Consider a hypothetical reaction between A, B, and C that is first order in A, zero order in B, and second order in C. (a) Write the rate law for the reaction.

Video transcript

Welcome back everyone in this example, we need to determine the rate law for a hypothetical reaction with reactant being X, Y and Z. We're told that the reaction is second order with respect to X. First order with respect to our reactant, Y and zero order with respect to react and see. So we have according to the prompt. The hypothetical reaction with X plus Y plus Z. We are not given products. So we'll just put a question mark here and we need to determine the rate law here. So we want to recall that the general format for our rate law is going to follow. And actually there should be a colon here where our rate of our reaction is equal to the value for our rate constant, which we recall is K multiplied by the concentration of each of our reactant. And so if we had two reactant, our first reactant would be the concentration of A. We can say times or to the exponents. Where X would represent our reactant order of A. With respect to the reaction, which is then multiplied by the concentration of our second reactant. We can say that that's B, which is raised as an exponents to its respective order. We can say why in regards to our reaction. And so to be clear, we can say that X and Y are going to be our reacting orders and then K. We recall is our rate constant. So this is something that we should recall. And so with respect to our reactions being X, Y and Z. Now according to the prompt, we need to write out our rate law and because we recall the above, we can say that for our rate law, we would have that our rate is equal to the unknown value for our rate constant case will just plug it in as K. Which is then multiplied by the concentration of each of our reactant. So our first reactant according to our prompt is X. So we would say times the concentration of X. And according to the prompt, X is going to be a second order reactant with respect to the reaction. So we would place that Value there as two and the exponents. So we've fulfilled this portion of our rate law. Then we have our second reactant which we have as why. And according to the prompt, why is going to be first order with respect to the reaction. So we filled that part in. And then lastly that leaves us with our concentration of our last reactant being Z. Which according to the prompt is zero order. So we'll raise that to an exponent of zero with respect to our reaction. And so now we want to go ahead and simplify this rate law. So we would say that our rate is equal to the rate constant K. Multiplied by X to the second power, which is then multiplied by Y. And we're going to end it off here. And this would complete our rate law for our given reaction of X, Y. And Z. Now we have simplified our brackets to just why here? For our concentration of why? Because we understand that we don't need to write out one in exponents, it's just implied and understood here and we should recall that anything raised to an exponent of zero is just going to equal one. And so we could technically just include the one here, but because we know that this is just all multiplied by one, we would simplify this so that our rate is equal to the constant K. Times our concentration of our first reacting X to the second, power times the concentration of why. So this would just lend us with the same rate law. And so this simplified expression here and sorry about that. This simplified expression here and we'll do that one more time. Is going to be our final simplified rate law for our given reaction described in the prompt. So what's highlighted in yellow here is our final answer to complete this example. I hope that everything that I reviewed was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video