Hess' Law

Hess' Law states that the *enthalpy of a
reaction is independent of whether the reaction occurs in one or several steps*.
If this was not the case energy would not be conserved. But because it is supported by expereimental data, it allows us to algebraically add equations and their accompanying DH's to obtain
the DH for the desired or **target equation**.

Keep the following rules in mind:

- If an equation is multiplied or divided by a number, that factor also applies to DH.
- If an equation is reversed, then the sign of DH changes.
- Remember the enthalpy changes with different states of matter.
Do not, for example, interchange H
_{2}O_{(l)}with H_{2}O_{(s).}

**Example 1**
Carbon disulfide is a very flammable solvent. It burns according to the
following equation:

CS_{2(l) }+
3 O_{2(g) }--> CO_{2(g) }+ 2 SO_{2(g)}

Calculate DH for the above reaction using the following data:

(1) C_{(s)} + 2 S_{(s)} --> CS_{2(l)} DH = 88 kJ

(2) C_{(s)} + O_{2(g)} --> CO_{2(g)} DH = -394 kJ

(3) S_{(s)}
+ O_{2(g)} --> SO_{2(g)} DH = -297 kJ

**Solution** Equation (1) is the only one with CS_{2(l)}, but it
has the compound as a product. Our target equation has CS_{2(l)} on the
left hand side. So we reverse equation (1) and change the sign of DH.

reverse(1) CS_{2(l)} --> C_{(s)}
+ 2 S_{(s)} DH = - 88 kJ

Equation (2) is the only one with CO_{2(g),} and,
compared to the target equation, it has the correct amount on the desired side
of the equation. So we keep equation (2) as is.

(2) C_{(s)}
+ O_{2(g)} --> CO_{2(g)} DH = -394 kJ

Equation (3) is the only one with SO_{2(g). }It 's
on the correct side of the equation, but the target equation needs twice as
much. So we multiply equation (3) by 2.

Eq(3) *2 2S_{(s)} + 2O_{2(g)}
--> 2SO_{2(g)} DH = 2(-297 kJ) = -594 kJ

Now if we add the above
three equations:

CS_{2(l) }+ C_{(s)} + O_{2(g) }+ 2S_{(s)} + 2O_{2(g) }--> C_{(s)}
+ 2 S_{(s)}_{ }+
CO_{2(g)} + 2SO_{2(g) }DH =- 88 -394-594 = -1076 kJ

Notice that C_{(s)} and 2S_{(s) } cancel. We are left
with the target equation

CS_{2(l) }+ 3 O_{2(g) }-->
CO_{2(g) }+ 2 SO_{2(g) }and of course
the DH which we needed.

Answer: DH = -1076 kJ