In the Combustion of Ethane, How Many Moles of Co2 Can Be Produced From 1.00 Mole of C2h6?

Heat of Reaction

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1937

The Inflame of Reaction (also known and Total heat of Reaction) is the change in the enthalpy of a chemical chemical reaction that occurs at a constant coerce. IT is a thermodynamic unit useful for scheming the amount of energy per mole either released or produced in a reaction. Since enthalpy is derived from pressure, volume, and internal energy, all of which are state functions, enthalpy is also a state function.

Introduction

\(ΔH\), or the change in enthalpy arose as a unit of measurement meant to calculate the vary in Department of Energy of a system when it became too rocky to find the ΔU, or change in the intrinsic muscularity of a system, aside at the same time measure the amount of heat and piece of work exchanged. Given a ceaseless imperativeness, the change in enthalpy can be measured every bit

\[ΔH=q\]

See section on enthalpy for a more detailed explanation.

The notation ΔHº or ΔHº_rxn then arises to explicate the precise temperature and pressure level of the heat of reaction ΔH. The orthodox enthalpy of reaction is symbolized by ΔHº or ΔHº_rxn and can take on both positive and negative values. The units for ΔHº are kiloJoules per mole, or kj/mol.

ΔH and ΔH^º _rxn

• Δ = represents the change in the enthalpy; (ΔH_products -ΔH_reactants)
  • a supportive value indicates the products have greater enthalpy, or that information technology is an endothermic response (heat is required)
  • a negative value indicates the reactants have greater enthalpy, or that it is an exothermal chemical reaction (high temperature is produced)
• º = signifies that the reaction is a standard H change, and occurs at a preset pressure/temperature
• _rxn = denotes that this change is the enthalpy of response

The Casebook State: The standard state of a solid or liquid is the unmixed substance at a insistency of 1 bar ( 10⁵ Dada) and at a related temperature.

The ΔHº_rxn is the basic heat of reaction or standard H of a chemical reaction, and alike ΔH also measures the enthalpy of a reaction. However, ΔHº_rxn takes identify under "standard" conditions, significant that the reaction takes locate at 25º C and 1 atm. The benefit of a measuring ΔH under standard conditions lies in the ability to relate one value of ΔHº to another, since they pass off under the Lapp conditions.

How to Direct ΔH Experimentally

Enthalpy can be measured experimentally through the use of a calorimeter. A calorimeter is an isolated system which has a staunch pressure, so ΔH=q=cp_sp x m x (ΔT)

How to calculate ΔH Numerically

To depend the standard total heat of reaction the standard enthalpy of formation must be utilised. Another, more detailed, form of the standard enthalpy of reaction includes the use of the standard enthalpy of formation ΔH^º _f:

\[ ΔH^\ominus = \sum \Delta v_p \Delta H^\ominus_f\;(products) - \sum \Delta v_r \Delta H^\ominus_f\; (reactants)\]

with

• v_p= stoichiometric coefficient of the intersection from the balanced reaction
• v_r= stoichiometric coefficient of the reactants from the balanced response
• ΔH^º _f= standard enthalpy of formation for the reactants or the products

Since enthalpy is a state function, the heat of reaction depends only on the final and first states, not on the path that the reaction takes. For example, the reaction \( A \rightarrow B\) goes through intermediate steps (i.e. \(C \rightarrow D\)), but A and B stay on uninjured.

Therefore, one can measure the enthalpy of reaction as the sum of the ΔH of the three reactions by applying Hess' Law.

Extra Notes

Since the ΔHº represents the total energy commutation in the reaction this value fire be either positive or negative.

• A plus ΔHº value represents an addition of energy from the reaction (and from the surroundings), resulting in an endothermic response.
• A negative value for ΔHº represents a removal of energy from the reaction (and into the surroundings) and sol the reaction is exothermic.

