(a) The gas-phase decomposition of SO2Cl2, SO2Cl21g2 ¡SO21g2 + Cl21g2, is first order in SO2Cl2. At 600 K the half-life for this process is 2.3 * 105 s. What is the rate constant at this temperature?

Video transcript

Hello everyone. Today, we have the following problem. The thermal cracking of ethane is a first order process and has a half life of 2.11 times 10 to the negative second seconds at 900 degrees Celsius, determine the rate constant at 900 degrees Celsius. So first, what we wanna do is you wanna draw the equation for half life. The equation for half life is going to be the natural log of two divided by some constant K. And so what we wanna do is they want to rearrange this equation. And so that we're solving for K in that K is going to be equal to the natural log of two divided by our half life simply plugging in the values that we have from the problem. We have the natural log if two can be divided by the half life, which was given to us in the question stem as 2.11 times 10 to the negative second seconds. When we plug this into our calculator, this is going to give us a rate constant of 32.9 seconds raised to the -1. And with that, we have the answer to our problem overall, I hope this helped and until next time.