General Chemistry

Hess’s law allows measuring the enthalpy change (ΔH) for a reaction without making calorimetric measurements. To do this, we need the enthalpies of some other reactions.

For example,

Using the given data for reactions (1) and (2), calculate the ΔH for the reaction:

 

2NO2(g) + Cl2(g) → 2NOCl(g) + O2(g), ΔH = ?

 __________________________________________________

1) 2NO(g) + Cl2(g) → 2NOCl(g), ΔH = -76 kJ

2) 2NO(g) + O2(g) → 2NO2(g), ΔH = -114 kJ

 

To find the ΔH for the target reaction, we need to modify equations 1 and 2 such that we add them together and get the target equation.

 

Of course, by doing so, we need to follow rules for manipulating thermochemical equations:

 

  • If the equation is multiplied by any factor, the ΔH must be multiplied by the same factor.
  • If the equation is reversed, the sign of ΔH must be changed.

 

So, to get the target equation, first look up which of its components appear in the equations with known ΔH (equations 1 and 2).

NO2 is the first reactant in the target equation, and it appears in equation (2) as a product. Therefore, reverse the second reaction to make NO2 a reactant like in the target reaction. Let’s label the new equation as (2a). Make sure to change the sign for ΔH:

 

2a) 2NO2(g) → 2NO(g) + O2(g), ΔH = +114 kJ

 

Pay attention to the coefficient as well; in both the target and (2a) equations, we have 2 NO2 and this is what you want. The component in the reference equation most often needs to have the same coefficient as in the target equation.

The Cl2, on the other hand, is a reactant in the target equation and so is it in equation (1), therefore, we keep equation (1) intact.

At this point, we can add equations (1) and (2a) to see if we get the target equation. Remember to add the enthalpies with correct signs as well:

 

1) 2NO(g) + Cl2(g) → 2NOCl(g), ΔH = -76 kJ

+

2a) 2NO2(g) → 2NO(g) + O2(g), ΔH = +114 kJ

__________________________________________

2NO(g) + Cl2(g) + 2NO2(g) → 2NOCl(g) + 2NO(g) + O2(g)

ΔH = -76 kJ + 114 kJ = +38 kJ

 

Cancel any molecules with the same coefficient that appear on both sides of the equation. In this case, it the NO:

 

2NO(g) + Cl2(g) + 2NO2(g) → 2NOCl(g) + 2NO(g) + O2(g)

 

The final equation is:

 

2NO2(g) + Cl2(g) → 2NOCl(g) + O2(g)  ΔH = +38 kJ

 

And this matches the target equation, therefore, the ΔH was determined correctly.

 

How does Hess’s Law Work?

The secret souse of Hess’s law is that enthalpy is a state function, and therefore, ΔHrxn is the same whether the reaction takes place in one step or in a series of steps.

Remember, a state function is a variable that only depends on the initial and final states and not how it was achieved. For example, altitude is a state function and wouldn’t matter how two hikers meet at a 500 ft altitude. One may be on his way to the top, and the other going back having behind a longer walk distance:

 

 

Now, by the same analogy, suppose we need to determine the enthalpy of the reaction 2A + B → 2D, given the enthalpies of the other two reactions:

 

2A + B → 2D ΔH = ?
_____________________

2A + B  →  C ΔH = +50 kJ

C  →  2D ΔH = -80 kJ

 

On an energy diagram, the objective is to go from  “2A + B” to “2D”, but we cannot directly measure the enthalpy change of this process. However, we know that if “2A + B” goes to C, it is +50 kJ, and “C” going to “2D” is -80 kJ.

 

 

And because enthalpy is a state function, it does not matter how “2A + B” goes to “2D”, so we add the enthalpy changes for these two routes/reactions to find the enthalpy change for going “2A + B” to “2D” directly:

 

 

So, to summarize, when solving a problem on the Hess’s law, remember your objective is to manipulate the reference equations such that when you add them up, the target equation is obtained. Remember, to multiply all the coefficients and the ΔH when needed, and to change the sign of ΔH when the equation is reversed.

 

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Practice

1.

Calculate the enthalpy for the oxidation of CO to CO2 using the enthalpy of reaction for the combustion of C to CO (ΔH = -221.0 kJ) and the enthalpy for the combustion of C to CO2H = -393.5 kJ).

2CO(g) + O2(g)  →  2CO2(g)  ΔH = ?

