Br₂(g) + Cl₂(g) → BrCl(g) ΔG°_f

Question

Br₂(g) + Cl₂(g) → BrCl(g) ΔG°_f for brcl(g) is -1.0 kj/mol

Accepted Answer

Hey everyone, let's take a look at this problem. The reaction below represents the decomposition of a generic diatonic molecule in its standard state. They give us the gibbs free energy of formation at two different temperatures. And we need to calculate the value of K at each temperature. And then we also need to determine the value of delta H. For the reaction. So let's get started by writing out the equation that we need to solve this problem. And this equation is delta G. Of our reaction is equal to negative R. T. Ln of K. And the first part of the problem is asking us to solve for the value of K at each temperature. And so we're going to have to K values here. And if we rearrange this equation to solve for K, we're going to get our L N. F K is equal to delta G. Of our reaction over negative R. T. And our delta G. Is our Gibbs free energy. Our is our constant and T. Is our temperature. So let's go ahead and plug in what we're given. So for the first one they tell us that the gibbs free energy is 8.1 to kill a jules. We need to convert this to jules because our constant is jules, per mole kelvin. So for our first For it to convert that to Jules, we have 8.1 to kill the jewels and And one kill a jewel. We have 1000 jewels. So our killer joules cancel. And we're left with 120 jewels. So let's go ahead and plug that in. L. N. F. K. Is equal our Delta G. And that is 8120 jewels Permal. And this is divided by R. R R. Is 8.314 jules per mole, kelvin times are temperature. So the temperature that goes with this delta G. Is 2500 kelvin, which is perfect because our our isn't kelvin. So let's just make sure our units cancel here. Our jewels cancel, our moles cancel and our kelvin's cancel. So we're left with Ln of K is equal to negative 0.3906. Now to get rid of this L. N, we're going to raise both sides by E and E as a function on our calculator. So once we raise both sides by E, our Ln will cancel and we'll be left with K. Is equal to 0.676. So that is our first K value because we are being asked to calculate the value of K at each temperature. So this is our K. Value at 2500 kelvin. So we need to do the same thing just for our 2nd Gibbs. Free energy and temperature. So we get Ln of K. Is equal to delta G. Of our reaction over negative R. T. So we need to convert Our second gibbs free energy into jewels. So we have negative 72. killer jewels. And in one killer jewel We have jewels. So this gives us - 200 jewels. So we'll plug that in - 200 jewels divided by negative are so that gives us a negative 8. jules over mall Calvin Times are temperature and that is Kelvin. So let's make sure our units cancel here. Both of our negatives cancel. Our jewels cancel, are moles canceled. This should be jewels per Molinar numerator. So our moles cancel and our Calvin's cancel and we're left with L. N. F. K. Is equal to 2.48. So now we can raise both sides by E. To get rid of R. L. N. And when we do that we get that R K. Is equal to 11.94. So this is our second K. And now we know the value of R K. At each temperature. The last part of this question asks us to determine the value of delta H. For these data, assuming that delta H. Is independent of temperature. So the equation that we can use to solve for that is Ln of K. two over K. One is equal to negative delta H. Of our reaction divided by or Times one over T two - over T one. So for this we're solving for delta age of our reaction. So let's go ahead and plug in because we have everything we need. We have K two and K one we have our which is our constant and we have both of our temperatures. So this is just a plug in and solve so L n f K two over K one is going to be Ln of 11.94 divided by 0. is equal to let me rewrite this. So this should be zero point 676 is equal to negative delta H. Of our reaction divided by R and r R is our constant eight point 314 jules over mall times kelvin and this is multiplied by one over T to our second temperature is 30 500 Calvin -1 over T one Is 2500 Kelvin. So let's work on the left side. So our Ln and Ln of 11.94 divided by 0.676 is going to equal 2.87. And This is over delta h of our reaction divided by 8.314 jules over more times kelvin. And when we simplify our Temperatures we get negative one .14 times to the negative for Calvin. So let's make sure our units cancel here are kelvin's cancel and we can now divide both sides of our equation by negative 1. times 10 to the negative four. And when we do that we get negative 2.52 times 10 to the four is equal to negative delta H. Of our reaction divided by 8.314 jules over mall. So now we can multiply both sides by 8. to get rid of our fraction. And when we do that we'll get a negative and we can cancel out our negatives. And so we get a final answer of delta H. Of our reaction is equal to 2.9 times 10 To the 5th jewels. And to convert this to kill jules, we will do one killer jewel Is equal to 1000 jules. And so our jewels will cancel. And we get a final answer of kila jewels per mole. And this is our final answer. So we calculated both of our case and our delta H. Of our reaction is 209 kg joules per mole. And that is the end of this problem. I hope this was helpful.

Struggling with General Chemistry?

Br₂(g) + Cl₂(g) → BrCl(g) ΔG°_f for brcl(g) is -1.0 kj/mol

Watch next

Gibbs Free Energy And Equilibrium practice set

Struggling with General Chemistry?

Br2(g) + Cl2(g) → BrCl(g) ΔG°f for brcl(g) is -1.0 kj/mol

Watch next

Gibbs Free Energy And Equilibrium practice set

Br₂(g) + Cl₂(g) → BrCl(g) ΔG°_f for brcl(g) is -1.0 kj/mol