## General Chemistry

The enthalpy change for a chemical reaction (ΔHrxn), also known as the enthalpy of reaction or heat of reaction is often given next to the chemical equation. These are called thermochemical equations.

For example, the enthalpy change for the combustion reaction of methane (CH4), the principal component of natural gas, is given as:

CH4(g) + 2O2(g) → CO2(g) + 2H2O(g) ΔHrxn = -2890.4 kJ

It is important to correctly interpret the information in this equation. First, we conclude that it is an exothermic reaction because of the negative sign of ΔH.

In addition, and this is the focus of this article, it tells us that when 1 mol of CH4 reacts with 2 mol of O2 to form 1 mol of CO2 and 2 mol of H2O, 2890.4 kJ of heat is released. So, the enthalpy change is part of the stoichiometric relationship of the equation just like the molar coefficients.

Therefore, if we are asked to determine the enthalpy change for a certain amount of any reactant or product of the reaction, we can write these relationships as molar conversion factors and do the necessary calculation.

For example,

How much heat will be released if 5 moles of CH4 is reacted with an excess of oxygen?

CH4(g) + 2O2(g) → CO2(g) + 2H2O(g) ΔHrxn = -2890.4 kJ

According to the equation, 2890.4 kJ of heat is released when 1 mol of CH4 is reacted. Therefore, the conversion factor would be:

$\;\frac{{2890.4\;{\rm{kJ}}}}{{{\rm{1}}\;{\rm{mol}}\,{\rm{C}}{{\rm{H}}_{\rm{4}}}}}\;$

So, to determine the ΔH for 5 moles of CH4, we can write:

$\Delta H\; = \;\;\frac{{2890.4\;{\rm{kJ}}}}{{{\rm{1}}\;\cancel{{{\rm{mol}}\,{\rm{C}}{{\rm{H}}_{\rm{4}}}}}}}\; \times \;5\cancel{{{\rm{mol}}\;{\rm{C}}{{\rm{H}}_{\rm{4}}}}}\;{\rm{ = }}\;14,452\;{\rm{kJ}}$

Keep in mind that, even though you are in the thermochemistry chapter, there might be questions needing to address some concepts covered earlier in the semester. Like any chemical equation, be sure to balance it when needed, consider the limiting reactant, percent yield etc.

If the amount of a reaction component is given in grams or other units, convert it to moles first.

For example,

Calculate how many kJ of heat energy will be released when 12.65 g of magnesium carbonate reacts with 650. mL of 0.400 M hydrochloric acid?

MgCO3(s) + 2HCl(aq)    MgCl2(aq) + H2O(l) + CO2(g), ΔH° = –112 kJ

First, convert all the quantities to moles.

${\rm{n}}\;{\rm{(MgC}}{{\rm{O}}_{\rm{3}}}{\rm{)}}\;{\rm{ = }}\,{\rm{12}}{\rm{.65 }}\cancel{{\rm{g}}}\;{\rm{ \times }}\;\frac{{{\rm{1}}\;{\rm{mol}}}}{{{\rm{84}}{\rm{.3}}\;\cancel{{\rm{g}}}}}\;{\rm{ = }}\;{\rm{0}}{\rm{.150 mol}}$

The moles of HCl are calculated using the equation for molarity:

${\rm{M}}\;{\rm{ = }}\;\frac{{\rm{n}}}{{\rm{V}}}\,\, \Rightarrow \;\,{\rm{n}}\,{\rm{ = }}\;{\rm{MV}}$

n (HCl) = MV = 0.400 M x 0.650 L = 0.260 mol

We have the moles of both reactants, and therefore, we need to find the limiting reactant in order to do the calculations for the heat of the reaction. Remember, the limiting reactant is the one that gives less product. So, to find the LR, we determine whether the MgCOor HCl could produce less product based on their moles and the reaction stoichiometry. Let’s do the calculations based on the number of MgCl2 moles formed:

