Thermochemistry

Thermochemistry is the study of the energy and heat associated with chemical reactions and/or physical transformations. A reaction may release or absorb energy, and a phase change may do the same, such as in melting and boiling. Thermochemistry focuses on these energy changes, particularly on the system's energy exchange with its surroundings. Thermochemistry is useful in predicting reactant and product quantities throughout the course of a given reaction. It is also used to predict whether a reaction is spontaneous or non-spontaneous, favorable or unfavorable. Endothermic reactions absorb heat. Exothermic reactions release heat. Thermochemistry coelesces the concepts of thermodynamics with the concept of energy in the form of chemical bonds. The subject commonly includes calculations of such quantities as heat capacity, heat of combustion, heat of formation, enthalpy, entropy, free energy, and calories.

History

Thermochemistry rests on two generalizations. Stated in modern terms, they are as follows:

1. Lavoisier and Laplace’s law (1780): The energy change accompanying any transformation is equal and opposite to energy change accompanying the reverse process.
2. Hess' law (1840): The energy change accompanying any transformation is the same whether the process occurs in one step or many.

These statements preceded the first law of thermodynamics (1845) and helped in its formulation.

Edward Diaz and Hess also investigated specific heat and latent heat, although it was Joseph Black who made the most important contributions to the development of latent energy changes.

Gustav Kirchhoff showed in 1858 that the variation of the heat of reaction is given by the difference in heat capacity between products and reactants: dΔH / dT = ΔC_p. Integration of this equation permits the evaluation of the heat of reaction at one temperature from measurements at another temperature.

Calorimetry

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Calorimetry is the quantitative measurement of the heat required or evolved during a chemical process. A Calorimeter is an instrument for measuring the heat of a reaction during a well defined process. The following diagram depicts a constant volume or 'bomb' calorimeter:
   You may see a much simpler, but less accurate calorimeter in the laboratory, which, by its construction, is necessarily constant pressure:

Constant volume calorimetry measures the Internal Energy change between Reactants and Products, but constant pressure calorimetery measures directly the Enthalpy change during the reaction.  These two heats are slightly different when gases are evolved or consumed during the transformation. (Gases evolved expand if at constant pressure and thus do Work in the surroundings. This energy must come from somewhere...)Both constant volume and constant pressure instruments use the fact that the heat evolved from the reaction changes the temperature of a working substance (usually a water bath) with a known heat capacity. Thus a measurement of the temperature rise in the surroundings (calorimeter body) allows a determination of the heat crossing the boundary between the system (where the reaction takes place) and the surroundings (where the temperature change is measured). For technical reasons, it is usually more accurate to measure constant volume heat flow (Internal Energy changes) and thus 'bomb' calorimeters are used almost exclusively for important measurements. We usually assume that the heat capacity of a given substance is roughly constant (independent of temperature) over a small changes in temperature. (If we need to be more accurate, we can correct for this assumption, but we won't do that in this course). Every substance has a heat capacity, and the values of this property vary greatly with that substance. There are a couple of things that we can say universally about this property:

Comments on Heat Capacity...

• The Heat Capacity itself is extensive (scales with the size of system), but we can think of making this quantity intensive (making it an intrinsic property of the material) by defining related quantities:
•     the Molar Heat Capacity is defined as the Heat Capacity of a homogeneous pure compound (or element) divided by the the number of moles of that compound (or element)
•     the Specific Heat is defined as the Heat Cpacity of a homogeneous sample divided by its mass.
• The Heat Capacity of any substance is positive.
• The Heat Capacity is discontinuous at phase transitions.
• For a gas, the Heat capacity depends on how one does the heating. The Heat Capacity at constant Volume, C_V, and the Heat Capacity at constant pressure, C_p, for any given substance are are almost exactly equal if the substance is a solid or a liquid.  This means that for a liquid or a solid, the heat capacity doesn't depend on how you perform the heating. C_p and C_V are not equal for a gas;  C_p is always greater than C_V by a constant value. For one mole of gas, the difference between C_p and C_V is the constant R (R is the so called universal gas constant)  and represents the capacity of the gas to perform expansion work at constant applied pressure. {C_p = C_V+R for an ideal gas}  Since, for solids and liquids, the constant pressure and constant volume Heat Capacities are the same, the subscript p or V on the 'C' is usually dropped.
• Q = m C DT
This means that the proportionality between the Heat flow into (or out of) an object and the Temperature change of that object is the total Heat Capacity, which can be expressed as a molar property or per mass.
• if m is moles and C is molar Heat Capacity
• if m is mass (grams) and C is the Specific Heat
• Q is positive for a temperature increase because the system has undergone an endothermic change of state

Here is a list of some Heat Capacities
Note: The molar heat capacities of most metals around room temperature are all around 25 J/K^.g. This is because the capacity to accomodate energy depends on the number of metal atoms. 

