of higher order, in which the rate changes as the reactant concentrations change, a zero order reaction maintains the same rate irrespective of the concentrations of the reactants involved.

In practical terms, when you measure the concentration of a reactant over time and plot it on a graph for a zero order reaction, the result would be a straight line. This line demonstrates that the reactant's concentration decreases at a steady rate over time. Recognizing these patterns in reaction rate graphs is fundamental for students in predicting and understanding how a reaction proceeds under various conditions.

Rate Law and Zero Order Reactions

Rate law expresses the relationship between the reaction rate and the concentration of reactants. For a zero order reaction, the rate law can be written as rate = k[Reactant]^0. Since any number to the power of zero is one, the rate law simplifies to rate = k. Here, the rate constant 'k' has units of concentration per time, reflecting that for zero order reactions, the rate is independent of the concentration of the reactant.

It is important to note that in zero order kinetics, even if the reactant concentration decreases, the reaction continues at the same rate until the reactant is depleted or another factor changes. This characteristic yields a linear plot of concentration versus time with a negative slope and a zero intercept when the concentration measured is from the initial concentration—a crucial concept to grasp for students understanding chemical kinetics and reaction mechanisms.