C(s) + O2(g)  →  CO2(g)  ΔH = -393.5 kJ

2C(s) + O2(g)  →  2CO(g)  ΔH = -221.0 kJ

answer

-566 kJ

Solution

The target reaction contains 2 moles of CO2 as a product, so we need to multiply equation 1 by two and do the same for the value of ΔH:

1a) 2C(s) + 2O2(g) → 2CO2(g), ΔH = -787 kJ

The second equation needs to be reversed since, in the target reaction, CO is a reactant while here it is a product:

2a) 2CO(g) → 2C(s) + O2(g), ΔH = 221.0 kJ

And now we can add the two equations:

1a) 2C(s) + 2O2(g) → 2CO2(g), ΔH = -787 kJ
+
2a) 2CO(g) → 2C(s) + O2(g), ΔH = 221.0 kJ

2C(s) + 2O2(g) + 2CO(g) → 2CO2(g) + 2C(s) + O2(g)

2CO(g) + O2(g) → 2CO2(g)

ΔH = -787 kJ + 221.0 kJ = -566 kJ

2.

Calculate the enthalpy for the combustion reaction of sulfur to sulfur trioxide using the enthalpies of the two reactions shown below:

2S(s) + 3O2(g)  →  2SO3(g)  ΔH = ?

S(s) + O2(g)  →  SO2(g)  ΔH = -297 kJ

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

answer

-792 kJ

Solution

The target reaction contains 2 moles of S as a reactant, so we need to multiply equation 1 by two and do the same for the value of ΔH:

1a) 2S(s) + 2O2(g)  →  2SO2(g)  ΔH = -594 kJ

The second equation needs to be reversed since in the target reaction, SO3 is a product while here it is a reactant:

2a) 2SO2(g) + O2(g) → 2SO3(g)  ΔH = -198 kJ

And now we can add the two equations:

1a) 2S(s) + 2O2(g)  →  2SO2(g)  ΔH = -594 kJ
+
2a) 2SO2(g) + O2(g) → 2SO3(g)  ΔH = -198 kJ

2S(s) + 2O2(g) + 2SO2(g) + O2(g) → 2SO2(g) + 2SO3(g)

2S(s) + 3O2(g) → 2SO3(g)

ΔH = -594 kJ + (-198 kJ) = -792 kJ

 

3.

Using the Hess’s law, calculate ΔHo for the combustion reaction of butene:

C4H8(g) + 6O2(g) → 4CO2(g) + 4H2O(l), ΔHo = ?

Use the following reactions and given ΔH’s:

1) 2H2(g) + O2(g) → 2H2O(g), ΔHo = -571 kJ

2) C4H8(g) + H2(g) → C4H10(g), ΔHo = -126 kJ

3) 2C4H10(g) + 13O2(g) → 8CO2(g) + 10H2O(l), ΔHo = -5754 kJ

answer

ΔHo = -2718 kJ

Solution

Because C4H8 appears as a reactant in the target reaction, we are not going to reverse equation 2. However, to get rid of C4H10, we need to multiply equation 2 by two since there are two moles of C4H10 in equation 3. Let’s label the new equation as 2a:

2a) 2C4H8(g) + 2H2(g) → 2C4H10(g), ΔHo = -252 kJ

 We cannot yet add equations 1, 2a, and 3 because there is going to be H2 only in the left side of the equation, but the target equation does not contain H2. This means we need to also reverse equation 1. Notice that reversing equation 2 for the same reason puts C4H8 as product and that is not what we have in the target reaction.

So, let’s reverse equation 1, changing the sign of the enthalpy, and label it as 1a:

1a) 2H2O(g) → 2H2(g) + O2(g), ΔHo = 571 kJ

Now, we can add equations 1a, 2a, and 3:

1a) 2H2O(g) → 2H2(g) + O2(g), ΔHo = 571 kJ
+
2a) 2C4H8(g) + 2H2(g) → 2C4H10(g), ΔHo = -252 kJ
+
3) 2C4H10(g) + 13O2(g) → 8CO2(g) + 10H2O(l), ΔHo = -5754 kJ

2H2O(g) + 2C4H8(g) + 2H2(g) + 2C4H10(g) + 13O2(g) → 2H2(g) + O2(g) + 2C4H10(g) + 8CO2(g) + 10H2O(l)

2C4H8(g) + 12O2(g) → 8CO2(g) + 8H2O(l)

ΔHo = 571 kJ + (-252 kJ) + (-5754 kJ) = -5435 kJ

The last step is to simplify the equation by dividing it by two. Remember, the same goes for the enthalpy value:

2C4H8(g) + 12O2(g) → 8CO2(g) + 8H2O(l), ΔHo = -2718 kJ

4.

Using the Hess’s law and the enthalpies of the three combustion reactions below, calculate the enthalpy of the reaction producing methanol (CH3OH) from carbon monoxide and hydrogen gas.

CO(g) + 2H2(g) → CH3OH(g), ΔH = ?

