Chemistry: Unit F322: Chains, Energy and Resources
Moles & Enthalpy
Molar mass is the mass per mole of a substance. A mole of any substance contains 6.03 x
1023 atoms. For elements, the molar mass is simply the relative atomic mass in g mol-1. To
obtain the molar mass of a molecule or compound, you must add together the relative
atomic masses of each atom in the formula.
The molar mass of carbon is 12 g mol-1.
The molar mass of oxygen is 16 g mol-1.
The molar mass of CO2 is 12 + (16 x 2) = 44 g mol-1
The number of moles of a substance can be calculated using the formula:
Number of Moles, n =
Mass
Molar Mass
The concentration of a solution is the amount of solute, in moles, dissolved in each dm3
(1000cm3) of solution. The number of moles in a solution can be calculated using this
formula:
Number of moles = Concentration x Volume in dm3
In order to obtain the volume in dm3 from cm3, divide the volume in cm3 by 1000, so the
formula becomes:
Number of moles = Concentration x Volume in cm3
1000
Enthalpy Changes: Enthalpy is the heat energy that is stored in a chemical system. An
enthalpy change, ΔH, is the heat energy exchange with the environment at constant
pressure.
Products
Enthalpy,
H
Reactants
ΔH -ve
Enthalpy,
H
Products
Reaction Pathway
In an exothermic reaction, ΔH is
negative, because heat is given out to
the surroundings so the reacting
chemicals lose energy.
ΔH +ve
Reactants
Reaction Pathway
In an endothermic reaction, ΔH is
positive, because heat is taken in
from the surroundings so the reacting
chemicals gain energy.
The first law of
thermodynamics
states that energy
may be exchanged
between a chemical
system and the
surroundings but the
total energy remains
constant. Energy
cannot be created nor
destroyed, only
changed from one
form into another.
Determination of Enthalpy Change using Calorimetry
The heat energy transferred in a reaction, q (IN JOULES), can be found using this equation:
Q = m c Δt
where m = mass of water, c = specific heat capacity and Δt is the temperature change.
The enthalpy change of a reaction can be found by:
ΔH = q
n
where q= heat energy transferred
IN KILOJOULES and n= the number
of moles of reactant not in excess.
Step 1: Calculate the energy transfer using q = mcΔt:
m=75 (1cm3 of water weighs 1g)
c = 4.2
t= 12.5
q = 75 x 4.2 x 12.5
q = 3937.5 joules
Step 2: Calculate the enthalpy change using ΔH =
q/n
q = -3.9375 kJ (negative because the reaction was
exothermic, and we have divided b 1000 to get q in
kilojoules rather than joules)
n = number of moles of reactant:
number of moles = mass/ molar mass
= 0.15/46 (the molar mass of ethanol)
n= 0.0036
Q1) The combustion of
0.15g of ethanol
(C2H5OH) in a spirit
burner increased the
temperature of 75cm3 of
water by 12.5˚c.
Calculate the enthalpy of
combustion for ethanol.
ΔH = q/n
= -3.9375 / 0.0036
= -1093.75 kJmol-1
Step 1: Calculate the energy transfer using q = mcΔt:
m=35 (1cm3 of water weighs 1g)
c = 4.2
t= 8.5
Q2) A student added
3.71g of NaHCO3 to
35cm3 of 1.5 moldm-3
HCl(aq). The
temperature fell by 8.5˚.
Calculate the enthalpy
change for the reaction.
q = 35 x 4.2 x 8.5
q = 1249.5 joules
Step 2: Calculate which reactant is not in excess:
No mol NaHCO3 = Mass/Mr = 3.71/84 = 0.044 mol
No mol HCl = Conc x Vol/1000 = 1.5 x 0.035 = 0.0525
The NaHCO3 is not in excess, and this therefore is the
value of n which will be used in ΔH = q/n.
Step 3: Calculate the enthalpy change using ΔH = q/n
q = 1249.5 / 1000 = 1.2495 kJ
n = 0.044 moles
ΔH = q/n
= 1.2495 / 0.044
= 28.4 kJmol-1
Standard enthalpy changes enable scientists to compare the enthalpy changes of
different reactions. A standard enthalpy change must be found using standard
conditions.
