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A flask contains a mixture of compounds $A$ and $B$. Both compounds decompose by first-order kinetics. The half-lives are 50.0 min for $A$ and 18.0 min for $B$. If the concentrations of $A$ and $B$ are equal initially, how long will it take for the concentration of A to be four times that of B?

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56.2 \mathrm{min}

Chemistry 102

Chapter 6

Chemical Kinetics

Kinetics

Sahar A.

February 12, 2022

Added equal amounts of material A, B to liter of suitable solvent and after 500 seconds reaction of half A, what is the amount of substance A that reacts after 800 seconds if the reaction of substance A: zero order reaction. First order reaction of A and

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In probability theory, the conditional probability of an event A given that another event B has occurred is defined as the probability of A given B, written as P(A|B). It is a function of the probability of B, the probability of A given B, and the probability of B.

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In chemistry, kinetics is the study of the rates of chemical reactions. The rate of a reaction is the change in concentration of a reactant over time. The rate of reaction is dependent on the concentration of the reactants, temperature, and the activation energy of the reaction.

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A flask contains a mixture…

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The half-life of a reactio…

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Hello. So today we're going to be looking at, uh, two compounds and be with the half lives shown here. And we know that they start out at the same initial concentration. But they have different half life, so their concentrations will change differently. We want to find out our time. Ah, the concentration off a will be four times the concentration of B. So how would we do this? Well, we know that the initial concentrations were both the same. So why don't we say that will be our bear the variable axe. And we want Teoh, uh, give expressions for the Constitution of A and B in terms of this x and time. So the concentration of a would be the initial concentration and then we're given the half life so the half eso for every half life it will be decreasing by half. So we will we find out how many half lives there are by dividing the time minutes by 50 and so we see if t equals zero, then this would all be one. And then it's just our initial concentration. And if it's 50 minutes, one half life would be half the initial concentration It's 100 minutes. Two half lives to known be ah, quarter of initial concentration. So that's our expression. Now let's take a look at our expression for the concentration of B. Well, it would be like a It would be the initial concentration times half to how many? The power of how many half life Sarah so t over 18. So At T equals zero again. The concentration would just be the initial concentration. AT T equals 18 1 half life. It would be half the initial concentration and so on. So now let's plug into this equation right here. So we're going tohave. It's one half t 50. So you call to four picks when half t over 18. So our initial concentrations would cancel. And so to make this simpler, let's divide both sides by half to the power of T over 50. So we would have won Is he called a four hymns half to the power of tea over 18 minus t to the 50. And if, as you look at this, you should probably see that if we want one. If we want this for to become one, this has to be one quarter So this right here has to be equal to two. So let's find out what time that would be equal to two. So let's multiply everything. My 18 times 50 which is 900. So this would become 50 t. This should become 18 t and this would become 1800. So now we can simplify. We will see that this would become 32 t and dividing 800 by 32. That will give us that. The time is 56 0.3 minutes. So there we go after 56.3 minutes has passed The constitution of a will be four times the concentration of B.

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