${\rm{n}}\left( {{\rm{MgC}}{{\rm{l}}_{\rm{2}}}\;{\rm{from}}\;{\rm{MgC}}{{\rm{O}}_{\rm{3}}}} \right){\rm{\; = }}\;{\rm{0}}{\rm{.150}}\;\cancel{{{\rm{mol}}\;{\rm{MgC}}{{\rm{O}}_{\rm{3}}}}}\;{\rm{ \times }}\;\frac{{{\rm{1}}\;{\rm{mol}}\;{\rm{MgC}}{{\rm{l}}_{\rm{2}}}}}{{{\rm{1}}\;\cancel{{{\rm{mol}}\;{\rm{MgC}}{{\rm{O}}_{\rm{3}}}}}}}\;{\rm{ = }}\;{\rm{0}}{\rm{.150}}\;{\rm{mol}}$

${\rm{n}}\left( {{\rm{MgC}}{{\rm{l}}_{\rm{2}}}\;{\rm{from}}\;{\rm{HCl}}} \right){\rm{\; = }}\;{\rm{0}}{\rm{.260}}\;\cancel{{{\rm{mol}}\;{\rm{HCl}}}}\;{\rm{ \times }}\;\frac{{{\rm{1}}\;{\rm{mol}}\;{\rm{MgC}}{{\rm{l}}_{\rm{2}}}}}{{{\rm{2}}\;\cancel{{{\rm{mol}}\;{\rm{HCl}}}}}}\;{\rm{ = }}\;{\rm{0}}{\rm{.130}}\;{\rm{mol}}$

So, HCl gives less MgCl2, therefore, it is the limiting reactant, and we need to calculate the amount of heat based on 0.260 mol HCl.

We can set up a cross multiplication, which would read as “2 mol HCl gives 112 kJ heat, 0.260 mol HCl will give an unknown amount of heat:

2 mol HCl  –  112 kJ

0.260 mol HCl  – X kJ

X = 14.6 kJ

Alternatively, we can do this by the unit conversion method shown in for the first reaction:

$\Delta H\; = \;\frac{{{\rm{112}}\;{\rm{kJ}}}}{{{\rm{2 }}\cancel{{{\rm{mol}}\;{\rm{HCl}}}}}}\;{\rm{ \times }}\;{\rm{0}}{\rm{.260}}\cancel{{{\rm{mol}}\;{\rm{HCl}}}}\;{\rm{ = }}\;14.6\;{\rm{kJ}}$

# ΔH When Changing the Chemical Equation

As we mentioned earlier, the ΔHrxn value corresponds to the given moles/coefficients of reactants and products. So;

1) If the equation is multiplied by a factor, then Hrxn must be multiplied by the same factor:

For example, the following equation indicates that when 2 mol of CH3OH reacts with 3 mol of O2 to form 2 mol of CO2 and 4 mol of H2O, 1453 kJ of heat is released.

2CH3OH(l) + 3O2(g) → 2CO2(g) + 4H2O(l) ΔHrxn = -1453 kJ

Now, if we multiply the coefficients by two, the enthalpy change must be multiplied by two as well:

2CH3OH(l) + 3O2(g) → 2CO2(g) + 4H2O(l) ΔHrxn = -1453 kJ

x2

4CH3OH(l) + 6O2(g) → 4CO2(g) + 8H2O(l) ΔHrxn = -2906 kJ

2) ΔHrxn changes the sign when a chemical equation is reversed:

CH4(g) + 3Cl2(g) → CHCl3(l) + 3HCl(g) H° = 334 kJ

CHCl3(l) + 3HCl(g) → CH4(g) + 3Cl2(g) H° = +334 kJ

Check Also

#### Practice

1.

How much heat will be released if 44.8 g of SO2 is reacted with an excess of oxygen according to the following chemical equation?

