Question

For the reaction: \(\mathrm{A}_{2}(\mathrm{~g}) \rightarrow \mathrm{B}(\mathrm{g})+\frac{1}{2} \mathrm{C}(\mathrm{g})\) pressure of the system increases from 100 to \(120 \mathrm{~mm}\) in 5 min. The average rate of disappearance of \(\mathrm{A}_{2}\) (in \(\mathrm{mm} / \mathrm{min}\) ) in this time interval is (a) 4 (b) 8 (c) 2 (d) 16

Short answer

The average rate of disappearance of A2 is 4 mm/min.

Step-by-step solution

Understand the concept of reaction rate

The average rate of a chemical reaction over a given time interval is defined as the change in concentration of a reactant or product per unit time. For disappearance of a reactant, it is calculated using the formula: Average rate = - (Change in concentration of A2) / (Change in time). The negative sign indicates that the concentration of the reactant is decreasing.

Calculate the change in concentration

The change in concentration of A2 is given by the change in pressure since it is a gaseous reactant, and pressure is directly proportional to concentration. Change in pressure = Final pressure - Initial pressure = 120 mm - 100 mm = 20 mm. This change in pressure occurred over a period of 5 minutes.

Calculate the average rate of disappearance of A2

The average rate of disappearance of A2 is then calculated by dividing the change in pressure by the change in time. Average rate = - (Change in pressure) / (Change in time) = - (20 mm) / (5 min) = -4 mm/min. The negative sign is conventional for the rate of disappearance of reactants.

Key concepts

Reaction Kinetics

Understanding reaction kinetics is essential when studying how reactions occur and at what rates they progress. Reaction kinetics, often simply called kinetics, looks into the factors that affect the speed of a chemical reaction and establishes the relationship between the reactivity of molecules and the rate at which a reaction proceeds.

Some of the main aspects of kinetics encompass the energy needed for reactions to occur, known as the activation energy, the orientation of reactant molecules when they collide, and the frequency of collisions. Factors like temperature, pressure, concentration of reactants, and the presence of catalysts are pivotal as they influence these aspects and thereby manipulate how fast a reaction can go from starting reactants to final products. A fundamental understanding of kinetics not only aids in predicting reaction rates but also in controlling processes in industries like pharmaceuticals and biochemical engineering.

Average Rate of Reaction

When we talk about the average rate of reaction, we're measuring how quickly reactants turn into products over a period of time. It's an indicator of the speed of a chemical reaction. Remember, for the disappearance of a reactant, we often use a negative sign because the quantity of reactant is diminishing.

By following the formula Average rate = - (Change in concentration of A2) / (Change in time), it becomes clearer that if the concentration of a reactant decreases rapidly, the reaction rate is high. Conversely, very gradual declines in reactant concentration indicate a slower reaction. This concept is instrumental in the field of chemistry, as it helps predict the time needed for a reaction to reach completion, which is crucial for planning and optimizing chemical production.

Pressure and Concentration Relationship

In the context of gases, pressure plays a significant role and is directly related to the concentration of gas molecules. According to the ideal gas law, pressure is directly proportional to the number of molecules in a given volume at a constant temperature. This implies that an increase in pressure results from an increase in the number of gas molecules - suggesting a higher concentration.

As pressure changes, it can affect the rate of a reaction by altering the concentration of the gaseous reactant or product involved. More molecules in the same volume mean that they are more likely to collide with energy greater than the activation energy, a requirement for successful reactions. Understanding this relationship is vital when controlling reaction conditions, particularly in reactions involving gases where pressure can be a more convenient measure of concentration than molarity, especially on an industrial scale.