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A certain first-order reaction is 35.5 percent complete in $4.90 \mathrm{min}$ at $25^{\circ} \mathrm{C}$. What is its rate constant?

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$$0.0895 \mathrm{min}^{-1}$$

Chemistry 102

Chapter 6

Chemical Kinetics

Kinetics

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Hello. So today we're going to be looking at a first order reaction. That is 35.5% complete in 4.9 minutes. So we want to find with every constant of this reaction. Well, how would we do that? Well, let's think about, Ah, what kind of an equation we could use where we could. Since we know how far in it is, how almost complete this, we can find out the ratio of the amount of reaction we had at the start to the amount of reactant we have right now. So is there an equation that relates the constant initial concentration to the current concentration and the time? Well, there is. There's an equation where we have the natural log. Since this is first order of the reactor, concentration at some time is equal to the natural log of the initial concentration. Subtracting okay, t India raging. That gives us that the ratio of the reactor we have at some time to the contract and we have had initially is equal to negative. Katie. So since we know how complete it is, we can figure out this ratio so 35.5% complete means that 35.5% off the reactant has reacted. So let's say that the A not would be 100% of what we started off with. And then what we have after 4.9 minutes is ah 100 subtracting the 35.5 that reacted. So it's 64.5 that we have after 4.9 minutes. So that s o then That would be the natural log of zero 0.6 45 is equal to the negative K after 4.9 minutes. So the natural log of 0.645 is negative. 0.4 39. So let's divide by negative 4.9. We see that our rate constant is equal to zero 0.0 eight nine five in verse minutes. So there you go. We used how far along the reaction is at a certain time to figure out the rain constant

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