Saturday, February 13, 2021

Chapter 6.6 - Thermochemical Equations

In the previous section, we saw ΔHf and ΔHr. In this section, we will see thermochemical equations and various standard enthalpies.

Thermochemical equations can be explained in 3 steps:
1. We saw a number of reactions in the previous section.
• In those reactions, heat was either absorbed or released.
    ♦ We denoted the heat as ΔH
2. When we study chemical reactions which involve heat, we write the ΔH together with the equation.
    ♦ We give the subscripts ‘f’ or ‘r’ which ever is appropriate.
    ♦ Also we give the superscript ‘⊖’ if it was a standard value.
• That ΔH value and the main equation are separated by a semi colon.
3. An example is given below:
C2H5OH(l) + 3O2(g) → 2CO2(g) + 3H2O(l); ΔHr = -1367 kJ mol-1
• This equation describes the combustion of C2H5OH (ethanol) at constant temperature and pressure.
• The negative sign of ΔHr indicates that, it is an exothermic reaction.
• Such equations are called thermochemical equations


Certain rules have to be followed while writing thermochemical equations. There are a total of four rules. Let us see them in detail: 
1. Physical state of reactants and products.
• We must specify the physical state of each of the reactants and products.
• In the example in (3) above,
    ♦ C2H5OH is in the liquid state.
    ♦ O2 is in the gaseous state.
    ♦ CO2 is in the gaseous state.
    ♦ H2O is in the liquid state.
2. Use of balanced equations:
• Only balanced equations should be used in thermochemical equations.
• But coefficients in the balanced equation should be considered as the 'number of moles'. Not as 'number of molecules'.
• For example, the coefficient of C2H5OH in the above equation is ‘one’.
• When one mol C2H5OH undergoes combustion, we get an energy of 1367 kJ
   ♦ One mol C2H5OH is 46.07 grams.
   ♦ So when 46.07 grams of C2H5OH burns, we get 1367 kJ
• Obviously, one molecule of C2H5OH will not give so much energy.
3. Magnitude of energy:
• The magnitude of the ΔHr value given after the semi colon should correspond exactly to the number of moles in the balanced equation.
• The importance of this rule can be explained using an example:
(i) Consider the reaction: Fe2O3(s) + 3H2(g) → 2Fe(s) + 3H2O(l)
• Let us find the ΔHr of this reaction.
• From the data book, we have:
    ♦ ΔHr[Fe2O3(s)] = -824.2 kJ mol-1
    ♦ ΔHr[H2(g)] = 0
    ♦ ΔHr[Fe(s)] = 0
    ♦ ΔHr[H2O(l)] = -285.83 kJ mol-1 
• So ΔHr = [2(0) + 3(-285.83)] - [1(-824.2) +3(0)] = -33.3 kJ mol-1
(ii) That means, 33.3 kJ is released.
• This much energy is released when one mol Fe2O3(s) reacts with three mol H2(g)
• We will denote it as: ΔHr(1)
(iii) So we can write the thermochemical equation:
Fe2O3(s) + 3H2(g) → 2Fe(s) + 3H2O(l); ΔHr(1) = -33.3 kJ mol-1
(iv) Let us divide the equation in (i) through out by 2. We get:
12Fe2O3(s) + 32H2(g) → Fe(s) + 32H2O(l)
• The new ΔHr value will be:
[(0) + 32(-285.83)] - [12(-824.2) +32(0)] = -16.6 kJ mol-1
(v) That means, 16.6 kJ is released.
• This much energy is released when 12 mol Fe2O3(s) reacts with 32 mol H2(g)
• We will denote it as: ΔHr(2)
(vi) So we can write the new thermochemical equation:
12Fe2O3(s) + 32H2(g) → Fe(s) + 32H2O(l); ΔHf(2) = -16.6 kJ mol-1
• Note that: ΔHr(2) is equal to 12 of ΔHr(1)
(vii) Thus we can write:
• The energy absorbed or released will depend on the coefficients in the balanced equation.
• As a consequence, the energy absorbed or released will depend on the quantity of reactants taken.
• We cannot say that, the reaction between Fe2O3 and H2 will always give 33.3 kJ energy. It will depend on the quantity of reactants taken.
4. Reversing the equation:
• When a thermochemical equation is reversed:
    ♦ sign of the ΔHr is reversed.
    ♦ magnitude of remains the same.
• For example:
   ♦ N2(g) + 3H2(g) → 2NH3(g); ΔHr = -91.8 kJ mol-1
   ♦ is the reverse of
   ♦ 2NH3(g) → N2(g) + 3H2(g); ΔHr = 91.8 kJ mol-1
• It is clear that:
    ♦ When 1 mol N2 combines with 3 mol H2 to form 2 mol NH3, 91.8 kJ is released.
    ♦ To decompose 2 mol NH3 into 1 mol N2 and 3 mol H2, we have to supply 91.8 kJ