Example Calorimeter Calculations 

  a.) A constant pressure calorimeter where the water bath has a mass of 150 grams.  1.00 g of diamond is burned to produce CO₂ and Water.  If the water bath in the Calorimeter is initially at 22 ^oC, what is the final temperature of the Calorimeter?   First, let's write a balanced chemical reaction for the combustion
C _(diamond) + O_{2 (gas)} = CO_{2 (gas)}
Next, the molar heat of reaction comes from the Heats of  Formation of the products minus the reactants.
DH_rxn = -393.5 kJ/mol - (1.88 kJ/mol + 0) = -395.4 kJ/mol
The actual heat released by 1.00g /12.011 g/mol = 8.326 x 10^-2 mol of diamond is
Q = (-395.4 kJ/mol) (8.326 x 10^-2 mol) = -3.292 x 10⁴ J
The temperature rise is the heat provided to the water (-Q) divided by the mass times the specific heat of water
DT = 3.292 x 10⁴ J/ ((150. g)(4.184 J/K.g) = 52.5 K
The final temperature of the water bath is then
T_final = 22 + 52.5 = 74.5 ^oC
b.) If 0.500 gram of another substance, H₂CO, is burned in the same Calorimeter, and the temperature of the bath in the calorimeter (150 g H₂0) changes from 24.0 to 39.2 ^oC, what is the molar heat of formation of the H₂CO? Again, lets see what kind of reaction we should have in the reactor
H₂CO _(gas) + O_{2 (gas)} = CO_{2 (gas)} + H₂O _(l)
So the Heat of that reaction for 0.500 g / 30.03 g/mol = 1.665 x 10^-2 mol of formaldehyde raised the temperature of 150. g of water by 15.2 K.  That means the heat released by that amount of reaction liberated:
-Q = (150 g)(4.184 J/g.K)(15.2 K) = 9.540 kJ
of heat.  One mole of reaction would liberate
-Q = 9.540 kJ/(1.665 x 10^-2 mol) = 572.9 kJ/mole
which is the heat of combustion, DH_comb, of formaldehyde.
The heat of formation of formaldehyde, DH_form{formaldehyde}, is related to the heat of combustion as:
DH_comb = DH_form{water (l)} + DH_form{CO_{2 (gas)}} - DH_form{formaldehyde}
So
-572.9 kJ/mol = -285.8 kJ/mol + -393.5 kJ/mol - DH_form{formaldehyde}
or
DH_form{formaldehyde} = -106.4 kJ/mol

 

Systems

Several thermodynamic definitions are very useful in thermochemistry. A system is the specific portion of the universe that is being studied. Everything outside the system is considered the surrounding or environment. A system may be: an isolated system — when it cannot exchange energy or matter with the surroundings, as with an insulated bomb reactor; a closed system — when it can exchange energy but not matter with the surroundings, as with a steam radiator; an open system — when it can exchange both matter and energy with the surroundings, as with a pot of boiling water.

Processes

A system undergoes a process when one or more of its properties changes. A process relates to the change of state. An isothermal (same temperature) process occurs when temperature of the system remains constant. An isobaric (same pressure) process occurs when the pressure of the system remains constant. An adiabatic (no heat exchange) process occurs when no heat exchange occurs.

Laws of Thermochemistry

 Understanding Enthalpy and Thermochemical Equations

Thermochemical equations are just like other balanced equations except they also specify the heat flow for the reaction. The heat flow is listed to the right of the equation using the symbol ΔH. The most common units are kilojoules, kJ. Here are two thermochemical equations:

H₂ (g) + ½ O₂ (g) → H₂O (l); ΔH = -285.8 kJ

HgO (s) → Hg (l) + ½ O₂ (g); ΔH = +90.7 kJ

When you write thermochemical equations, be sure to keep the following points in mind:

1. Coefficients refer to the number of moles. Thus, for the first equation, -282.8 kJ is the ΔH when 1 mol of H₂O (l) is formed from 1 mol H₂ (g) and ½ mol O₂.
2. Enthalpy changes for a phase change, so the enthalpy of a substance depends on whether is it is a solid, liquid, or gas. Be sure to specify the phase of the reactants and products using (s), (l), or (g) and be sure to look up the correct ΔH from heat of formation tables. The symbol (aq) is used for species in water (aqueous) solution.
3. The enthalpy of a substance depends upon temperature. Ideally, you should specify the temperature at which a reaction is carried out. When you look at a table of heats of formation, notice that the temperature of the ΔH is given. For homework problems, and unless otherwise specified, temperature is assumed to be 25°C. In the real world, temperature may different and thermochemical calculations can be more difficult.

