Question

For which one of the following reactions is the value of ΔH°rxn equal to ΔHf° for the product?

1) A + B → C
2) 2A + B → C
3) A + 2B → C
4) A + B → 2C

Answer 1

The fourth reaction option, A + B → 2C, can be associated with the enthalpy change ΔH°rxn being equal to ΔH°f for the product, as it involves the formation of the product directly from its constituent elements.

Step-by-step explanation:

The student's question pertains to identifying which reaction's enthalpy change (ΔH°rxn) is equal to the standard enthalpy of formation (ΔH°f) for the product formed. Among the given reactions, the enthalpy change of a reaction is equal to the enthalpy of formation of the product only when 1 mole of a compound forms from its elements in their standard states. From the reaction options provided, the answer is the fourth reaction: A + B → 2C. This is because the enthalpy change for the reaction, when divided by 2, due to the stoichiometric coefficient of 2 in front of C, will give ΔH°f for the product C.

To solve problems like these, one needs to apply Hess's Law and manipulate the given reactions so that, when added together, they yield the desired reaction. The result of this summation will be the ΔH°rxn, which can sometimes directly represent the ΔH°f if it pertains to the formation of a product from its constituent elements in their standard states and the product coefficient is one.

Answer 2

For the reaction A + 2B → C, the value of ΔH°rxn is equal to ΔHf° for the product C. Therefore, the correct option is 3) A + 2B → C.

Step-by-step explanation:

In a chemical reaction, the enthalpy change (ΔH°rxn) is the amount of heat energy that is either absorbed or released during the reaction. The standard enthalpy of formation (ΔHf°) is the enthalpy change that occurs when one mole of a compound is formed from its constituent elements in their standard states.

In the given reactions, we can see that in reaction 3, A reacts with 2 moles of B to form C. This means that for every mole of C formed, there are 2 moles of B consumed. Therefore, the number of moles of reactants and products are not balanced. As a result, the enthalpy change for this reaction (ΔH°rxn) will not be equal to the sum of the enthalpies of formation for the products (ΔHf° for C) minus the sum of the enthalpies of formation for the reactants (ΔHf° for A and B).

On the other hand, in reaction 4, A and B react to form 2 moles of C. This means that for every mole of C formed, there are 2 moles of A and B consumed. Since there are equal numbers of moles for both reactants and products, we can say that the enthalpy change for this reaction (ΔH°rxn) will be equal to twice the enthalpy change required to form one mole of C from its constituent elements (2 x ΔHf° for C).

Now let's look at reaction 3 again. We can see that in this reaction, we have one mole of A and two moles of B reacting to form one mole of C. This means that we can write this reaction as:

A + 2B → C

To calculate the enthalpy change for this reaction (ΔH°rxn), we need to find the sum of the enthalpies of formation for all the species involved in the reaction. The enthalpies of formation for each compound can be found in a standard reference such as "NIST Chemistry WebBook" or "CRC Handbook".

Let's say that A has an enthalpy of formation (ΔHf°) equal to -100 kJ/mol, B has an enthalpy of formation (ΔHf°) equal to -50 kJ/mol, and C has an enthalpy of formation (ΔHf°) equal to -300 kJ/mol. Using these values, we can calculate the enthalpy change for each step in this reaction:

Step 1: Formation of A from its constituent elements (-100 kJ/mol)

Step 2: Formation of B from its constituent elements (-50 kJ/mol) x 2 = -100 kJ/mol

Step 3: Formation of C from its constituent elements (-300 kJ/mol)

Total: -500 kJ/mol = ΔH°rxn

Now let's compare this value with the enthalpy change required to form one molecule of C from its constituent elements (-300 kJ/mol). We can see that they are not equal. Therefore, we cannot say that ΔH°rxn is equal to ΔHf° for C.

Next, let's look at reaction 4 again. We can see that in this reaction, we have one molecule of A and one molecule of B reacting to form two molecules of C. This means that we can write this reaction as:

A + B → 2C

To calculate the enthalpy change for this reaction (ΔH°rxn), we need to find twice the enthalpy change required to form one molecule of C from its constituent elements (-300 kJ/mol). This gives us a total value of -600 kJ/mol = ΔH°rxn. Now let's compare this value with the sum of the enthalpies of formation for all the species involved in the reaction:

Step 1: Formation of A from its constituent elements (-100 kJ/mol)

Step 2: Formation of B from its constituent elements (-50 kJ/mol)

Step 3: Formation of two molecules of C from their constituent elements (-600 kJ/mol) = -300 kJ/mol x 2 = -600 kJ/mol

Total: -850 kJ/mol = ΔH°rxn

We can see that they are equal. Therefore, we can say that in this case, ΔH°rxn is equal to twice the enthalpy change required to form one molecule of C from its constituent elements (-300 kJ/mol). This means that when two moles of B react with one molecule of A to form two moles of C, all the heat energy released or absorbed during this process is equivalent to twice the heat energy required to form one molecule of C from its constituent elements. Therefore, the correct option is 3) A + 2B → C.