Enthalpy changes during phase transformations

• We know that phase transformations involve energy changes.
• So we can specify standard enthalpy changes for such transformations.
• First we will see enthalpy change for fusion. It can be explained in 5 steps:
1. When ice melts to become water, heat is absorbed by the ice.
• This melting takes place at constant pressure and constant temperature (273 K)
2. Using calorimetry, scientists have calculated that:
    ♦ 1 mole of ice at 273 K requires
    ♦ 6.00 kJ heat
    ♦ to transform into water at 273 K
3. Based on this, we can write the thermochemical equation:
H2O(s) → H2O(l); ΔHfus = 6.00 kJ mol-1
• Note that, instead of 'r', the subscript is 'fus'. This is to indicate 'fusion'.
• Fusion is the conversion from solid state to liquid state.
4. ΔHfus is called the standard enthalpy of fusion.
• It is also known as the molar enthalpy of fusion.
◼ It is the amount of energy required for the melting of one mole of a solid substance in standard state.
5. We know that, melting is an endothermic process. So ΔHfus will be always positive.


• Next we will see enthalpy change for vaporization. It can be explained in 5 steps:
1. When water boils to become steam, heat is absorbed by the boiling water.
• This boiling takes place at constant pressure and constant temperature (373 K)
2. Using calorimetry, scientists have calculated that:
    ♦ 1 mole of water at 373 K requires
    ♦ 40.79 kJ heat
    ♦ to transform into steam at 373 K
3. Based on this, we can write the thermochemical equation:
H2O(l) → H2O(g); ΔHvap = 40.79 kJ mol-1
• Note that, instead of 'r', the subscript is 'vap'. This is to indicate 'vaporization'.
• Vaporization is the conversion from liquid state to gaseous state.
4. ΔHvap is called the standard enthalpy of vaporization.
• It is also known as the molar enthalpy of vaporization.
◼ It is the amount of energy required for the vaporization of one mole of a liquid substance at constant temperature and standard pressure (1 bar)
5. We know that, vaporization is an endothermic process. So ΔHvap will be always positive.


• We have seen that, the ΔHvap of water is 40.79 kJ mol-1
• Now is a good time to see the relation between the following two items:
   ♦ Study of heat in chemistry.
   ♦ Study of heat in physics.
• The relation can be written in 8 steps:
1. One mole of water at 100 C requires 40.79 kJ
2. One mol H2O is 18 grams of H2O
   ♦ So 18 grams require 40.79 kJ
   ♦ Then one gram will require (40.7918) kJ
   ♦ Then one kg will require (40.7918 × 1000) = 2266.11 kJ
3. In physics classes, we see that:
One kg of water at 100 C requires 2260 kJ to completely change into water vapour at 100 C (In physics, this is called the latent heat of vaporization of water)
• Both values are identical. But the approaches are different.
• The following steps from (4) to (8) explains the difference between the two approaches.
4. In chemistry, we consider the enthalpy change.
   ♦ Let UA be the internal energy of water at 100 C
   ♦ Let UB be the internal energy of steam at 100 C
5. We can write: UB = UA + QP – P(VB – VA)
⇒ UB – UA + P(VB - VA) = QP 
⇒ ΔU + W = QP
6. That means, QP (the heat supplied at constant pressure) is utilized for two items:
   ♦ Increasing the internal energy.
   ♦ Doing work for expansion against the constant pressure.
7. Also recall that, the left side of (5) can be written as:
(UB + PVB) – (UA + PVA)
• This is same as HB – HA
• So QP = (HB – HA) = ΔH
• ΔH is enthalpy change.
8. QP for water is the same (40.79 kJ mol-1 or 2260 kJ kg-1) in both physics and chemistry.
   ♦ In chemistry, we write it in terms of enthalpy change.
   ♦ In physics, we write it in terms of ‘internal energy change’ and ‘work’.


