From the following data for the first-order gas-phase isomerization of CH3NC at 215 C, calculate the firstorder rate constant and half-life for the reaction: Time (s) Pressure CH3nC (torr) 0 502 2000 335 5000 180 8000 95.5 12,000 41.7 15,000 22.4

Video transcript

Hello everyone today. We are being given the falling problem. The hypothetical gas phase isomerization of A. B two B. A. At 425°C was observed. Let me have the following table here. What are its rate constant and half life if the reaction is first order. So the first thing you must know is that the rate constant is essentially Kay or negative K. So we'll have a negative slope. And to find that slope we simply have to use the equation that our slope is equal to. And we'll use these two values. For the first two values Y two minus Y. One equals X two minus X. To our pressure is in the white Xs. And our exes in our temper our time is on our X axis. So for time we'll have 1000 minus zero. And then for our pressure we will have 662 minus 89 incorporating that negative sign. We will get 1.76 times 10 to the negative four seconds To the -1 power. So that's our rate constant. As for our half life we must then use the formula that T 1/2 sub one half is equal to 0.693 over K. And that 0.693 comes from the equation itself. And when we do that we get 0.693 divided by the slope that we determined 1.76 times 10 to the negative fourth. And we get 3.94 times 10 to the third seconds. And so we have solved for our slope or our rate constant as well as our half life overall. I hope this helped, and until next time.