2SO2(g) + O2(g) → 2SO3(g), ΔH° = –198 kJ

69.2 kJ

Solution

The ΔH value for a reaction is given specifically based on the coefficients in the balanced equation. So, in this reaction, the combustion of two moles of SOproduces 198 kJ of heat. What we need to do here is first convert the mass of SO2 to moles, and then calculate the amount of heat that will be released from this amount considering that burning two moles of SO2 gives 198 kJ of heat.

n(SO2) = 44.8 g/64.1 g/mol = 0.699 mol

Let’s now set up a cross multiplication, which would read as “2 mol SOgives 198 kJ heat, 0.699 mol SOwill give an unknown amount of heat:

2 mol SO– 198 kJ

0.699 mol SO– X kJ

X = 69.2 kJ

Alternatively, we can do this by unit conversion method:

$\Delta H\; = \;\frac{{{\rm{198}}\;{\rm{kJ}}}}{{\cancel{{{\rm{2}}\;{\rm{mol}}\;{\rm{S}}{{\rm{O}}_{\rm{2}}}}}}}\;{\rm{ \times }}\;{\rm{0}}{\rm{.699 }}\cancel{{{\rm{mol}}\;{\rm{S}}{{\rm{O}}_{\rm{2}}}}}\;{\rm{ = }}\;{\rm{69}}{\rm{.2}}\;{\rm{kJ}}$

So, 69.2 kJ heat will be released if 44.8 g (0.699 mol ) of SOis reacted according to the given chemical equation.

2.

What is ΔH° for the following reaction

2C6H6 (l) + 15O2 (g) → 12CO2 (g) + 6H2O (l), ΔH° = ? kJ

if the consumption of 27.3 g of benzene (C6H6) produces 1144 kJ of heat?

6.54 x 103 kJ

Solution

The ΔH value for a reaction is given specifically based on the coefficients in the balanced equation. So, in this reaction, we need to determine the combustion of two moles of C6H6.

Convert the mass of C6H6 to moles, and then calculate the amount of heat that will be released from 2 moles of C6H6 considering that burning 27.3 g C6H6 gives 1144 kJ of heat.

n(C6H6) = 27.3 g/78.1 g/mol = 0.350 mol

Let’s now set up a cross multiplication, which would read as “0.350 mol C6H6 gives 1144 kJ heat, 2 mol C6H6 will give an unknown amount of heat:

0.350 mol C6H6 – 1144 kJ

2 mol C6H6 – X kJ

X = 6.54 x 103 kJ

Alternatively, we can do this by unit conversion method:

$\Delta H\; = \;\frac{{{\rm{1144}}\;{\rm{kJ}}}}{{\cancel{{{\rm{0}}{\rm{.350}}\;{\rm{mol}}\;{{\rm{C}}_{\rm{6}}}{{\rm{H}}_{\rm{6}}}}}}}\;{\rm{ \times }}\;{\rm{2}}\cancel{{{\rm{mol}}\;{{\rm{C}}_{\rm{6}}}{{\rm{H}}_{\rm{6}}}}}\;{\rm{ = }}\;{\rm{6}}{\rm{.54}}\;{\rm{ \times }}\;{10^3}\;{\rm{kJ}}$

3.

Based on the heat of reaction for the chlorination of methane, how much heat will be released if 233.6 grams of hydrochloric acid are formed?

CH4(g) + 3Cl2(g) → CHCl3(l) + 3HCl(g), ΔH° = -334 kJ

713 kJ

Solution

The ΔH value for a reaction is given specifically based on the coefficients in the balanced equation which imply their mole numbers. Therefore, converting the mass to moles is always going to be a good idea.

n(HCl) = 233.6/36.5 g/mol = 6.40 mol

According to the chemical equation, for every three moles of HCl forming, there is 334 kJ heat released. So, we need to find how much heat will be released if 6.40 mol HCl is formed.

We can set up a cross multiplication, which would read as “3 mol HCl gives 334 kJ heat, 6.40 mol HCl will give an unknown amount of heat:

3 mol HCl – 334 kJ

6.40 mol HCl – X kJ

X = 713 kJ

Alternatively, we can do this by unit conversion method:

$\Delta H\; = \;\frac{{{\rm{334}}\;{\rm{kJ}}}}{{{\rm{3 }}\cancel{{{\rm{mol HCl}}}}}}\;{\rm{ \times }}\;{\rm{6}}{\rm{.40}}\cancel{{{\rm{mol}}\;{\rm{HCl}}}}\;{\rm{ = }}\;713\;{\rm{kJ}}$