Problem 80 - Chemistry The Science in Context

Question

Why is the standard enthalpy of formation of \(\mathrm{CO}(g)\) difficult to measure experimentally?

Step-by-Step Solution

Answer

Short Answer: The standard enthalpy of formation for carbon monoxide (CO) gas is difficult to measure experimentally because it involves the reaction between solid carbon (graphite) and gaseous oxygen (O2). Mixing and measuring a solid and a gas precisely is challenging due to the nature of gases, which disperse and have varying concentrations depending on temperature and pressure. Additionally, isolating the gaseous products from the reactants is difficult. As a result, indirect methods such as Hess's Law are typically used to determine the standard enthalpy of formation for CO(g) instead of direct experimental measurements.

Step 1: Understand the standard enthalpy of formation

The standard enthalpy of formation is the change in enthalpy during the formation of 1 mole of a substance from its constituent elements in their standard states. For CO(g), this involves the reaction: C(s) + 1/2 O2(g) → CO(g)

Step 2: Identify the problem in measuring the enthalpy change for CO(g)

In this reaction, the standard states of the reactants are a solid carbon (graphite) and gaseous oxygen (O2). The issue with measuring the enthalpy of formation for CO(g) arises as a direct result of the difference in physical states between the reactants. Carbon, in its standard state, is a solid (graphite), and oxygen, in its standard state, is a diatomic gas (O2).

Step 3: Explain the difficulty for an experimental setup

Attempting to directly measure the enthalpy change of this reaction would involve mixing a solid and a gas. It is difficult to control and measure the exact amount of gaseous oxygen that reacts with the solid carbon in an experiment. This is due to the nature of gases, which tends to disperse and have varying concentrations depending on factors such as temperature and pressure. Additionally, the reaction between carbon and oxygen produces a gas, making it difficult to isolate the products from the reactants.

Step 4: Indirect measurement necessity

Due to these difficulties, the standard enthalpy of formation for carbon monoxide (CO) gas is generally determined by indirect methods rather than direct experimental measurement. These methods may involve measuring the enthalpy change for a series of related reactions, and then using these values to calculate the desired enthalpy change for the formation of CO(g) using Hess's Law or other thermodynamic relationships.

Key Concepts

Standard States

Standard states refer to the physical states of substances under specific conditions. These conditions are typically set at 1 atm pressure and a defined temperature, usually 25°C (298 K). Standard states ensure a common reference point for thermodynamic calculations.

For example:

• Graphite is the standard state for carbon.
• Diatomic oxygen ( O_2 ) is the standard for oxygen.

When calculating the standard enthalpy of formation, each element must be in its standard state. This ensures that any enthalpy changes are only due to the process of formation and not influenced by variations in molecular structure or phases of the substances involved.

Understanding these states is crucial because they provide a uniform basis that allows chemists to compare different chemical reactions. Without standard states, it would be challenging to compare enthalpy data across different studies.

Measurement Challenges

Measuring the standard enthalpy of formation can be challenging, particularly for reactions like the formation of carbon monoxide ( CO ). In this case, solid carbon and gaseous oxygen need to react perfectly.
The challenges stem from:

• Different states of substances (solid vs gas) make it difficult to control reaction conditions.
• Gases naturally disperse, which could lead to imprecise measurements.
• Ensuring complete reaction without interference from side reactions.

These hurdles make direct measurement arduous. Hence, scientists often rely on indirect methods, improving accuracy while accommodating the physical constraints of the reactants. This complexity requires precise control over experimental conditions to achieve reliable data.

Hess's Law

Hess's Law is a crucial tool for calculating enthalpy changes indirectly. It postulates that the total enthalpy change for a chemical reaction is the same, no matter how the reaction occurs, provided the initial and final conditions are the same.

Using Hess's Law, we can sum the enthalpy changes of multiple related reactions to find the enthalpy change of a troublesome reaction like the formation of CO . For example, if we can't measure the reaction directly between solid carbon and gaseous oxygen, we find other measurable reactions that lead to the same product state.

This method is advantageous because:

• It does not require direct measurement under potentially difficult experimental conditions.
• It allows for more accurate and feasible calculations.

Hess's Law, therefore, aids scientists in determining enthalpy changes that are otherwise difficult to achieve directly, adding a powerful tool to the experimental design arsenal.