Question

The space shuttle orbiter utilizes the oxidation of methylhydrazine by dinitrogen tetroxide for propulsion: \(4 \mathrm{~N}_{2} \mathrm{H}_{3} \mathrm{CH}_{3}(l)+5 \mathrm{~N}_{2} \mathrm{O}_{4}(l) \longrightarrow 12 \mathrm{H}_{2} \mathrm{O}(g)+9 \mathrm{~N}_{2}(g)+4 \mathrm{CO}_{2}(g)\) Calculate \(\Delta H^{\circ}\) for this reaction using data in Appendix \(4 .\)

Short answer

The standard enthalpy change for the given reaction involving the oxidation of methylhydrazine by dinitrogen tetroxide is approximately \(-4201.3 \space kJ/mol\).

Step-by-step solution

Identify the standard enthalpies of formation for each compound

Look up the standard enthalpies of formation of each compound involved in the reaction in Appendix 4. Here are the values we need: - \(\Delta H_{f}^{\circ}(N_{2}H_{3}CH_{3}(l)) = -80.7 \space kJ/mol\) - \(\Delta H_{f}^{\circ}(N_{2}O_{4}(l)) = 9.7 \space kJ/mol\) - \(\Delta H_{f}^{\circ}(H_{2}O(g)) = -241.8 \space kJ/mol\) - \(\Delta H_{f}^{\circ}(N_{2}(g)) = 0 \space kJ/mol\) (elemental nitrogen is in its standard state) - \(\Delta H_{f}^{\circ}(CO_{2}(g)) = -393.5 \space kJ/mol\)

Calculate the sum of standard enthalpies of formation for reactants and products

Use the coefficients in the balanced equation to find the sum of the standard enthalpies of formation for both the reactants and the products: Reactants: \(4 \times \Delta H_{f}^{\circ}(N_{2}H_{3}CH_{3}(l)) + 5 \times \Delta H_{f}^{\circ}(N_{2}O_{4}(l))\) Products: \(12 \times \Delta H_{f}^{\circ}(H_{2}O(g)) + 9 \times \Delta H_{f}^{\circ}(N_{2}(g)) + 4 \times \Delta H_{f}^{\circ}(CO_{2}(g))\)

Calculate the standard enthalpy change for the reaction

Now, apply the general formula for the standard enthalpy change for the reaction: \[\Delta H^{\circ} = \sum_{i} \Delta H_{f}^{\circ}(\mathrm{Products}) - \sum_{i} \Delta H_{f}^{\circ}(\mathrm{Reactants})\] \[\Delta H^{\circ} = (12 \times (-241.8) + 9 \times 0 + 4 \times (-393.5)) - (4 \times (-80.7) + 5 \times 9.7)\] \[\Delta H^{\circ} = (-2901.6 + 0 - 1574) - (-322.8 + 48.5)\] \[\Delta H^{\circ} = -4475.6 + 274.3\] \[\Delta H^{\circ} = -4201.3 \space kJ/mol\] The standard enthalpy change for the given reaction is approximately \(-4201.3 \space kJ/mol\).

Key concepts

Enthalpy of Formation

The enthalpy of formation, which is also known as the standard heat of formation, represents the change in enthalpy when one mole of a compound is formed from its elements in their standard states. For many chemical reactions, calculating the change in enthalpy on the basis of the enthalpies of formation is quite common. This process helps in understanding how much energy is absorbed or released during the formation process.

In the exercise, we calculated the enthalpy change by utilizing the standard enthalpies of formation for each reactant and product. These values are typically tabulated and can be found in appendices like Appendix 4 mentioned in the solution.

• When elements are in their standard state, their enthalpy of formation is usually zero.
• Compounds have varying enthalpies based on their chemical properties and bonds.
• By subtracting the total potential energy of the reactants from that of the products, the reaction's enthalpy change is determined.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products. This transformation is accompanied by energy changes, often measured as heat in the surroundings. For our exercise, the transformation involves substances that react explosively to release a large amount of energy.

The balanced chemical equation provides us with stoichiometric coefficients, which help determine the ratios and quantities of substances involved. These coefficients are crucial for calculating the enthalpy change as they dictate the amount of energy transferred.

• Reactants are the starting substances in a chemical reaction.
• Products are the substances formed as a result of the reaction.
• The conservation of mass ensures that the mass of reactants equals the mass of products in a closed system.

Oxidation Reactions

Oxidation reactions are a type of chemical reaction where a substance loses electrons, often accompanied by gaining oxygen or losing hydrogen. They are fundamental in the propulsion systems of rockets such as the space shuttle, as seen in our exercise.

The specific reaction between methylhydrazine and dinitrogen tetroxide is a redox reaction, where methylhydrazine acts as a reducing agent and dinitrogen tetroxide acts as an oxidizing agent.

• Redox reactions involve both reduction and oxidation processes.
• These reactions can release significant amounts of energy, which is harnessed to perform work, like propelling a shuttle.
• In balancing these reactions, it is essential to account for both mass and charge conservation.

Thermodynamics in Chemistry

Thermodynamics is the branch of science that deals with the relationships between heat and other forms of energy. In chemistry, it helps in predicting the feasible direction of reactions and the energy changes involved.

The standard enthalpy change calculated in the exercise is a thermodynamic property. It provides insight into the heat exchange under standard conditions, thereby helping us understand the reaction dynamics without conducting an actual experiment.

• First Law of Thermodynamics states that energy can neither be created nor destroyed, only transformed.
• Enthalpy ( H) measures the total heat content of a system.
• The concept of Gibbs free energy combines enthalpy and entropy to determine a reaction's spontaneity.