Question

Make any changes needed in each of the following equations so that the enthalpy change is equal to \(\Delta H_{i}^{\circ}\) for the compound: (a) \(\mathrm{Cl}(g)+\mathrm{Na}(s) \longrightarrow \mathrm{NaCl}(s)\) (b) \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \longrightarrow 2 \mathrm{H}(g)+\frac{1}{2} \mathrm{O}_{2}(g)\)

Short answer

(a) \frac{1}{2} \mathrm{Cl}_{2}(g)+\mathrm{Na}(s) \longrightarrow \mathrm{NaCl}(s) \ (b) \mathrm{H}_{2}(g) + \frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(g)

Step-by-step solution

Understand standard enthalpy change

The standard enthalpy change, \( \Delta H_{i}^{\circ} \), refers to the heat absorbed or released under standard conditions (298 K, 1 atm), when a compound is formed from its elements in their standard states.

Analyze reaction (a)

The given reaction is \( \mathrm{Cl}(g)+\mathrm{Na}(s) \longrightarrow \mathrm{NaCl}(s) \). To provide the standard enthalpy change for this reaction. The elements should be in their standard states: Solid sodium and gaseous chlorine.

Modify reaction (a)

The correct reaction representing standard enthalpy change involves chlorine in its standard state, which is diatomic gaseous form, \( \mathrm{Cl}_{2}(g) \). Therefore, \( \frac{1}{2}\mathrm{Cl}_{2}(g)+\mathrm{Na}(s) \longrightarrow \mathrm{NaCl}(s) \) is the equation needed.

Analyze reaction (b)

The given reaction is \( \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \longrightarrow 2 \mathrm{H}(g) + \frac{1}{2} \mathrm{O}_{2}(g) \). To provide the standard enthalpy change, the elements should be in their standard states: Diatomic hydrogen and oxygen gases.

Modify reaction (b)

In reaction (b), the enthalpy change must represent the formation of water from hydrogen and oxygen gases. The reverse reaction should be used to show formation, \( \mathrm{H}_{2}(g) + \frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(g) \).

Key concepts

enthalpy change

Enthalpy change is the amount of heat absorbed or released during a chemical reaction at constant pressure. It's usually represented by the symbol \(\triangle H\). When we talk about the standard enthalpy change, \(\triangle H_{i}^{\bullet}\), it refers to the heat change when substances are in their standard states.

This is measured under standard conditions, which are 298 K (25°C) and 1 atmosphere of pressure. Enthalpy change is important because it helps us understand how much energy is required or released in a reaction. For example, if a reaction has a negative \(\triangle H\), the reaction releases heat, making it exothermic. On the other hand, a positive \(\triangle H\) means the reaction absorbs heat, making it endothermic.

Understanding these changes helps chemists manipulate conditions to favor certain reactions, design energy-efficient processes, and predict reaction behavior. When looking at an enthalpy change, always remember to consider the entire reaction process, including the state of the reactants and products.

standard states

Standard states refer to the physical and chemical conditions under which substances are typically found. For elements, the standard state means the most stable form of the element at 298 K and 1 atm pressure.

For instance, the standard state of oxygen is \(\text{O}_{2}(g)\), a diatomic gas, while the standard state of carbon is \(\text{C}(s)\), in the form of graphite. The concept of standard states is crucial for determining the standard enthalpy changes because the heat involved when chemicals form or react is measured from these standard conditions.

In practice, this means reactions must be written with elements in their standard states to correctly represent the enthalpy changes. For example, reaction (a) initially used \(\text{Cl}(g)\), but for the correct standard enthalpy change, it should use \(\text{Cl}_{2}(g)\) because chlorine naturally exists as \(\text{Cl}_{2}(g)\) in standard conditions. Similarly, reaction (b) must account for hydrogen and oxygen in their standard diatomic forms: \(\text{H}_{2}(g)\) and \(\text{O}_{2}(g)\).

chemical reactions

Chemical reactions involve the transformation of reactants into products through the breaking and forming of chemical bonds. Reactions can be described by chemical equations, which provide a symbolic representation of the changes.

In the context of enthalpy changes, reactions often need to be balanced and expressed with all the participating substances in their standard states. For instance, the reaction \(\text{Cl}(g) + \text{Na}(s) \rightarrow \text{NaCl}(s)\) needed adjustment to align with standard states, resulting in \(\frac{1}{2}\text{Cl}_{2}(g) + \text{Na}(s) \rightarrow \text{NaCl}(s)\).

Similarly, the reaction for the formation of water from hydrogen and oxygen gases can be represented through the equation \(\text{H}_{2}(g) + \frac{1}{2}\text{O}_{2}(g) \rightarrow \text{H}_{2}\text{O}(g)\). This shows how elements in their standard states combine to form compounds, allowing for accurate calculation of enthalpy changes.

Understanding these principles is critical for predicting the energy changes in reactions, which has applications in everything from industrial processes to everyday chemical applications. Knowing how to correctly modify and interpret chemical equations ensures accurate results in both theoretical and practical chemistry.