1) 2CO(g) + O2(g) → 2CO2(g), ΔH = -566 kJ

2) 2H2(g) + O2(g) → 2H2O(g), ΔHo = -571 kJ

3) 2CH3OH(g) + 3O2(g) → 2CO2(g) + 4H2O(g), ΔHo = −1430 kJ

answer

-139 kJ

Solution

The first two equations seem to be in the correct directions since they contain CO and H2 as reactants which is what we have in the target equation.

The third equation, however, must be reversed because the methanol here is a reactant while in the target equation, it is a product. So, let’s reverse it and label it as 3a:

3a) 2CO2(g) + 4H2O(g) → 2CH3OH(g) + 3O2(g), ΔHo = +1430 kJ

Let’s add equations 1, 2, and 3a and see what we get:

 

1) 2CO(g) + O2(g) → 2CO2(g), ΔH = -566 kJ
+
2) 2H2(g) + O2(g) → 2H2O(g), ΔHo = -571 kJ
+
3a) 2CO2(g) + 4H2O(g) → 2CH3OH(g) + 3O2(g), ΔHo = +1430 kJ

 

You may notice that there are four moles of water on the left side (equation 3a), but only two moles on the right side (equation 2). This means we need to multiply equation two with its enthalpy value by two. Let’s do that and label the new equation as 2a:

 

2a) 4H2(g) + 2O2(g) → 4H2O(g), ΔHo = -1141 kJ

 

And now, we can add equations 1, 2a, and 3a:

1) 2CO(g) + O2(g) → 2CO2(g), ΔH = -566 kJ
+
2a) 4H2(g) + 2O2(g) → 4H2O(g), ΔHo = -1141 kJ
+
3a) 2CO2(g) + 4H2O(g) → 2CH3OH(g) + 3O2(g), ΔHo = +1430 kJ
__________________________________________________

2CO) + O2 + 4H2 + 2O2 + 2CO2 + 4H2O → 2CO2 + 4H2O + 2CH3OH + 3O2

 

Cancel the same molecules on both side of the equation:

2CO + O2 + 4H2 + 2O2 + 2CO2 + 4H2O → 2CO2 + 4H2O + 2CH3OH + 3O2

ΔHo = -566 kJ + (-1141 kJ) + 1430 kJ/mol = -277 kJ

So, we have:

2CO(g) + 4H2(g) → 2CH3OH(g), ΔHo = -277 kJ

The last step is to divide the equation by two to match the target reaction:

CO(g) + 2H2(g) → CH3OH(g), ΔHo = -139 kJ

5.

Using the Hess’s law and the enthalpies of the given reactions, calculate the enthalpy of the combustion reaction of CH3Cl:

CH3Cl(g) + O2(g) → CO(g) + HCl(g) + H2O(l), ΔH = ?

1) CO(g) + 2H2(g) → CH3OH(g), ΔHo = -139 kJ

2) 2H2(g) + O2(g) → 2H2O(g), ΔHo = -571 kJ

3) CH3OH(g) + HCl(aq) → CH3Cl(g) + H2O(l), ΔHo = -28 kJ

answer

-404 kJ

Solution

The first reaction needs to be reversed because the CO is a reactant, while in the target reaction it is a product. Let’s reverse it and label it as 1a:

1a) CH3OH(g) → CO(g) + 2H2(g), ΔHo = +139 kJ

The second reaction is good as it is. However, the third reaction needs to be reversed as well in order to make CH3Cl as a reactant as it is in the target equation:

3a) CH3Cl(g) + H2O(g) → CH3OH(g) + HCl(aq), ΔHo = +28 kJ

 

We can now add equations 1a, 2, and 3a:

1a) CH3OH(g) → CO(g) + 2H2(g), ΔHo = +139 kJ
+
2) 2H2(g) + O2(g) → 2H2O(g), ΔHo = -571 kJ
+
3a) CH3Cl(g) + H2O(l) → CH3OH(g) + HCl(aq), ΔHo = +28 kJ
____________________________________________

CH3OH(g) + 2H2(g) + O2(g) + CH3Cl(g) + 2H2O(l) → CO(g) + 2H2(g) + 2H2O(g) + CH3OH(g) + HCl(aq)

 

Cancel the same molecules on both side of the equation:

CH3OH(g) + 2H2(g) + O2(g) + CH3Cl(g) + H2O(l) → CO(g) + 2H2(g) + 2H2O(g) + CH3OH(g) + HCl(aq)

CH3Cl(g) + O2(g) → CO(g) + HCl(g) + H2O(g)

ΔHo = +139 kJ + (-571 kJ) + 28 kJ = -404 kJ

6.

