Problem 11 - General Chemistry

Question

If an equation for a reaction is doubled and then reversed, how is the value of \(\Delta H\) changed?

Step-by-Step Solution

Answer

\( \Delta H \) becomes \(-2x\) after doubling and reversing the reaction.

Step 1: Understand the Initial Reaction and \( \Delta H \)

When we have a chemical reaction, the change in enthalpy (\( \Delta H \)) is provided or can be calculated for the reaction as written. The sign and magnitude of \( \Delta H \) depend on the particular reaction and the direction in which it is written.

Step 2: Effect of Doubling the Reaction

Doubling a reaction means multiplying all the reactants and products by 2. When the equation of a reaction is doubled, the value of \( \Delta H \) is also doubled. For example, if the original \( \Delta H \) is \( x \), after doubling, \( \Delta H \) becomes \( 2x \).

Step 3: Reverse the Reaction

Reversing the reaction involves changing all reactants to products and vice versa. When a reaction is reversed, the sign of \( \Delta H \) changes. So if after doubling the \( \Delta H \) was \( 2x \), reversing the reaction will change \( \Delta H \) to \( -2x \).

Step 4: Combine the Changes

Both the doubling and reversing of the reaction have their individual effects on \( \Delta H \). Doubling makes \( \Delta H = 2x \) and reversing changes the sign. So, combining these transformations, the final \( \Delta H \) is \( -2x \).

Key Concepts

Chemical Reaction

When we talk about a chemical reaction, we refer to a process where substances, called reactants, are transformed into different substances, known as products. This transformation involves the breaking and forming of chemical bonds, which either absorbs or releases energy. This energy change is often expressed as a change in enthalpy, noted as \( \Delta H \), which serves as a measure of the heat absorbed or released during the reaction.

• A negative \( \Delta H \) indicates an exothermic reaction that releases heat.
• A positive \( \Delta H \) signals an endothermic reaction where heat is absorbed.

Understanding \( \Delta H \) is crucial because it influences how the reaction proceeds and affects its equilibrium. Whether working in a lab or analyzing chemical data, recognizing these changes can help predict reaction outcomes and their impacts on the surroundings.

Reversing Reaction

Reversing a reaction involves swapping the reactants and the products, essentially turning the reaction around. When this happens, the sign of the enthalpy change \( \Delta H \) also reverses. This is because the direction of the energy flow is switched:

• If the forward reaction is exothermic (releases heat), the reverse reaction will be endothermic (absorbs heat), resulting in a positive enthalpy change.
• Conversely, if the forward reaction absorbs heat, reversing it will cause it to release heat, changing \( \Delta H \) to a negative value.

By reversing a reaction, you change not only the chemicals involved but also the energetic balance, which plays a critical role in industrial applications and chemical pathways. It's akin to retracing your steps on a map, where each path covers the same distance but in the opposite direction.

Doubling Reaction

When you double a chemical reaction, you simply multiply all the amounts of reactants and products by two. This effectively scales up the reaction, which directly impacts the enthalpy change. By doing this, everything, including \( \Delta H \), doubles, since enthalpy is proportional to the amount of substance undergoing the change. For instance:

• If the original reaction had a \( \Delta H \) of \( x \), doubling it would make \( \Delta H \) equal to \( 2x \).
• This basic principle can be extended to scaling reactions by any factor, say tripling or halving, by simply multiplying \( \Delta H \) by the same factor.

Doubling reactions is a common technique used in chemical equations and stoichiometry to ensure the conservation of mass and energy. It's essential for calculating yields and preparing reactions at different scales, from small lab experiments to industrial processes.