ΔH Ѳ refers to an enthalpy change under standard conditions. These conditions are;



A pressure of 100 kPa
A stated temperature, usually 298 K (25˚C) used
A concentration of 1 moldm-3 for aqueous solutions
Standard Enthalpy change of Reaction: ΔH r
The enthalpy change when the amounts of reactants as shown in the reaction
equation react together under standard conditions, all reactants and products being
in their standard states.
H2 + ½ O2
H2 O [ΔHr =-286 kJmol-1]
Standard Enthalpy change of Combustion: ΔH c
The enthalpy change that takes place when one mole of substance reacts completely
with oxygen under standard conditions, all reactants and products being in their
standard states.
CH4 + 2O2
CO2 + 2H2 O [ΔH c =-890 kJmol-1]
Standard Enthalpy change of Formation: ΔH f
The enthalpy change that takes place when one mole of a compound in its standard
state is formed from its constituent elements in their standard states under standard
conditions.
2Na + C + 1 ½ O2
Na2CO3
[ΔH f = -1131 kJmol-1]
Hess’ Law states that the enthalpy change of a reaction depends only on its initial
and final states, and is independent of the route taken. The enthalpy change of the
indirect route = the enthalpy change of the direct route.
A
ΔH1
ΔH2
C
B
ΔH3
Direct Route = Indirect Route
ΔH1 = ΔH2 + ΔH3
Calculating Enthalpy Change from Combustion data
1. Write the balanced symbol equation of what you want to find across the top
2. Write the oxide combustion products at the bottom (H2O and CO2)
3. Work out reaction route – ARROWS POINT DOWNWARDS
Calculate the
standard enthalpy
change of the
formation of
methane, using the
values in the table.
C
ΔHѲc
-394 kJmol-1
-286 kJmol-1
-890 kJmol-1
Substance
Carbon, C
Hydrogen, H2
Methane, CH4
+
2H2
2ΔH3
ΔH2
CO2
CH4
ΔH1
ΔH4
+ 2H2O
ΔH1 = ΔH2 + 2ΔH3 – ΔH4
ΔH1 = [-394 + (2 x -286)] – (-890)
ΔH1 = -76 kJmol-1
Calculating Enthalpy Change from Formation data
The enthalpy of a reaction = the enthalpy change of the formation of the
products - the enthalpy change of the formation of the reactants.
ΔHr = ΣΔHf (products) - ΣΔHf (reactants)
Substance
Methane, CH4
Water, H2O
Carbon Monoxide, CO
Calculate the enthalpy change for the
reaction between methane and steam,
producing carbon monoxide and hydrogen.
CH4 + H2O
ΔHѲf
-75 kJmol-1
-242 kJmol-1
-110 kJmol-1
CO + 3H2
ΔHr = ΣΔHf (products) - ΣΔHf (reactants)
ΔHr = (-110) – [-75+(-242)]
ΔHr = 207 kJmol-1
Average Bond Enthalpy is the average enthalpy change when breaking 1 mole of
bonds in a compound which is in its gaseous state.
Breaking Bonds is an endothermic process. It has a positive sign, as energy must
be put into the system to break the chemical bonds.
Making bonds in an exothermic process. It has a negative sign as energy is
released from the system.
Calculating Enthalpy Change from average bond enthalpies
Calculate the standard
enthalpy change of the
combustion of methane
using average bond
enthalpies.
Bond
C-H
O=O
C=O
O-H
Average Bond
Enthalpy
413
497
740
463
ΔHr = Σ Bonds Broken + Σ Bonds formed
CH4 + 2O2
CO2 + 2H2O
Endothermic – Bonds
are broken, so energy
is taken in (+ve)
4 x C-H = 413x4
2 x O=O = 2x497
= +2646
Exothermic – Bonds
are formed, so energy
is given out (-ve)
2 x C=O = 2 x 740
4 x O-H = 4 x 463
= - 3332
2646 + (-3332)
= -686 kJmol-1