Using the Hess’s law and the enthalpies of the given reactions, calculate the enthalpy of the following oxidation reaction of ammonia:

4NH3(g) + 5O2(g) → 4NO(g) + 6H2O(g), ΔH = ?

1) N2(g) + 3H2(g) → 2NH3(g), ΔH = -92 kJ

2) 2H2(g) + O2(g) → 2H2O(g), ΔH = -484 kJ

3) N2(g) + O2(g) → 2NO(g), ΔH = 181 kJ

answer

-906 kJ

Solution

The first reaction needs to be reversed because the NH3 is a product, while in the target reaction it is a reactant. Let’s reverse it and label it as 1a:

1a) 2NH3(g) → N2(g) + 3H2(g), ΔH = +92 kJ

Let’s put the three equations together and see what the sum would look like:

1a) 2NH3(g) → N2(g) + 3H2(g), ΔH = +92 kJ

2) 2H2(g) + O2(g) → 2H2O(g), ΔH = -484 kJ

3) N2(g) + O2(g) → 2NO(g), ΔH = 181 kJ

One problem is that the hydrogens in equation 1a and 2 do not cancel each other since we have 3 moles in equation 1a and 2 moles in equation 2. Therefore, let’s multiply equation 1a by two, and multiply equation 2 by three:

1b) 4NH3(g) → 2N2(g) + 6H2(g), ΔH = +184 kJ

2a) 6H2(g) + 3O2(g) → 6H2O(g), ΔH = -1452 kJ

And now let’s put these three equations together:

1b) 4NH3(g) → 2N2(g) + 6H2(g), ΔH = +184 kJ

2a) 6H2(g) + 3O2(g) → 6H2O(g), ΔH = -1452 kJ

3) N2(g) + O2(g) → 2NO(g), ΔH = 181 kJ

The problem now is the number of moles of nitrogen in equations 1b and 3. We need to multiply equation 3 by two:

3a) 2N2(g) + 2O2(g) → 4NO(g), ΔH = 362 kJ

 And now we can add equations 1b, 2a, and 3a:

1b) 4NH3(g) → 2N2(g) + 6H2(g), ΔH = +184 kJ
+
2a) 6H2(g) + 3O2(g) → 6H2O(g), ΔH = -1452 kJ
+
3a) 2N2(g) + 2O2(g) → 4NO(g), ΔH = 362 kJ
____________________________________________

4NH3(g) + 6H2(g) + 3O2(g) + 2N2(g) + 2O2(g) → 2N2(g) + 6H2(g) + 6H2O(g) + 2NO(g)

4NH3(g) + 5O2(g) → 6H2O(g) + 2NO(g)

ΔH = +184 kJ + (-1452 kJ) + 362 kJ = -906 kJ

 

7.

Using the Hess’s law and the enthalpies of the given reactions, calculate the enthalpy of the following oxidation reaction between CuO and HCl:

2CuO(s) + 4HCl(g) → 2CuCl(s) + Cl2(g) + 2H2O(g), ΔH = ?

1) CuO(s) + H2(g) → Cu(s) + H2O(g), ΔH = -85 kJ

2) 2Cu(s) + Cl2(g) → 2CuCl(s), ΔH = -274 kJ

3) H2(g) + Cl2(g) → 2HCl(g), ΔH = -184 kJ

answer

-76 kJ

Solution

We need to multiply equation 1 by two since there are two moles of CuO(s) in the target equation. Let’s label the new equation as 1a:

1a) 2CuO(s) + 2H2(g) → 2Cu(s) + 2H2O(g), ΔH = -170 kJ

Equation 2 seems to be fine, so let’s leave it as it is.

There are 2H2(g) in equation 1a, and this means that we need to reverse equation 3 and multiply it by two so that we can have 2H2(g) as a product and cancel them with the ones in equation 1a:

3a) 4HCl(g) → 2H2(g) + 2Cl2(g), ΔH = 368 kJ

 Let’s add equations 1a, 2, and 3a and see if they add up:

1a) 2CuO(s) + 2H2(g) → 2Cu(s) + 2H2O(g), ΔH = -170 kJ

2) 2Cu(s) + Cl2(g) → 2CuCl(s), ΔH = -274 kJ

3a) 4HCl(g) → 2H2(g) + 2Cl2(g), ΔH = 368 kJ

2CuO(s) + 2H2(g) + 2Cu(s) + Cl2(g) + 4HCl(g) → 2Cu(s) + 2H2O(g) + 2CuCl(s) + 2H2(g) + 2Cl2(g)

2CuO(s) + 4HCl(g) → 2CuCl(s) + 2H2O(g) + Cl2(g)

ΔH = -170 kJ + (-274 kJ) + 368 kJ = -76 kJ

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