Hess's Law - Online Tutor, Practice Problems & Exam Prep

Hess's Law is a principle in thermochemistry that allows us to determine the enthalpy change (ΔH_rxn) of an overall reaction by summing the enthalpy changes of individual steps in a reaction pathway. The law states that the total enthalpy change for a reaction is the same, regardless of the number of steps or the route taken, as long as the initial and final conditions are the same. When manipulating thermochemical equations, any changes made to the coefficients or the direction of the reaction must be reflected in the enthalpy value. For instance, if a reaction is reversed, the sign of ΔH_rxn is also reversed. If coefficients are multiplied or divided by a factor, ΔH_rxn must be multiplied or divided by the same factor. By applying Hess's Law, we can cancel out intermediate species that appear on both sides of the combined reactions and derive the ΔH_rxn for the overall process, which is crucial for understanding energy changes in chemical reactions.

Hess's Law

Now Hesa's law has to do with the rearrangement of thermochemical equations to help us fund the overall enthalpy of reaction. Now recall a thermochemical equation is a chemical equation that involves or includes an enthalpy of reaction. Now we're going to say the thermochemical equation and its enthalpy of reaction, which is ΔHRXN are directly proportional. This means that any change to the original equation will cause the same change within your enthalpy of reaction.

So let's say we have an original equation here. Original thermochemical equation where we have two moles of magnesium is solid plus O2 gas and it produces 2 moles of magnesium oxide. The enthalpy associated with this is -1204 kilojoules. Now I can do different things, different rearrangements to this thermochemical equation that'll affect it, but also affect my delta H of reaction. So the things I can do is I can multiply this equation by a value, I can divide it by a number, or I can reverse the reaction.

So let's say we multiply it. Here we have our original equation, and let's say multiply it by two. Now if I multiply it by two, the coefficient's now become four, two and four. If I multiply the equation by two, then that means I also have to multiply my delta H by two. This original value of -1204 kilojoules gets multiplied by two, and now my new enthalpy of the reaction is -2408 kilojoules.

Now let's say instead of multiplying, I divided so my original equation again. Now I divide it by two. Dividing it by two changes my coefficients now to one for magnesium solid, to 1/2 for O2 and one for magnesium oxide. Again, whatever I do to the equation, I must do the same thing to my delta H. So -1204 gets divided by two so it becomes -602 kilojoules.

Finally, the last thing I can do to my thermochemical equation is I can reverse it. What was a product can become a reactant, so that's 2 MgO solid. And what was a reactant can now become products, so 2 Mg solid plus one O2. Now when I reverse the reaction, what that does is it reverses the sign of Delta H so it was a -1204. Now it's going to become a +1204. Just realize that if I reverse the reaction, I reverse the sign of Delta H. So just remember these are the three things I can do to a thermochemical equation and they have a direct impact on my Delta H of reaction for that particular thermochemical equation.

Hess's Law Example 1

In this example question, it says if the formation equation for boron trioxide is given as the following: 4   moles   B   solid + 3   moles   O2   gas   →   2   moles   boron   trioxidesolid   has   an   enthalpy   of   - 2547   kilojoules, what will be the new enthalpy value when it's rearranged? All right. So we have to see what are the changes that the original equation underwent to determine the new delta H.

Well, we can see one thing that happened is what was a product is now a reactant and what was a reactant are now products. So we reversed it. The next thing we should notice are the coefficients. Here it was a 2, but now it's a 4. This was a 4, but now it's an 8. This was a 3, but now it's a 6. So we didn't only reverse the reaction, but we multiplied by two.

Now remember when you reverse the reaction, that's going to reverse the sign of delta H, So now it's going to be positive. And whatever number I multiply my equation by, I multiply delta H by that same number. So you'd multiply this by two. When you do that, it gives you 5094   kilojoules. So for my new equation it would be a + 5094   kilojoules.

Reversing the reaction reverses the sign. Multiplying it by a value means I multiply my delta H value by that same number.

Calculate the ∆Hrxn for the following thermochemical equation: 

When given the following: 

• A. -296.8 kJ
• B. -148.4 kJ
• C. 148.4 kJ
• D. 296.8 kJ

Hess's Law

Many reactions cannot be carried out in a single step, but instead require multiple steps to get to the final product. We're going to say Hess's law states that the enthalpy of reaction of an overall reaction is the sum of the enthalpies, the standard enthalpy values of these multiple steps. So here we have a partial reaction one and a partial reaction 2. By combining them together they help to give me my overall reaction down here.