Exemplar \(\PageIndex{1}\): the combustion of acetylene

Calculate the enthalpy change for the combustion of acetylene (\(\C.E.{C2H2}\))

Result

1) The first stair is to make sure that the equality is balanced and correct. Remember, the burning of a hydrocarbon requires oxygen and results in the production of carbon dioxide and water.

\[\ce{2C2H2(g) + 5O2(g) -> 4CO2(g) + 2H2O(g)}\]

2) Future, locate a table of Common Enthalpies of Formation to look up the values for the components of the reaction (Tabular array 7.2, Petrucci Text)

3) First find the enthalpies of the products:

ΔHº_f CO₂ = -393.5 kJ/groin

Multiply this economic value past the stoichiometric coefficient, which in that case is touch to 4 mole.

v_pΔH^º _f CO₂ = 4 mol (-393.5 kJ/gram molecule)

= -1574 kJ

ΔH^º _f H₂O = -241.8 kJ/mole

The ratio coefficient of this trilobated is equal to 2 mole. So,

v_pΔH^º _f H₂O = 2 mol ( -241.8 kJ/seawall)

= -483.6 kJ

Now bring these two values in plac to arrive the sum of the products

Sum of products (Σ v_pΔHº_f(products)) = (-1574 kJ) + (-483.6 kJ) = -2057.6 kJ

Now, find the enthalpies of the reactants:

ΔHº_f C₂H₂ = +227 kJ/mole

Multiply this value by the stoichiometric coefficient, which in this case is isometric to 2 mol.

v_pΔHº_f C₂H₂ = 2 mol (+227 kJ/mole)

= +454 kJ

ΔHº_f O₂ = 0.00 kJ/mole

The ratio coefficient of this compound is equal to 5 mole. So,

v_pΔHº_f O₂ = 5 mol ( 0.00 kJ/mole)

= 0.00 kJ

Sum up these two values in order to get the sum of the reactants

Sum of reactants (Δ v_rΔHº_f(reactants)) = (+454 kJ) + (0.00 kJ) = +454 kJ

The sum of the reactants and products terminate right away be inserted into the formula:

ΔHº = Δ v_pΔHº_f(products) - ? v_rΔHº_f(reactants)

= -2057.6 kJ - +454 kJ

= -2511.6 kJ

Practice Problems

1. Calculate ΔH if a piece of metal with a ad hoc hot up of .98 kJ·kg−1·K−1 and a mass of 2 kg is heated up from 22^oC to 28^oC.
2. If a calorimeter's ΔH is +2001 Joules, how much heat did the substance inside the cup suffer?
3. Calculate the ΔH of the tailing chemical reaction: CO_{2 (g)} + H₂O _{(g) -->} H₂CO_{3 (g)} if the standard values of ΔH_f are As follows: CO_{2 (g)}: -393.509 KJ /gram molecule, H₂O _(g) : -241.83 KJ/mol, and H₂CO_{3 (g)} : -275.2 KJ/mol.
4. Work out ΔH if a piece of aluminum with a ad hoc oestrus of .9 kJ·kg−1·K−1 and a mass of 1.6 kg is heated from 286^oK to 299^oK.
5. If the calculated value of ΔH is positive, does that gibe to an endothermic reaction or an heat-releasing response?

Solutions

1. ΔH=q=cp_sp x m x (ΔT) = (.98) x (2) x (+6^o) = 11.76 kJ
2. Since the heat gained by the calorimeter is equal to the heat lost by the scheme, and so the subject matter inside must have lost the negative of +2001 J, which is -2001 J.
3. ΔH^º = ∑Δv_pΔH^º _f(products) - ∑Δ v_rΔH^º _f(reactants) so this substance that you tot up the sum of the ΔH's of the products and take off away the ΔH of the products: (-275.2kJ) - (-393.509kJ + -241.83kJ) = (-275.2) - (-635.339) = +360.139 kJ.
4. ΔH=q=cp_sp x m x (ΔT) = (.9) x (1.6) x (13) = 18.72 kJ
5. Endothermic, since a incontrovertible value indicates that the system GAINED heat.

References

1. Petrucci, et alii. General-purpose Chemistry: Principles & Modern Applications. 9th ed. Upper Saddle River, Freshly Jersey 2007.
2. Zumdahl, Steven S., and Susan A. Zumdahl. Chemistry. Boston: Houghton Mifflin Company, 2007.

Contributors and Attributions

• Rachel Martin (UCD), Eleanor Yu (UCD)

In the Combustion of Ethane, How Many Moles of Co2 Can Be Produced From 1.00 Mole of C2h6?

Source: https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Thermodynamics/Energies_and_Potentials/Enthalpy/Heat_of_Reaction

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