Lecture 4: Hess’s Law Reading: Zumdahl 9.5 Outline: Definition of Hess’ Law Using Hess’ Law (examples)

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Lecture 4: Hess’s Law Reading: Zumdahl 9.5 Outline: Definition of Hess’ Law Using Hess’ Law (examples)

Q: What is Hess’s Law ? Recall (lecture 3) Enthalpy is a state function. As such,  H for going from some initial state to some final state is pathway independent. Hess’s Law:  H for a process involving the transformation of reactants into products is not dependent on pathway. (This means we can calculate  H for a reaction by a single step, or by multiple steps)

Using Hess’s Law When calculating  H for a chemical reaction as a single step, we can use combinations of reactions as “pathways” to determine  H for our “single step” reaction.

The reaction of interest is: N 2 (g) + 2O 2 (g) 2NO 2 (g)  H = 68 kJ This reaction can also be carried out in two steps: N 2 (g) + O 2 (g) 2NO(g)  H = +180 kJ 2NO (g) + O 2 (g) 2NO 2 (g)  H = -112 kJ

If we take the previous two reactions and add them, we get the original reaction of interest: N 2 (g) + O 2 (g) 2NO(g)  H = +180 kJ 2NO (g) + O 2 (g) 2NO 2 (g)  H = -112 kJ N 2 (g) + 2O 2 (g) 2NO 2 (g)  H = + 68 kJ

Note: the important things about this example is that the sum of  H for the two reaction steps is equal to the  H for the reaction of interest. Big idea: We can combine reactions of known  H to determine the  H for the overall “combined” reaction.

Hess’s Law: An Important Detail One can always reverse the direction of a reaction when making a combined reaction. When you do this, the sign of  H changes. N 2 (g) + 2O 2 (g) 2NO 2 (g)  H = +68 kJ 2NO 2 (g) N 2 (g) + 2O 2 (g)  H = - 68 kJ

One more detail: The magnitude of  H is directly proportional to the quantities involved. (This means  H is an “extensive” quantity). So, if the coefficients of a reaction are multiplied by a number, the value of  H is also multiplied by the same number. N 2 (g) + 2O 2 (g) 2NO 2 (g)  H = 68 kJ  N 2 (g) + 4O 2 (g) 4NO 2 (g)  H = 136 kJ

Using Hess’s Law: tips When trying to combine reactions to form a reaction of interest, it is usually best to work backwards from the reaction of interest. Example: What is  H for the following reaction? 3C (gr) + 4H 2 (g) C 3 H 8 (g)

3C (gr) + 4H 2 (g) C 3 H 8 (g)  H = ? You’re given the following reactions: C (gr) + O 2 (g) CO 2 (g)  H = -394 kJ C 3 H 8 (g) + 5O 2 (g) 3CO 2 (g) + 4H 2 O (l)  H = kJ H 2 (g) + 1/2O 2 (g) H 2 O (l)  H = -286 kJ

Step 1. Only reaction 1 has C (gr). Therefore, we will multiply by 3 to get the correct amount of C (gr) with respect to our final equation. (x3) C (gr) + O 2 (g) CO 2 (g)  H = -394 kJ 3C (gr) + 3O 2 (g) 3CO 2 (g)  H = kJ

Step 2: To get C 3 H 8 on the product side of the reaction, we need to reverse reaction 2, and change the sign of  H. 3CO 2 (g) + 4H 2 O (l) C 3 H 8 (g) + 5O 2 (g)  H = kJ C 3 H 8 (g) + 5O 2 (g) 3CO 2 (g) + 4H 2 O (l)  H = kJ

Step 3: Add two “new” reactions together to see what remains: 3C (gr) + 3O 2 (g) 3CO 2 (g)  H = kJ 3CO 2 (g) + 4H 2 O (l) C 3 H 8 (g) + 5O 2 (g)  H = kJ 2 3C (gr) + 4H 2 O (l) C 3 H 8 (g) + 2O 2  H = kJ

Step 4: Compare previous reaction to final reaction, and determine how to reach final reaction: 3C (gr) + 4H 2 O (l) C 3 H 8 (g) + 2O 2  H = kJ H 2 (g) + 1/2O 2 (g) H 2 O (l)  H = -286 kJ 3C (gr) + 4H 2 (g) C 3 H 8 (g) Need to multiply second reaction by 4

Example (cont.) Step 4: Compare previous reaction to final reaction, and determine how to reach final reaction: 3C (gr) + 4H 2 O (l) C 3 H 8 (g) + 2O 2  H = kJ 4H 2 (g) + 2O 2 (g) 4H 2 O (l)  H = kJ 3C (gr) + 4H 2 (g) C 3 H 8 (g)

3C (gr) + 4H 2 O (l) C 3 H 8 (g) + 2O 2  H = kJ 4H 2 (g) + 2O 2 (g) 4H 2 O (l)  H = kJ 3C (gr) + 4H 2 (g) C 3 H 8 (g)  H = -106 kJ Which is the one step reaction of interest

Another Example: Calculate  H for the following reaction: H 2 (g) + Cl 2 (g) 2HCl(g) Given the following: NH 3 (g) + HCl (g) NH 4 Cl(s)  H = -176 kJ N 2 (g) + 3H 2 (g) 2NH 3 (g)  H = - 92 kJ N 2 (g) + 4H 2 (g) + Cl 2 (g) 2NH 4 Cl(s)  H = kJ

Step 1: Only the first reaction contains the product of interest (HCl), but as a reactant. Therefore, reverse this reaction and multiply by 2 to get stoichiometry correct. NH 3 (g) + HCl (g) NH 4 Cl(s)  H = -176 kJ 2NH 4 Cl(s) 2NH 3 (g) + 2HCl (g)  H = +352 kJ

Step 2: Need Cl 2 as a reactant, therefore, add reaction 3 to result from step 1 and see what is left. 2NH 4 Cl(s) 2NH 3 (g) + 2HCl (g)  H = 352 kJ N 2 (g) + 4H 2 (g) + Cl 2 (g) 2NH 4 Cl(s)  H = -629 kJ N 2 (g) + 4H 2 (g) + Cl 2 (g) 2NH 3 (g) + 2HCl(g)  H = -277 kJ

Step 3: Use remaining known reaction in combination with the result from Step 2 to get final reaction. N 2 (g) + 4H 2 (g) + Cl 2 (g) 2NH 3 (g) + 2HCl(g)  H = -277 kJ ? ( N 2 (g) + 3H 2 (g) 2NH 3 (g)  H = -92 kJ) H 2 (g) + Cl 2 (g) 2HCl(g)  H = ? Key: need to reverse the middle reaction

Step 3. Use remaining known reaction in combination with the result from Step 2 to get final reaction. N 2 (g) + 4H 2 (g) + Cl 2 (g) 2NH 3 (g) + 2HCl(g)  H = -277 kJ 2NH 3 (g) 3H 2 (g) + N 2 (g)  H = +92 kJ H 2 (g) + Cl 2 (g) 2HCl(g)  H = -185 kJ 1 This is the desired reaction and resultant  H!