Calculate Heat of Reaction at an Elevated Temperature

LearnChemE
13 Oct 202005:23
EducationalLearning
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TLDRThe script explains a method to calculate the heat of reaction at 600 Kelvin using temperature-dependent heat capacities and heats of formation at 298 Kelvin. It involves cooling hydrazine to 298K, reacting it to form nitrogen and hydrogen, and then heating the products back to 600K. The process is detailed with integral calculations of heat capacities and the use of a spreadsheet to determine the final heat of reaction, illustrating the temperature effect on reaction heat.

Takeaways
  • 🔍 The script discusses calculating the heat of reaction at 600 Kelvin using heat capacities that vary with temperature.
  • 🌡 The process involves using the heat of formation at 298 Kelvin and adjusting for the temperature change to 600 Kelvin.
  • 🔗 The concept of state functions is utilized, allowing for the calculation through a series of steps involving cooling and heating.
  • ⚛ The reaction of interest is the decomposition of hydrazine into nitrogen and hydrogen at 600 Kelvin.
  • 📊 The calculation requires integrating the heat capacities of the products and reactants over the temperature range.
  • 📚 Heat capacities are given as a function of temperature with constants A, B, C, and D for hydrazine.
  • 📈 The integral calculation for the heat change involves evaluating the polynomial expression of heat capacity over the specified limits.
  • ⚖ The heat of reaction at 298 Kelvin is derived from the heats of formation of the products and reactants, with some being zero.
  • 🔢 The units of heat capacities are in joules per mole per Kelvin, and the calculated heat changes are converted to kilojoules per mole.
  • 📊 A spreadsheet is used to perform the calculations and to show how the heat capacity and thus the heat of reaction changes with temperature.
  • 📉 The final calculated heat of reaction at 600 Kelvin is approximately 88.7 kilojoules per mole, indicating a change with temperature.
  • 📋 The script also includes a data table in the spreadsheet to visualize how the heat capacity varies over a range of temperatures.
Q & A

  • What is the primary goal of the process described in the script?

    -The primary goal is to calculate the heat of reaction at 600 Kelvin for the reaction of hydrazine to nitrogen and hydrogen using heat capacities that are a function of temperature.

  • Why is it necessary to cool hydrazine down to 298 Kelvin before the reaction?

    -It is necessary because the heat of formation data for the reaction at 298 Kelvin is readily available from tables, allowing for a more straightforward calculation.

  • What is the significance of state functions in this calculation?

    -State functions allow for the calculation of the heat of reaction by considering the system's state at different temperatures and integrating the heat capacities over the temperature range.

  • How many steps are involved in calculating the heat of reaction at 600 Kelvin?

    -There are three steps involved: cooling hydrazine to 298K, carrying out the reaction at 298K, and heating the products back up to 600K.

  • What formula is used to integrate the heat capacity of hydrazine from 600 to 298 Kelvin?

    -The formula used is the integral of (A + B*T + C*T^2 + D*T^3), where A, B, C, and D are constants representing the heat capacity of hydrazine.

  • What is the unit of heat capacities provided in the script?

    -The heat capacities are provided in joules per mole per Kelvin.

  • How does the heat of reaction at 298 Kelvin relate to the heat of formation of the products and reactants?

    -The heat of reaction at 298 Kelvin is calculated as the sum of the heats of formation of the products minus the heat of formation of the reactants.

  • What is the final calculated heat of reaction at 600 Kelvin in kilojoules per mole?

    -The final calculated heat of reaction at 600 Kelvin is 88.7 kilojoules per mole.

  • How does the heat of reaction change over a 300 Kelvin temperature range?

    -The heat of reaction changes from approximately -95 kilojoules per mole at 298 Kelvin to -88.7 kilojoules per mole at 600 Kelvin.

  • What tool is used to perform the calculations and create a data table in the script?

    -A spreadsheet is used to perform the calculations and create a data table showing how the heat capacity changes over a temperature range.

Outlines
00:00
🔥 Calculating Reaction Heat at Different Temperatures

This paragraph discusses a method for calculating the heat of reaction at 600 Kelvin using heat capacities that vary with temperature. The process involves cooling hydrazine to 298 Kelvin, performing the reaction at this temperature, and then heating the products back to 600 Kelvin. The heat capacities for nitrogen, hydrogen, and hydrazine are integrated over the temperature range, and the heat of formation from tables is used to determine the heat of reaction at 298 Kelvin. The calculation is detailed, including the integration of heat capacity equations and the use of stoichiometric coefficients. The final result is a heat of reaction at 600 Kelvin, which is found to be 88.7 kilojoules per mole, demonstrating a change in heat reaction over a 300 Kelvin temperature range.

05:01
📊 Heat Capacity Variation Over Temperature

In this paragraph, the focus shifts to a data table created in a spreadsheet, which illustrates how heat capacity changes over a range of temperatures. This additional information provides a visual representation of the temperature dependence of heat capacities, which is crucial for understanding the behavior of substances in different thermal conditions. The data table complements the theoretical calculations by showing empirical trends in heat capacity, which can be useful for further analysis and applications in thermodynamics.