Now what we do is this Xenon difluoride is a reactant, so it comes down. Then we're going to say here that this fluorine, which is a solid, I'm not solid. A product cancels out with one of these fluorines, which is a reactant. Remember, they can't exist on both sides. OK, this causes an imbalance. These are called reaction intermediates and they will cancel one another out. So this cancels out with one of these, leaving us with one behind.

This xenon here is a product, and this one here is a reactant. Again, it can exist as both there's one and one on each, so they both cancel out each other entirely. What's left behind comes down South. This F₂ comes down to give me this reactant, and then this Xenon triford comes down to give me this final product.

To find the overall enthalpy of reaction for this overall reaction, you add up each of these partial standard entropy values. So when you add 123 and you subtract it, subtract 262. That's how we come up with this new delta H of reaction. That's a -139 kilojoules. This in essence is what Hessel's law tries to do. It takes partial reactions and from them helps us to determine the overall reaction and associated with it in overall enthalpy of reaction.

Hess's Law Example 2

Here it says to calculate the enthalpy of reaction for the overall reaction. So we have carbon monoxide plus nitrogen monoxide producing carbon dioxide and half a mole of nitrogen gas. Now here we're given these partial reactions below with their own known standard enthalpies of reaction. Now what do we do? Well, let's follow the rules.

Step one says that I need to start with the first compound in the overall equation and locate it in the set of partial reactions. Compound from partial reaction must match in terms of number and type, and we'll see what that means with the one from the overall equation. This may require you to reverse, multiply or divide the partial reaction, which will also affect your standard enthalpy value. Step two says keep moving on to the next compound in the overall equation until you locate all compounds in the partial reaction. So let's do steps one and two initially.

All right, so we have two. So if we go back to step one, it says that we need to locate the compound, we must locate the first component in the overall equation and locate it in the set of partial reactions. All right, so in my overall equation, I have carbon monoxide gas as a reactant, and there's one of it, 1 mole of it. So if I look in the partial reactions, we see carbon monoxide is right here. But we have an issue. Although there is one mole of it, like I want, it is a product, we need it to match up with the overall equation. We need it to be a reactant.

To do that, that means I'm going to have to reverse the reaction. Now, when I reverse the reaction, it's now going to become a reactant. O₂ also becomes a reactant and CO₂ becomes a product. Now remember, when I reverse the reaction, that's going to reverse the sign for delta H. So now my carbon monoxide, there's one mole of it. So the number is good, and the type is also good because it's also a reactant. Now, just like in my overall equation, this equation is gone now because it's been reversed and is represented by this bottom one.

Next, I need to find NO gas. I need it to be 1 mole of it and I need it to be a reactant. Here I see it. Two issues. First, it has a two in front of it. I need it to have a coefficient of one just like in my overall equation. Also, I need it to be a reactant. So what I'm going to do here is I'm going to divide by 2 and reverse. So here I'm going to divide by two and reverse it. So that's going to become NO gas. And then when I reverse and when I divide by two, this becomes half N₂ plus half O₂.

When I reverse the equation, remember that's going to change the sign, so this becomes negative. And when I divide by two, I have to divide delta H by two so this is -90.3 kilojoules. So now this NO matches up exactly with the overall equation. Keep going. We need one mole of CO₂ as product which we have here. We need half a mole of N₂ product which we have here. So all the compounds I need match up with the overall equation.

So now we go to step three, combine the partial reactions and cross out reaction intermediates if present. Reaction intermediates are compounds that look the same with one as a reactant and the other as a product. Once we do that, we go to step four and we add all the standard enthalpy values of my partial reactions to obtain the enthalpy of reaction of the overall reaction. Alright, so who are intermediates? Things that look the same, but one's a product and one's a reactant. We have half O₂ here as a reactant, which will cancel out with this half O₂. That's a product.

Those are our only reaction intermediates. Everything else comes down. If you look when everything comes down, it should give you back the overall equation you were looking for in the first place. It doesn't matter the order that you write them in. All that matters is that the coefficients match the overall equation and that they're on the right side. Reactants here should match up with the reactants up in the overall products here should match up with the products up here. All we do now is we add up these enthalpies of reaction. So when I add up -283 plus this -90.3 that gives me a total enthalpy of reaction equal to -373.3 kilojoules. So this would be our Hess's Law question, where we solved for the overall enthalpy of the reaction for the overall reaction.

