Question

When hydrazine reacts with oxygen, nitrogen gas and steam are formed. (a) Write a thermochemical equation for the reaction. (b) How much heat is evolved or absorbed if \(1.683 \mathrm{~L}\) of steam at \(125^{\circ} \mathrm{C}\) and \(772 \mathrm{~mm} \mathrm{Hg}\) are obtained?

Short answer

Answer: 40.8 kJ

Step-by-step solution

Write the balanced chemical equation for the reaction of hydrazine with oxygen

For the given reaction, we have the following: Hydrazine: \(\mathrm{N_2H_4}\) Oxygen: \(\mathrm{O_2}\) Products: Nitrogen gas (\(\mathrm{N_2}\)) and steam (\(\mathrm{H_2O}\)) We will begin by writing a balanced chemical equation: \(\mathrm{N_2H_4} + \mathrm{O_2} \rightarrow \mathrm{N_2} + 2\mathrm{H_2O}\) To balance the equation, we need to add a coefficient for oxygen: \( \mathrm{N_2H_4} + \frac{1}{2}\mathrm{O_2} \rightarrow \mathrm{N_2} + 2\mathrm{H_2O}\)

Determine the number of moles of steam produced

We are given that \(1.683 \mathrm{~L}\) of steam at \(125^{\circ}\mathrm{C}\) and \(772 \mathrm{~mm} \mathrm{Hg}\) is obtained. We can convert pressure and temperature to SI units to use the ideal gas equation. Temperature: \(125^{\circ}\mathrm{C} + 273.15 = 398.15~\mathrm{K}\) Pressure: \(\frac{772 \mathrm{~mm} \mathrm{Hg}}{760} = 1.0158~\mathrm{atm}\) Using the ideal gas equation (\(PV=nRT\)), we can determine the number of moles of steam (n) produced: \(1.0158~\mathrm{atm} \cdot 1.683~\mathrm{L} = n \cdot 0.08206~\frac{\mathrm{atm} \cdot \mathrm{L}}{\mathrm{mol} \cdot \mathrm{K}} \cdot 398.15~\mathrm{K}\) Solving for n, we have: \(n = \frac{1.0158~\mathrm{atm} \cdot 1.683~\mathrm{L}}{0.08206~\frac{\mathrm{atm} \cdot \mathrm{L}}{\mathrm{mol} \cdot \mathrm{K}} \cdot 398.15~\mathrm{K}} = 0.0656~\mathrm{mol}\)

Calculate the heat evolved or absorbed

We can find the change in heat (\(\Delta H\)) for the reaction from a thermochemical table or by searching online for standard enthalpy change of reaction values. For the given reaction, we find that \(\Delta H = -622.2 \frac{\mathrm{kJ}}{\mathrm{mol}}\) (negative sign indicates heat is evolved). Using the stoichiometry of the reaction and the number of moles of steam produced, we calculate the heat evolved or absorbed: Heat evolved = \(0.0656~\mathrm{mol} \cdot -622.2~\frac{\mathrm{kJ}}{\mathrm{mol}} = -40.8~\mathrm{kJ}\) So, \(40.8 \mathrm{kJ}\) of heat is evolved when \(1.683 \mathrm{~L}\) of steam at \(125^{\circ} \mathrm{C}\) and \(772 \mathrm{~mm} \mathrm{Hg}\) are obtained.

Key concepts

Chemical Reaction

A chemical reaction is a process that leads to the transformation of one set of chemical substances to another. Through breaking and forming bonds, reactants are converted into products with different chemical properties.

In our example, hydrazine (H₄) reacts with oxygen (O₂) to form nitrogen gas (N₂) and steam (H₂O). Balancing such reactions requires careful adjustment of coefficients to ensure that the number of atoms of each element is conserved. This is a foundational skill in chemistry, as balancing equations reflects the conservation of mass. It's simply a matter of making sure that for every atom going into a reaction, it must either be accounted for in the product or released as a gas, ion, or some other form.

Enthalpy Change

The term enthalpy change, denoted as H, refers to the heat energy transferred during a chemical reaction at constant pressure. It's a critical concept in thermochemistry, indicating whether a reaction is exothermic (releases heat) or endothermic (absorbs heat).

To find the enthalpy change for a reaction, standardized H values are used, often referred to as the standard enthalpy of formation or reaction. This value tells us the amount of heat that is either absorbed or released when a reaction occurs under standard conditions for every mole of substance involved.

Understanding enthalpy change is crucial because it affects how chemical reactions proceed and can be a determining factor in the feasibility of industrial chemical processes. In our problem, the enthalpy change for the reaction was found to be -622.2 kJ/mol, implying the reaction is exothermic; heat is released, making the surroundings hotter.

Ideal Gas Law

The ideal gas law is a fundamental equation in chemistry relating the pressure (P), volume (V), temperature (T), and number of moles (n) of an ideal gas with the gas constant (R). The mathematical expression of this law is PV = nRT.

It's widely used to calculate one of the four variables if the other three are known. Real gases approximate ideal behavior at high temperatures and low pressures, where the gas molecules are far apart and do not interact significantly.

In applying the ideal gas law, ensure that units are consistent and appropriate. For example, pressure should be in atmospheres (atm), volume in liters (L), temperature in kelvins (K), and the gas constant (R) has a value of 0.08206 L atm/mol K. With these in hand, you can predict the behavior of gases under various conditions, like in our exercise where we used it to determine the moles of steam produced.

Stoichiometry

Stoichiometry is at the heart of the quantitative interpretation of chemical reactions. It involves using the balanced chemical equation to calculate the masses, volumes, and moles of reactants and products.

In practice, this can show us how much product can be formed from a given amount of reactant or how much reactant is needed to create a desired amount of product—a crucial element in both laboratory and industrial chemical processes.

For our reaction, by first determining the moles of steam produced and knowing the enthalpy change per mole, the stoichiometry allows us to calculate the total heat evolved during the reaction. It's a clear illustration of how stoichiometry can bridge the gap between the microscopic world of atoms and molecules and the macroscopic world of grams and liters that we measure practically.