Half-Life Concept 2

Jules Bruno
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now when it comes to first order in half life first realized that all radioactive processes follow a first order rate law. So for reactions with first order, we use the following equation and that is half black equals Ln two over K. Now, if you plug in Ln two Ln two in your calculator, you're gonna get 20.693 And it will still be over K. Okay, so just be aware of that. You may see on your formula sheet instead of Ln two, you may see .693. That's where it comes from. Now. Here we're gonna say Ln two is our constant. In this case we're going to say K is our rate constant. And here we'd say since it's dealing with first order it would be units of time. And verse T of course is time when it's T. Half its half life. Now, what can we say about this half life equation and concentration? Well, if we take a look, half life equals Ln two over K. We don't see initial concentration of our reactant anywhere. So that means half life does not depend on the initial concentration of our reactant. And as a result of this, it's going to be constant throughout the whole reaction. So that means how five she's gonna stay flat because K. Is going to be a number that's not gonna change. And Ellen too is always the same number as well. So half life is going to stay consistent throughout the whole reaction. Now, you remember if we do a plot of Y versus X. Why here would be half life? So that's why it's on the Y axis, and X. Here is T for time. That's why it's on over here on the X axis. So keep these little facts in the back of your mind when dealing with half life and first order rate law equations.