Consider two reactions. Reaction (1) has a constant halflife, whereas reaction (2) has a half-life that gets longer as the reaction proceeds. What can you conclude about the rate laws of these reactions from these observations?

Video transcript

hey everyone today, we're being told that there are two reactions that have been observed. The first reaction has a half life, that is twice as long as the last one and the second reaction has a half life. That is not affected at all by the concentration of the reactant and is constant over time. Very important. And we're being asked to identify the order of each of the rate laws for the reactions based on these observations. So we can go ahead and take a look back at our different orders and what they signify. So we have zeroth order first order and second order half lives. Let's write each of these out. So for zeroth order Or for a zero order half life we will end up with a formula with the initial enzyme uh concentration divided by two times the rate constant. So in this case the half life both the half life and the enzyme concentration. Or sorry, the reacting concentration are directly proportional T half is directly proportional to the reactant initial concentration. So the half life will decrease as the reactant concentration decreases and vice versa. Taking a look at a first order reaction, We know that the half life is equal to the natural log of two divided by the decay rate or the rate constant. And as such, we know that this will be constant. This is constant and is unaffected by the reacting concentration. Unaffected. Bye react in concentration. Finally the half life for a second order equation which is T half will be one over K times d initial substrate concentration which means that t the half life is actually inversely proportional to the initial reactant concentration. What this means is that as the half life increases, the reactant concentration will decrease and vice versa. So looking back at this, let's go ahead and take a look at the two reactions in the questions. The first is stated that has a half life, that is twice as long as the last one. So since it is twice as long as the last one, that means we can say that it is second order because if it is twice as long, that means the enzyme concentration will decrease by that same amount. In other words it'll be one over K times to for example. So we can say that the first reaction, the first reaction will be second order second order and the second reaction, the second reaction, which says it is not affected by the concentration of reacting and its constant will therefore be first order. I hope this helps. I hope this makes sense. And I look forward to seeing you all in the next one