Certain laws or rules apply when using thermochemical equations:

1. ΔH is directly proportional to the quantity of a substance that reacts or is produced by a reaction.
   Enthalpy is directly proportional to mass. Therefore, if you double the coefficients in an equation, then the value of ΔH is multiplied by two. For example:
   H₂ (g) + ½ O₂ (g) → H₂O (l); ΔH = -285.8 kJ
   2 H₂ (g) + O₂ (g) → 2 H₂O (l); ΔH = -571.6 kJ
2. ΔH for a reaction is equal in magnitude but opposite in sign to ΔH for the reverse reaction.
   For example:
   HgO (s) → Hg (l) + ½ O₂ (g); ΔH = +90.7 kJ
   Hg (l) + ½ O₂ (l) → HgO (s); ΔH = -90.7 kJ
   This law is commonly applied to phase changes, although it is true when you reverse any thermochemical reaction.
3. ΔH is independent of the number of steps involved.
   This rule is called Hess's Law. It states that ΔH for a reaction is the same whether it occurs in one step or in a series of steps. Another way to look at it is to remember that ΔH is a state property, so it must be independent of the path of a reaction.
   If Reaction (1) + Reaction (2) = Reaction (3), then ΔH₃ = ΔH₁ + ΔH₂

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   Heat and Enthalpy Changes
   
   When a chemical reaction occurs in an open container most of the energy gained or lost is in the form of heat. Almost no work is done (i.e. nothing is being moved).
   Heat flows between the system and surroundings until the two are at the same temperature.
   • When a chemical reaction occurs in which the system absorbs heat, the process is endothermic (it feels cold)
   • When a chemical reaction occurs in which the system produces heat it is exothermic (it feels hot)
   EnthalpyUnder conditions of constant pressure (e.g. most biological processes under constant atmospheric pressure) the heat absorbed or released is termed enthalpy (or "heat content").
   We do not measure enthalpy directly, rather we are concerned about the heat added or lost by the system, which is the change in enthalpy (or DH).
   In formal terms: The change in enthalpy, DH, equals the heat, q_p, added to or lost by the system when the process occurs under constant pressure:
   
   DH=q_p
   DH represents the difference between the enthalpy of the system at the beginning of the reaction compared to what it is at the end of the reaction:
   DH = H_final - H_initial
   We are considering the enthalpic state of the system. Thus:
   • if the system has higher enthalpy at the end of the reaction, then it absorbed heat from the surroundings (endothermic reaction)
   • if the system has a lower enthalpy at the end of the reaction, then it gave off heat during the reaction (exothermic reaction)
   Therefore:
   • For endothermic reactions H_final > H_initial and DH is positive (+DH)
   • For exothermic reactions H_final < H_initial and DH is negative (-DH)

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   Enthalpies of Reaction
   
   Because the enthalpy change for a reaction is described by the final and initial enthalpies:
   DH = H_final - H_initial
   we can also describe DH for a reaction by comparing the enthalpies of the products and the reactants:
   DH = H(products) - H(reactants)
   The enthalpy change that accompanies a reaction is called the enthalpy of reaction (DH_rxn).
   It is sometimes convenient to provide the value for DH_rxn along with the balanced chemical equation for a reaction (also known as a thermochemical equation):
   2H₂(g) + O₂(g) -> 2H₂O(g) DH = -483.6 kJ
   Note the following:
   • DH is negative, indicating that this reaction results in the release of heat (exothermic)
   • The reaction gives of 483.6 kilo Joules of energy when 2 moles of H₂ combine with 1 mole of O₂ to produce 2 moles of H₂O.
   The relative enthalpies of the reactants and products can also be shown on an energy diagram:
   
   Properties of enthalpy:
   1. Enthalpy is an extensive property. The magnitude of DH is dependent upon the amounts of reactants consumed. Doubling the reactants, doubles the amount of enthalpy.
   2. Reversing a chemical reaction results in the same magnitude of enthalpy but of the opposite sign. For example, splitting two moles of water to produce 2 moles of H₂ and 1 mole of O₂ gas requires the input of +483.6 kJ of energy.
   3. The enthalpy change for a reaction depends upon the state of the reactants and products. The states (i.e. g, l, s or aq) must be specified.
   CH₄(g) + 2O₂(g) -> CO₂(g) + 2H₂O(g) DH = -802 kJ
   Given the above thermochemical equation for the combustion of methane, how much heat energy is released when 4.5 grams of methane is burned (in a constant pressure system)?
   
   
   The negative sign (exothermic) indicates that 225.5 kJ of energy are given off by the system into the surroundings.

Heat Transfer

1.