We've said previously that the change in enthalpy for a reaction is given for the reaction as written, according to the coefficients in the chemical equation. This is why we can use it as a conversion factor in dimensional analysis. So if we multiply all of the coefficients in our equation by some factor, we also need to multiply the change in enthalpy for the reaction by that same factor. Or if we reverse a chemical reaction, we change the sign on the change in enthalpy. We saw this when we discussed endothermic and exothermic processes. If the forward reaction is endothermic, transferring thermal energy from the surroundings to the system, then the reverse reaction is exothermic, transferring thermal energy from the system to the surroundings. If the chemical equation can be expressed as the sum of a series of steps, then the change in enthalpy for the overall reaction is the sum of the changes in enthalpy for the individual steps. This is called Hess's law. For example, if we add together the reactions A plus 2B produces C and C decomposes to produce 2D, the overall reaction is A plus 2B produces 2D. So the change in enthalpy for the overall reaction is the change in enthalpy for the first step plus the change in enthalpy for the second step. Hess's law works because change in enthalpy is a state function. It doesn't matter the route we take to get from reactants to products in determining the overall change in enthalpy for a reaction. Let's practice using Hess's law. We want to find a change in enthalpy for the reaction dinitrogen monoxide gas combines with nitrogen dioxide gas to produce three nitrogen monoxide gas. We're given three equations with these compounds. We'll need to add together combinations of the three equations that are given to get the overall reaction. We'll start by looking through our reactants and products in the overall reaction to find substances that show up in only one of the given reactions. For example, dinitrogen monoxide gas only shows up in the third reaction, so we know all of the dinitrogen monoxide gas in the overall reaction must come from the third equation. We want one mole of dinitrogen monoxide gas as a reactant and in the third equation, we have two moles of dinitrogen monoxide gas as a reactant. So we'll need one half of the third equation. Since we multiply our reaction times one half, we also need to multiply our change in enthalpy by one half. Let's look at nitrogen dioxide next. The only reaction that contains nitrogen dioxide is the first reaction, so we know all of the nitrogen dioxide in the overall equation must come from our first reaction. We want one mole of nitrogen dioxide as a reactant, but in the first reaction, we have two moles of nitrogen dioxide as a product. So we need to reverse reaction one and multiply it by one half. Since we're reversing the reaction, we multiply the change in enthalpy by -1 and since we multiplied our reaction by one half we also multiply the change in enthalpy by one half. The last compound in the overall reaction is nitrogen monoxide. We want three moles of nitrogen monoxide as a product. We already have one mole of nitrogen monoxide as a product from the equation we just used so we need two more moles as a product. Our last equation has two moles of nitrogen monoxide as a product so we can add the equation as it is. Since we didn't adjust the equation in any way, we can also add the enthalpy of reaction as it is. Now we can add all of these equations together. When adding reactions, all of the reactants stay reactants and all of the products stay products. Anything that shows up the same on both sides can be canceled out. One mole of N2 gas and one mole of O2 gas show up on both sides, so we can cancel these out. We're left with the overall reaction: N2O plus NO2 produces 3 NO. So we've correctly added together our given equations. According to Hess's law, the enthalpy of our overall reaction is the sum of the enthalpy changes for each step. So we add -81.6 kilojoules plus 56.55 kilojoules plus 182.6 kilojoules to get 157.6 kilojoules for the enthalpy change of our overall reaction.