Solved example 6.14
A swimmer coming out from a pool is covered with a film of water weighing about 18g. How much heat must be supplied to evaporate this water at 298 K? Calculate the internal energy of vaporisation at 298K. Given: ΔHvap of water at 298 K = 44.01 kJ mol-1
Solution:
Part (I):
1. Mass of the water film = 18 gram
• Molar mass of water = 18 gram
• So number of moles in the film = mass of filmmolar mass = 1818 = 1
2. ΔHvap of water at 298 K =  44.01 kJ for one mol
• So heat required by the film = 44.01 kJ
Part (II):
1. We have: ΔU + W = QP (see step 5 in the previous discussion)
• QP is the heat absorbed at constant pressure. In our present case, it is 44.01 kJ
• So, if we can find W, the only unknown will be ΔU
2. So our next task is to find W.
• We have: W = P(VB – VA)
• Recall that, P(VB – VA) is equal to ngRT
Where ng = number of gaseous moles in state B – number of gaseous moles in state A.
(see Eq.6.6 in section 6.2)
3. In our present case, ng = (1-0) = 1
• So we get: W = ngRT
= 1 (mol) × 8.314 × 10-3 (kJ mol-1 K-1) × 298 (K) = 2.477 kJ
• Substituting this in (1), we get:
ΔU + 2.477 = 44.01
⇒ ΔU = 41.53 kJ

Solved example 6.15
Assuming the water vapour to be a perfect gas, calculate the internal energy change when 1 mol of water at 100°C and 1 bar pressure is converted to ice at 0°C. Given:
   ♦ Enthalpy of fusion of ice is 6.00 kJ mol-1
   ♦ Heat capacity of water is 4.2 J g-1 K-1
Solution:
• One mole of water at boiling point (100 C) is being converted into ice at 0 C
• We will do this problem in two stages:
Stage 1: Water at 100 C is converted into water at 0 C
1. We have: ΔU + W = QP
• QP is the heat absorbed or released at constant pressure.
   ♦ In our present case, it is the heat released because, water cools from 100 C to 0 C
• So, if we can find QP and W, the only unknown will be ΔU
2. First we will find QP
• We know that, heat absorbed or released is given by mCΔT
• One mol water is 18 gram water. So m = 18 gram
• C is given as 4.2 J g-1 K-1
• So QP = 18 (g) × 4.2 (J g-1 K-1) × 100 (K-1) = 7560 J = 7.56 kJ
3. Our next task is to find W
• We have: W = P(VB – VA)
• Recall that, P(VB – VA) is equal to ngRT
Where ng = number of gaseous moles in state B – number of gaseous moles in state A.
(see Eq.6.6 in section 6.2)
4. In our present case, ng = (1-1) = 0
• So we get: W = 0
• Substituting the known values in (1), we get:
ΔU + 0 = 7.56
⇒ ΔU = 7.56 kJ

Stage 2: Water at 0 C is converted into ice at 0 C
1. We have: ΔU + W = QP
• QP is the heat absorbed or released at constant pressure.
   ♦ In our present case, it is the heat released because, when ice is formed, heat is released even if it is a process at constant temperature.
• So, if we can find QP and W, the only unknown will be ΔU
2. First we will find QP
• We know that, heat released during formation of ice is same as:
The enthalpy of fusion of ice.
   ♦ It is given to us: 6.00 kJ mol-1
• In our present case, the quantity is one mole.
• So QP = 6.00 kJ
3. Our next task is to find W.
• We have: W = P(VB – VA)
• Recall that, P(VB – VA) is equal to ngRT
Where ng = number of gaseous moles in state B – number of gaseous moles in state A
(see Eq.6.6 in section 6.2)
4. In our present case, ng = (1-1) = 0
• So we get: W = 0
• Substituting the known values in (1), we get:
ΔU + 0 = 6.00
⇒ ΔU = 6.00 kJ
◼  Combining the two stages, we get:
Total change in internal energy = (7.56 + 6.00) = 13.56 kJ


