Question

Given the following reactions, $$ \begin{aligned} \mathrm{N}_{2} \mathrm{H}_{4}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) & \Delta H^{\circ} &=-534.2 \mathrm{~kJ} \\ \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(g) & \Delta H^{\circ} &=-241.8 \mathrm{~kJ} \end{aligned} $$ calculate the heat of formation of hydrazine.

Short answer

Answer: The heat of formation of hydrazine is 50.6 kJ.

Step-by-step solution

Reverse the first given reaction

We will reverse the first given reaction to get: $$ N_{2}(g) + 2H_{2}O(g) \rightarrow N_{2}H_{4}(l) + O_{2}(g) $$ When reversing a reaction, the enthalpy change for the reversed reaction is the opposite of the enthalpy change for the original reaction. Therefore, the new enthalpy change is: $$ \Delta H_{1}^{\circ} = 534.2\mathrm{~kJ} $$

Multiply the second given reaction by 2

Multiply the second given reaction by 2 to balance the number of hydrogen and oxygen atoms in the final reaction: $$ 2H_{2}(g) + 1O_{2}(g) \rightarrow 2H_{2}O(g) $$ When scaling a reaction, the enthalpy change must also be scaled by the same factor. Therefore, the new enthalpy change is: $$ \Delta H_{2}^{\circ} = 2 \times (-241.8)\mathrm{~kJ} = -483.6\mathrm{~kJ} $$

Add the modified reactions

Now, we will add the modified reactions to get the target reaction: $$ \begin{aligned} &N_{2}(g) + 2H_{2}O(g) \rightarrow N_{2}H_{4}(l) + O_{2}(g) \\ + &2H_{2}(g) + 1O_{2}(g) \rightarrow 2H_{2}O(g) \\ \hline &N_{2}(g) + 2H_{2}(g) \rightarrow N_{2}H_{4}(l) \end{aligned} $$ By Hess's Law, we also add the enthalpy changes for the modified reactions to obtain the enthalpy change for the target reaction: $$ \Delta H_{f}^{\circ} = \Delta H_{1}^{\circ} + \Delta H_{2}^{\circ} = 534.2\mathrm{~kJ} - 483.6\mathrm{~kJ} = 50.6\mathrm{~kJ} $$ Therefore, the heat of formation of hydrazine is 50.6 kJ.

Key concepts

Enthalpy Change

Enthalpy change is a measure of the heat energy absorbed or released in a chemical reaction at constant pressure, symbolized by \( \Delta H \) and is expressed in kilojoules per mole (kJ/mol). It's an essential concept in thermodynamics and tells us whether a reaction is exothermic (releasing heat) or endothermic (absorbing heat).

For instance, when hydrazine (\( \mathrm{N}_2\mathrm{H}_4 \) ) reacts with oxygen to form nitrogen and water, the enthalpy change can be negative or positive. If \( \Delta H \) is negative, as in the given exercise, this indicates that the reaction releases energy, making it exothermic. In more straightforward terms, we can think of the enthalpy change as the difference in energy between the products and reactants, a value that can be determined through experiments or calculated using Hess's Law.

Hess's Law

Hess's Law states that the total enthalpy change for a chemical reaction is the same, regardless of the number of steps the reaction is carried out in. This law relies on the principle of conservation of energy, meaning that if you start with certain reactants and end with certain products, the energy change will be the same, no matter the pathway taken.

Using Hess's Law, we can calculate enthalpy changes (\( \Delta H \) ) for reactions that are difficult to study directly. As seen in the exercise, by reversing and scaling existing reactions with known enthalpy values, we can determine the \( \Delta H \) for a target reaction, like the formation of hydrazine. It's like piecing together a puzzle — by rearranging and combining pieces that we understand well (standard reactions), we construct a new picture (target reaction) and deduce its associated energy changes.

Chemical Reaction Stoichiometry

Chemical reaction stoichiometry involves the quantitative relationship between reactants and products in a chemical reaction. It's like a recipe that tells you how much of each reactant you need to produce a certain amount of product.

In the context of the exercise, stoichiometry tells us how many moles of each substance react and the proportion in which they combine to form new substances. For example, to create hydrazine, the correct number of moles of nitrogen gas (\( \mathrm{N}_2 \) ) and hydrogen gas (\( \mathrm{H}_2 \) ) must react. Adjusting reactions to ensure the correct stoichiometry is essential. It ensures that all atoms from the reactants are accounted for in the products, and no atom is lost or gained in the process, following the Law of Conservation of Mass. By understanding stoichiometry, we can manipulate and combine reactions using Hess's Law to find out the enthalpy change of reactions that are too complicated to observe directly.