Problem 220 - A Complete Resource Book in Chemistry for JEE Main

Question

The rate of a chemical reaction doubles for every \(10^{\circ} \mathrm{C}\) rise of temperature. If the temperature is raised by \(50^{\circ} \mathrm{C}\), the rate of the reaction increases by about: [2011] (a) 16 times (b) 42 times (c) 32 times (d) 20 times

Step-by-Step Solution

Answer

The rate of the reaction increases by 32 times.

Step 1: Understanding the Problem

The problem states that the rate of a chemical reaction doubles with every increase of \(10^{\circ} \mathrm{C}\) in temperature. We are asked to determine how many times the rate increases if the temperature is increased by \(50^{\circ} \mathrm{C}\).

Step 2: Calculate the Number of Doublings

For a \(50^{\circ} \mathrm{C}\) increase, we need to determine how many \(10^{\circ} \mathrm{C}\) increments are present. This is calculated as \( \frac{50}{10} = 5\).

Step 3: Determine the Exponential Increase of Rate

Since the rate doubles for each \(10^{\circ} \mathrm{C}\) increase, and there are 5 such increments in \(50^{\circ} \mathrm{C}\), the increase in rate can be calculated as \( 2^5 \).

Step 4: Calculate the Final Rate Increase

Calculate \( 2^5 = 32 \). Hence, the rate of the reaction increases by 32 times.

Key Concepts

Rate of Reaction

The rate of a chemical reaction refers to how quickly or slowly a reaction takes place. It is determined by the change in concentration of a reactant or product per unit time. For reactions occurring at the same conditions, a faster reaction is distinguished by a higher rate. Several factors can influence the rate of reaction, including:

• Temperature: A higher temperature usually increases the rate of reaction.
• Concentration: More concentration of reactants can lead to a faster rate.
• Particle Size: Smaller particles have a greater surface area, which can increase reaction rate.
• Catalysts: These substances can speed up reactions without being consumed.

Understanding these factors enables us to control and optimize reactions for specific purposes in various fields such as industry and research.

Temperature Dependence

Temperature is a crucial factor influencing the rate of chemical reactions. Generally, an increase in temperature results in a higher reaction rate. This is because higher temperatures provide energy to the reacting molecules, causing them to move faster. Consequently, collisions among particles become more frequent and energetic. It is commonly observed that for many reactions, the rate doubles for every increase of around 10°C. This does not apply to all reactions but is a helpful guideline for those that follow this pattern. Calculating the exact impact involves understanding the specific kinetics of the reaction involved.

Reaction Kinetics

Reaction kinetics is the study of the speed or rate at which chemical reactions occur and the factors affecting them. It involves exploring the steps by which reactants are converted into products. Key aspects include:

• Reaction Mechanism: The step-by-step sequence of elementary reactions, showing how products are formed from reactants.
• Rate Laws: Mathematical expressions that describe the relationship between the rate of reaction and the concentration of reactants.
• Activation Energy: The minimum energy required for a reaction to occur.

Through understanding reaction kinetics, chemists can predict reaction behavior, manipulate conditions to increase rates, and understand the fundamental nature of reacting substances.

Chemical Reactions

Chemical reactions are processes in which substances, known as reactants, are transformed into different substances, known as products. These reactions are governed by the laws of chemistry and are accompanied by energy changes. They play a crucial role in nature and industry:

• Natural Processes: Chemical reactions are involved in processes such as respiration, photosynthesis, and digestion.
• Industrial Applications: Many materials, including plastics and pharmaceuticals, are produced via chemical reactions.
• Energetic Changes: Reactions can be exothermic (release energy) or endothermic (absorb energy).

Understanding chemical reactions allows us to harness them for practical uses, including energy production, material synthesis, and environmental management.