The evaporation of a 120-nm film of n-pentane from a single crystal of aluminum oxide is zero order with a rate constant of 1.92⨉1013 molecules/cm²•s at 120 K. a. If the initial surface coverage is 8.9⨉1016 molecules/cm², how long will it take for one-half of the film to evaporate?

Video transcript

hey everyone in this example we have the decomposition of ammonia over hot tungsten as a zero order reaction, we're told the rate constant by this value here And we need to or we're also told the initial amount of Ammonia as .00475 moller. So we need to calculate the time when the concentration of ammonia is half of its original amount. So we should recall that the half life of a reaction for a zeroth order reaction according to the prompt is going to equal the concentration of our original sample initially Divided by two times the rate constant K. So plugging in what we know from the prompt, we would have that our half life is equal to our initial initial concentration of our sample of ammonia. From the prompt in the numerator would be 0. Molar. And we want to recall that polarity can be interpreted as moles per leader so we can go ahead and write this in as units of moles per leader. Then in our denominator we're going to plug in two times our rate constant, which from the prompt is given as 1.31 times 10 to the negative six power moles per leaders time seconds. And so getting rid of our units. We can cancel out leaders as well as moles and we're left with seconds for our half life and we're going to get a value equal to 1812.98. And we're left with units of seconds. However, we can go ahead and write this in scientific notation so that we get our half life equal to 1.81 times 10 to the third power seconds. And so for our final answer, this is the value that we get for the time when the concentration of ammonia is half of its original amount. So this would be the half life of our ammonia. So I hope that everything I explained was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video.