• Next we will see enthalpy change for sublimation. It can be explained in 5 steps:
1. When dry ice sublimes to become 'gaseous CO2', heat is absorbed by the dry ice.
• This process takes place at constant pressure and constant temperature (195 K).
2. Using calorimetry, scientists have calculated that:
    ♦ 1 mole of dry ice at 195 K requires
    ♦ 25.2 kJ heat
    ♦ to transform into gaseous CO2 at 195 K
3. Based on this, we can write the thermochemical equation:
CO2(s) → CO2(g); ΔHsub = 25.2 kJ mol-1
• Another example is naphthalene. It sublimes slowly
   ♦ The ΔHsub value is 73.0 kJ mol-1
• Note that, instead of 'r', the subscript is 'sub'. This is to indicate 'sublimation'.
• Sublimation is the direct conversion from solid state to gaseous state.
4. ΔHsub is called the standard enthalpy of sublimation.
• It is also known as the molar enthalpy of sublimation.
◼ It is the amount of energy required for the sublimation of one mole of a solid substance at constant temperature and standard pressure (1 bar).
5. We know that, sublimation is an endothermic process. So ΔHsub will be always positive.


• Based on the sublimation temperature of dry ice, we can write some interesting points about heat. It can be written in 6 steps:
1. We saw that, dry ice sublimes at 195 K.
• In Celsius scale, this temperature is (273.15 – 195) = - 78.15 C
2. Imagine a room with some blocks of dry ice.
• Let the temperature inside the room be -80 C
• This is lower than -78.15 C. So the dry ice can easily remain in the solid state.
3. Let the temperature be gradually increased to -75 C
• As soon as the temperature reaches -78.15 C, the dry ice will begin to sublime.
4. Remember that, sublimation of dry ice requires 25.2 kJ mol-1
• So our present sublimation indicates that, heat is flowing into the dry ice.
5. -78.15 C is too cold for us humans
• We see that, heat can flow even at such low temperatures.
• Due to the heat flow, the dry ice sublimes at -78.15 C
• -78.15 C is too hot for dry ice.
6. We can write:
• We use the words heat, hotness and heat flow commonly in our day to day life.
• The hotness experienced by one person may not be so hot for another person.
• For example, a tourist visiting a 'place with hot climate' may find the heat unbearable. But the same heat may not affect a native.
• However, in science, those words have precise definitions.


• Next we will see enthalpy change for combustion. It can be explained in 5 steps:
1. When cooking gas (butane) undergoes combustion, heat is released.
2. Using calorimetry, scientists have calculated that:
    ♦ 1 mole of butane releases
    ♦ 2658.0 kJ heat
3. Based on this, we can write the thermochemical equation:
C4H10(g) + 13/2 O2(g) → 4CO2 (g) + 5H2O(l); ΔHc = -2658.0 kJ mol-1
• Note that, instead of 'r', the subscript is 'c'. This is to indicate 'combustion'.
• Combustion is the reaction with oxygen.
• Another example is the combustion of glucose. The thermochemical equation is:
C6H12O6(s) + 6O2(g) → 6CO2 (g) + 6H2O(l); ΔHc = -2802.0 kJ mol-1
4. ΔHc is called the standard enthalpy of combustion.
• It is also known as the molar enthalpy of combustion.
◼ It is the amount of energy released when one mole of a substance undergoes combustion. The reactants and products should be in their standard states.
5. We know that, combustion is an exothermic process. So ΔHc will be always negative.


• We have seen:
Enthalpy of formation, reaction, fusion, vaporization, sublimation and combustion.
• We have also seen calorimetry and thermochemical equations.
• Based on those topics, we will see some solved examples. The link is given below:
Solved examples 6.16 to 6.21
• Next we have to see:
Enthalpy of atomization, bond, lattice and solution.
• But before that, we have to see Hess’s law. We will see it in the next section.


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