Using Hess's Law To Determine K - Online Tutor, Practice Problems & Exam Prep

Understanding how alterations to a chemical reaction affect the equilibrium constant (K) is crucial. Multiplying the coefficients of a reaction will raise the K value exponentially; for instance, tripling the coefficients results in K being cubed. Conversely, reversing a reaction yields the inverse of K, changing the direction of the reaction and flipping the reactants and products. Dividing the reaction by a number raises K to the reciprocal of that number, such as halving the reaction coefficients resulting in the square root of K. These changes demonstrate that the relationship between K and the coefficients of a reaction is not linear but exponential, significantly impacting the equilibrium constant and the system's behavior.

Using Hess's Law To Determine K

Recall with Hesse's law that the enthalpy of reaction or Delta H reaction it changes for proportionally to the coefficients of a reaction. Meaning that if I have a chemical reaction and I multiply it by three, I'd multiply delta H by three. If I divide that reaction by two, I divide delta H by two. If I reverse the direction of the reaction, I reverse the sine of delta H, We're going to say. However, the relationship between your equilibrium constant K and the coefficients of a reaction is exponential.

OK, so when we say exponential, we're going to say there were three possible rearrangements or changes of a chemical reaction. So here we have our balance chemical equation, which is 2 moles of sulfur dioxide gas combined with one mole of oxygen gas to produce 2 moles of sulfur trioxide gas. Associated with this is our original equilibrium constant value of 71.3. Here we're going to take a look at three types of changes that can happen. We can multiply the reaction, we can reverse the reaction, or we could divide the reaction by a value.

What effect will this have on my equilibrium constant, K? Well, for the first one, multiplication, we're going to say if you multiply the reaction, we're going to raise K to the same factor. So for example, I'm going to multiply the reaction by three. So I'm multiplying this reaction by three. So all the coefficients get multiplied by three. I'll have 6, so two gas +302. Gas gives me 6, so three gas. When I multiply the reaction by a value, K is raised by that number. So here our new K would be K3, so it would be 71.33. So that will come out to be a pretty large number. It's going to be 362467.097 he. We don't care about sick figs per se, we're just seeing how the value is being affected.

What happens if I reverse the reaction? Well, if I reverse the reaction then I get the inverse of K Here this K value is when we have K1 that's its number. When I reverse it becomes K-1 the inverse. So here are new reaction I'm going to reverse it. It becomes 2SO₃ gas. Gives me two, so two gas plus 102 gas. I'm just flipping the reaction. My reactants have become products. My product has become a reactant. So now my new case K-1 which is 71.3-1 which is .0140. That'd be my new K value.

Then finally we could divide the reaction. We divide the reaction. You raise K to a reciprocal of that factor. So here I'm dividing by two. Dividing by two really means that I'm raising it to the half power. If I divide it by three, it be K1/3. If I / 4 become K1/4 except. All right, so here I'm dividing the reaction by two, so this becomes. Remember I'm dividing all the coefficients by two, so this becomes 1SL₂ gas. Plus half O₂ gas gives me one SO₃ gas, so then it's going to become K1/2. So that's going to be 71.3, which gives me an answer of 84 four as my new equilibrium constant.

All right, so remember the effects that we the changes that we do to our chemical reaction has an exponential change on my equilibrium constant, K It affects the exponent involved with K So keep this in mind. Whether you're multiplying, reversing, or dividing your chemical reaction, the changes that it does to equilibrium constant K.

Using Hess's Law To Determine K Example

For the following reaction, we're told that the K_P value is 7.5 * 10 to the -2. Here we need to calculate K_P of the reactions below. So basically what's going on here is we have this original equation with its original K_P value, and we're changing it either through a multiplication, reversal, or division in some way that will produce a whole new K_P value. It's up to us to determine what that new K_P value is.

If we take a look at the first one in option A, we can see that what is the change that occurred? It looks like we divided the original equation by two, right? So we divided the original equation by two, so this becomes one mole. Divide this by two. This became one mole, divided this by two became two, and divided one by two gives me 1/2. Remember, we say that if you're dividing by a number that you're doing the reciprocal of that factor, basically meaning that I / 2. So the new K is going to be K to the half. So here we'd say K_P to the half. So that's going to be 7.5 * 10 to the -2 to the one half power. Remember, 1/2 power is the same thing as square root. So this comes out as an answer of .27 for our new K_P value.

For the next one. What's the change that we see? All right. So it looks like our products are now reactants and it looks like our reactants here are now products. So what do we do? We reverse the reaction, so it's a reversal. When we do a reversal, it's going to be the inverse of our original K value. So it's going to be K_P to the -1. So that's 7.5 * 10 to the -2 to the -1, which equals 13. Here all our answers aren't too sick fix because 7.5 * 10 negative 2 has two significant figures.

And then finally, let's look at the last one. What's the last one? Well, it looks like in the last one we still reversed it. Our products on our reactants and our reactants are now products. But what's the other change that occurred? Well, here we had a coefficient of four. Now it's 16. This was a one, now it's a four. This these two were both twos and now they're eights. So this one will represent a reversal and also we multiply it by 4. Well when we reverse, that's going to give us the reciprocal. But then when you rate, when you multiply, you raise that as a power, so it's to the 4th. Alright, so it's going to be 7.15 * 10 negative 2 to the -1, which we know gave us 13, and then we raised that 13 to the four. So this comes out to 3.2 * 10 to the four. This would be our final answer for K_P.

So just remember, we affect these chemical reactions either through multiplication, reversal or division. Changing the chemical reaction has an exponential change on the chemical reaction. OK, so we're going to change the exponent here in order to get our new K value.

K_c = 6.5 x 10² at a particular temperature for a reaction: 2 NO(g) + 2 H(g) ⇌ N₂(g) + 2 H₂O(g). Calculate K_c at same temperature for the following reaction: 1/3 N₂(g) + 2/3 H₂O(g) ⇌ 2/3 NO(g) + 2/3 H(g).

• A. 8.7
• B. 0.12
• C. 0.54
• D. 3.6×10^–9