# (c) A second order reaction; in which the initial concentration of both the reactants are same, and 25% completed in 600 sec. How long ` will it take for the reaction to go to 75% completion?

(c) A second order reaction; in which the initial concentration of both the reactants are same, and 25% completed in 600 sec. How long ` will it take for the reaction to go to 75% completion?

### Video Transcript

other students in this question, we have been given a second order reaction. Where to react, tents react with each other to form product and concentration of A. Is equal to concentration of B. Thus to simplify our equation will write it as a palace A. Giving those two B. So we'll write the ice taken for it. So initially the concentration of this, the act and pool will be a good at time. T. It will change to X. And because it is degrading and it is forming products so it will be X. Now at equilibrium the concentration of a left will be a minus X. And it will be X. Okay Now 2nd order reaction is given by running bye concentration of reacting but B equal to Katie plus one. Barry concentration. The initial. So if you rearrange that equation we will get Katie is equal to one by concentration A. P miners one bite concentration of that is concentration of at the initial table. So Kay is april to run by the into one by concentration of A. A. T minus run by. That's interesting. You did not. Now if we solve this ahead we get is equal to one by the into concentration of minors concentration of 80. Do you want? And inclusion of 80. I'm concentrating fair enough. Now we'll just put the values from here. You know. Run by T. Is equal to you know it is mm hmm- at 80. It is a minus X. In the bottom 8 20 a minus X. Into. Okay. Now if we open the brackets, we'll get one by T. Me too a minus a plus takes be worried by a minus X and two. Yeah. Now this will get canceled. So in the end will be given one by three into eggs a minus X. Me too. So finally our equation comes down to this. Okay, So I will keep this equation. I will move it over here and clean this space so that we can solve our questions. Just give me a second. So in the question we are given that people do 600. The change in the reactant is 25%. That is 25% reaction is completed. Okay. No, to solve these, We need to find the value of X. X. is equal to 25% off. Mm hmm. Which is equal to 23-85. Into a which is equal to 0.25. Mm hmm. Now, now we have to Use the equation K is equal to one by T into X. Destroyed by A -1 into a. To find the value of. Okay, So K is equal to one by 600 into X. 0.2 zero. Going to fight a right by mm hmm -0.25 into a. So a. And they will get canceled. K is equal to one x 600 into 0.25. Right by 0.75 A. So K is equal to run by 908 2nd in verse mall in verse Peter. Okay, so I'll be right Run by 900 a second inwards alone in world's leader, I will clean this and we will do the last part. So we are asked at what temperature Will the reaction reach 75% completion. Okay. For that X is equal to 75% of which is equal to 0.75. Hey, no, from the previous equation. They know OK. is equal to one by T into X. Divided by a minus X into a. Now to solve this. For time team Is equal to one by K. X rated by a minus eggs into a No, we'll put them a new Okay, Which is one x 900 a into X access calculated by 0.75. Be worried by 1 0 75. Mhm. So that is equal to run by and and then we will have this. So this is one x 1 into 900. Mm hmm. Him too. 0.75 0.25. Hey, when you cancel this, this comes out to weak 2700 second. So it will take 700 27:00 two reach film initial point two 75%. And pollution

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