the solar question about the catalysts, and there's actually a little bit looks advanced, but not really so. Actually, everything is easy. Wants to get to graphs. What the question says is we have a reaction. And the energy off actuacion for distraction is 125 Que jewels perm ALS and we use a catalyst. And we have any energy off actuacion list called this energy off activation, too. And this is brought down to 55 Cure Joel Permal. And this whole thing is happening at two and five Celsius degrees in there, asking us by what factor would you expect the reaction rate to increase at 25 Celsius? So since this energy of activation is decreased, what we're looking to see is how much off this second reaction is faster than the first one. So let's right. The artiness equation for K one K one is without the catalyst, and this is going to be equal to a E to the power of minus e A or arty. And K two is equal to a e to the power. If e a two or arty now, Bye bye factor. I'm just going to make simply que wanna work A to and eight are going to cancel and K one over K two means we need to Dwight Bolt right hand sides to So if the base are the same, what we do is we subtract powers so initially we have Yea once over rt minus minus e a to over rt. This is for this obstruction and this negative is coming from the second one. So if you proceed, K one over K two equals to eat the power off minus now yea. One over here is 125 killer jewels per mel's we wanted in jewels. So how we're going to write that is under 25,000 Jules and negative Negative except poll stiff. So a plus and the second one is going to be 55,000 and these guys are divided by r. R 8.31 floor times the tea Now R T is student five Celsius, but we want this in Calvin. So how we do that is than five plus 273 equals to 298 Now, Once we solve this equation, what we will get is crazy. Increase five point towards the six times tend to the poor off negative 13. So the first one is 5.36 times 10 to the power of negative, 13 times smaller than the second one. This is a huge ratio. So you can basically see a catalyst making effect off such a huge number in, uh, such a small drop.