Mindmap
Keywords
💡Heat Capacities
Heat capacities are measures of the amount of heat energy required to raise the temperature of a substance by a certain amount. In the context of the video, heat capacities are temperature-dependent and are used to calculate the heat of reaction at different temperatures. The script discusses using heat capacities to determine the heat of reaction for hydrazine at 600 Kelvin, emphasizing the integral role of heat capacities in thermodynamic calculations.
💡Hydrazine
Hydrazine is a chemical compound with the formula N2H4. It is the reactant in the chemical reaction discussed in the video, which reacts to form nitrogen and hydrogen. The script focuses on the reaction of hydrazine at 600 Kelvin and uses it as an example to illustrate the calculation of heat of reaction based on temperature-dependent heat capacities.
💡Nitrogen
Nitrogen is a chemical element with the symbol N and is one of the products of the hydrazine decomposition reaction featured in the video. The script calculates the heat of reaction for the formation of nitrogen from hydrazine, highlighting the importance of nitrogen's heat capacity in the overall thermodynamic process.
💡Hydrogen
Hydrogen is a chemical element with the symbol H and is also a product of the hydrazine decomposition reaction. The script mentions hydrogen twice, indicating that there are two moles of hydrogen produced, which is crucial for the calculation of the integral heat capacity and the overall heat of reaction.
💡State Functions
State functions are properties in thermodynamics that depend only on the current state of a system and not on the path taken to reach that state. The video uses the concept of state functions to calculate the heat of reaction at 600 Kelvin by considering the system's state at 298 Kelvin and then changing it to 600 Kelvin, illustrating the path independence of state functions in thermodynamic calculations.
💡Heat of Reaction
The heat of reaction, or enthalpy change, is the amount of heat absorbed or released in a chemical reaction. The video's main theme revolves around calculating this value at 600 Kelvin for the decomposition of hydrazine. The script details a step-by-step process to determine the heat of reaction using heat capacities and formation heats.
💡Integral
In the context of the video, an integral represents the mathematical process of summing up a series of small quantities to find a total. The script uses integrals to calculate the change in heat (delta H) by integrating the heat capacities of the substances involved over a temperature range, which is essential for determining the heat of reaction at 600 Kelvin.
💡Stoichiometric Coefficients
Stoichiometric coefficients are numbers that indicate the proportion of reactants and products in a balanced chemical equation. The video mentions these coefficients in relation to the heat capacity of nitrogen and hydrogen, showing how they are used in the calculation of the integral heat capacity for the reaction.
💡Heat of Formation
Heat of formation is the change in enthalpy during the formation of a compound from its elements in their standard states. The script refers to the heat of formation for nitrogen and hydrogen to calculate the heat of reaction at 298 Kelvin, using standard values from tables to simplify the process.
💡Spreadsheet
A spreadsheet is a computer application for organization, analysis, and storage of data in tabular form. The video mentions using a spreadsheet to perform calculations and to create a data table that shows how heat capacity changes over a temperature range, demonstrating a practical application of technology in processing thermodynamic data.
💡Temperature Range
The temperature range in the video refers to the difference in temperature between two states of a system, specifically from 298 Kelvin to 600 Kelvin. The script discusses how the heat capacities and the heat of reaction change over this range, emphasizing the importance of temperature in thermodynamic calculations.
Highlights

Use of temperature-dependent heat capacities to calculate heat of reaction at 600 Kelvin.

Hydrazine reacts to form nitrogen and hydrogen at 600 Kelvin, and the heat of reaction at this temperature is the focus.

Concept of state functions utilized to calculate the heat of reaction in three steps: cooling, reaction at 298K, and heating back to 600K.

Heat capacities for nitrogen and hydrogen are integrated from 298 to 600 Kelvin to calculate the first part of the reaction heat.

Hydrazine's heat capacity is integrated from 600 to 298 Kelvin for the second part of the reaction heat calculation.

Integration of heat capacity expressions involves coefficients A, B, C, and D, and is evaluated between temperature limits.

Heat of reaction at 298 Kelvin is derived from heats of formation of reactants and products, with elements having zero heat of formation.

Heat capacities are in joules per mole per Kelvin, requiring conversion to kilojoules for the final heat of reaction calculation.

Heat of reaction at 600 Kelvin is calculated by summing the three delta H values and converting from joules to kilojoules.

Spreadsheet is used to perform calculations and visualize the integration of heat capacities.

Heat of reaction changes over a 300 Kelvin temperature range, indicating the importance of temperature in thermodynamic calculations.

Heat capacities are represented as products of stoichiometric coefficients and their respective heat capacities.

A data table in the spreadsheet shows how heat capacity changes over a range of temperatures.

The concept of delta CP is introduced to represent the difference in heat capacities between reactants and products.

Final heat of reaction at 600 Kelvin is calculated to be 88.7 kilojoules per mole.

The method demonstrates the practical application of thermodynamic principles in calculating reaction heats at different temperatures.

The spreadsheet provides a clear and organized way to perform complex thermodynamic calculations.

Transcripts

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ThermochemistryHeat CapacityIntegral CalculusReaction HeatHydrazine ReactionTemperature Effect298K Reference600K AnalysisEnergy CalculationChemical Engineering