Calculate the ∆H_rxn for 

Given the following set of reactions: 

• A. -494.4 kJ
• B. -692.8 kJ
• C. 494.4 kJ
• D. -346.4 kJ

Calculate the ∆H_rxn for 

Given the following reactions:

• A. -177.85 kJ
• B. -355.73 kJ
• C. -258.36 kJ
• D. -487.27 kJ

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What is Hess's Law?

Hess's Law, named after Russian chemist Germain Hess, is a principle in chemistry that states the total enthalpy change for a chemical reaction is the same, no matter how many steps the reaction is carried out in. Enthalpy, denoted by H, is a measure of the total energy of a thermodynamic system, usually expressed in kilojoules per mole (kJ/mol).

In simpler terms, Hess's Law implies that if you have a series of chemical reactions leading from a specific set of reactants to a particular set of products, the total enthalpy change will be the same whether the reaction takes place in one step or through multiple steps. This is because enthalpy is a state function, which means its value depends only on the initial and final states of the system, not on the path taken to get from one to the other.

This principle is particularly useful for calculating the enthalpy changes of reactions where the direct measurement is difficult. Instead, you can sum the enthalpy changes of individual steps that are known, which together give the overall reaction's enthalpy change.

How can Hess's law be used?

Hess's Law can be used to calculate the overall change in enthalpy (ΔH) for a chemical reaction when that reaction can be expressed as the sum of multiple steps for which enthalpy changes are known. This is particularly useful when the direct measurement of the enthalpy change of a reaction is not possible or practical.

To apply Hess's Law, you would follow these steps:

1. Write down the chemical equations for all the intermediate steps of the reaction.
2. Ensure that the sum of these steps gives the overall reaction you're interested in.
3. For each step, write down the known enthalpy change.
4. If necessary, reverse or multiply the intermediate reactions to match the overall reaction; remember to also reverse or multiply the enthalpy values accordingly (reversing a reaction changes the sign of ΔH, multiplying changes the magnitude).
5. Add up all the enthalpy changes from the intermediate steps to find the total enthalpy change for the overall reaction.

Hess's Law is based on the principle that the total enthalpy change for a chemical reaction is the same, no matter how it occurs, as enthalpy is a state function. This makes it a powerful tool in the field of thermochemistry for determining the energy changes involved in chemical reactions.

How do you use Hess's law for enthalpy change?

Hess's Law states that the total enthalpy change for a chemical reaction is the same, no matter how the reaction occurs, as long as the initial and final conditions are the same. To use Hess's Law to calculate enthalpy change, follow these steps:

1. Write down the chemical equations for the steps of the reaction for which you know the enthalpy changes. These steps should add up to the overall reaction.
2. Ensure that the equations are balanced in terms of both mass and charge.
3. Adjust the enthalpy changes to correspond with the coefficients used in the balanced equations. If you reverse an equation, change the sign of its enthalpy change. If you multiply the coefficients in an equation by a factor, multiply the enthalpy change by that factor as well.
4. Add up the enthalpy changes for the steps. This sum will give you the overall enthalpy change for the reaction.

By following these steps, you can determine the enthalpy change of a reaction even if it does not occur in a single step or if the enthalpy change for the overall reaction is not directly measurable.

How is Hess's law applied in calculating enthalpy?

Hess's Law is a principle that states the total enthalpy change for a chemical reaction is the same, regardless of the number of steps the reaction is carried out in. This is because enthalpy is a state function, which means its value is determined only by the initial and final states of the system, not the path taken to get from one to the other.

To apply Hess's Law in calculating enthalpy, follow these steps:

1. Write down the chemical equations for the steps of the reaction for which you know the enthalpy changes. These steps could be hypothetical or actual intermediate reactions.
2. Ensure that the equations are correctly balanced.
3. Adjust the enthalpy values for these steps if the equations are multiplied or divided to match the molar quantities of the overall reaction.
4. Add or subtract these enthalpy changes to reflect the overall process, paying attention to the stoichiometry of the reactions.
5. The sum of these enthalpy changes will give you the total enthalpy change for the overall reaction.

This method allows you to calculate the enthalpy change for a reaction that may be difficult to measure directly by using known enthalpy changes from related reactions.