2168 Shares

Help with Integrated Rate Laws?

Help with Integrated Rate Laws? Topic: How to write an equation with a slope of 0
June 26, 2019 / By Paise
Question: A certain reaction has the following general form: aA -----> bB At a particular temperature and [A]o = 2.80 x 10^-3 M, concentration vs. time data were collected for this reaction, and a plot of 1/ [A] vs time resulted in a straight line with a slope value of 3.60 x 10^/2 L/mol s. a. Determine the rate law, the integrated rate law, and the value of the rate constant for this reaction. b. Calculate the half-life for this reaction. c. How much time is required for the concentration of A to decrease to 7.00 x 10^-4 M? Thank you!!! Help is much appreciated!!
Best Answer

Best Answers: Help with Integrated Rate Laws?

Maralyn Maralyn | 3 days ago
let's start here... for the rxn. A --> B + C rate = change in amount of A per unit time.. right? and if the volume is constant.. rate = change in concentration of A per time and in math we write "change in" with "d"... and in chemistry we write concentration with [ ] ... so that rate = -d[A] / dt where.. - is because [A] is decreasing [A] is concentration of A ok so far? ******* also... we know that rate is proportional to concentration... the higher the concentration of A, the faster the rate because the more frequent the collisions. In math we write proportions as rate α [A] and in math we solve proportions by inserting a constant and an = sign rate = k x [A] and since some reaction mechanisms involve 1 molecule of A decomposing and others involve 2 or more A's colliding...there is an exponent on that [A] rate = k x [A]^n where n is the "order" of the reaction n = 0 is zero order n = 1 is first order n = 2 is second order etc **** combining those 2 rate = -d[A] / dt = k x [A]^n **** now we just need to solve.. the idea is.. we have two data points.. point 1 is.. time = zero.. [A] = [Ao].. (ie we start with initial conc = Ao) point 2 is.. time = t.. [A] = [At].. (ie.. after time = t has elapsed, conc = At) and we integrate.. **** for n=0 -d[A] / dt = k x [A]^0 d[A] = -k x dt integrating from (0, [Ao]) to (t, [At]) .. . . [At]... . ..... t [A]...|... = -k x t.. | ... .. .[Ao]... ... .. 0 or.. [At] = -kt + [Ao] ***** if n=1 -d[A] / dt = k x [A]^1 1/[A] x d[A] = -k x dt ln[At] = - kt + ln[Ao] ****** if n=2.. -d[A] / dt = k x [A]² 1/[A]² d[A] = -k x dt integrating.. - 1/[At] - - 1/[Ao] = -kt 1/[At] = +kt +1/[Ao] ***** now we have these equations.. n = 0.. .. [At] = -kt + [Ao] n = 1.. .. ln[At] = -kt + ln[Ao] n = 2.. .. 1/[At] = +kt + 1/[Ao] and if you look just at the 3rd equation..and.. let y = 1/[At] x = t m = +k b = 1/[Ao] you get this equation y = mx + b which is a line.. right? so.. IF the reaction is 2nd order.. a plot of 1/[A] vs t will give a straight line likewise.. if the rxn is 0 order.. [A] vs t gives a line if the rxn is 1st order.. ln[A] vs t gives a line ***** ***** so.. you have a plot of 1/[A] vs t give a straight line.. therefore.. the rxn is 2nd order in [A] rate = k x [A]² and of course.. +k = the slope of the line = 3.60x10^-2 /Mxsec.. so that.. rate = +3.60x10^-2 / Mxsec x [A]² the integrated rate law is then. 1/[A] = +3.60x10^-2 / Mxsec x time + 1/(2.80x10^-3M) **** half life is when [At] = 1/2 [Ao].. 1/[At] = +kt + 1/[Ao] t 1/2 = (1/[At] - 1/[Ao]) / k t 1/2 = (1/(1/2[Ao]) - 1/[Ao]) / k t 1/2 = (2/[Ao] - 1/[Ao]) / k t 1/2 = (1/[Ao]) / k t 1/2 = (1 / 2.80x10^-3M) / (3.60x10^-2 /Mxsec) = 9920 sec *** [At] = 7.00x10^-4M 1/[At] = +kt + 1/[Ao] t = (1/[At] - 1/[Ao]) / k t = (1/7.00x10^-4M - 1/2.80x10^-3M) / (3.60x10^-2 /Mxsec) = ___ sec I'll let you finish.
👍 134 | 👎 3
Did you like the answer? Help with Integrated Rate Laws? Share with your friends

We found more questions related to the topic: How to write an equation with a slope of 0


Maralyn Originally Answered: Can an LDS marriage last if you do not like your in-laws?
Look, if the rest of this family even makes it into the Celestial Kingdom, they're not going to be mentally ill anymore. So I doubt being sealed to them is going to be as big an issue there as it seems to you here. Let it go. Take the advice of your church leaders and keep your distance from them - since they are obviously dangerous and harmful people to be around. Honestly, your leaders at church seem to be giving you perfectly fine advice on the matter. I wonder why you thought they weren't enough, and felt the need to come on here asking for additional validation. Oh, and I don't know what sort of family culture you grew up in, but I grew up without seeing most of my extended family for years at a time. Not that we disliked them (we liked them quite a bit), but we lived far away. So we didn't see them. Trust me, your kids won't die not seeing their aunts and uncles - and even grandparents. They'll likely be just fine.
Maralyn Originally Answered: Can an LDS marriage last if you do not like your in-laws?
IMO there are two things that would make this situation something that would destroy your marriage. The first is if your husband didn't get how wacko they are and sided with them against you. The second is if you let this hate get into your soul and eat you up from the inside out. Hate is like a disease, like cancer. It will eat you up as surely as a cancer if you let it. It sounds like your husband is with you on the whole concept of these people not being good for your family so that shouldn't be a problem. You're both on the same page and that right there is a HUGE win on your side. Many people are fighting not only their crazy in-laws but their spouse who either doesn't get how crazy their family is or insist on spending lots of time with them anyway. I think right now your focus is in the wrong place. You seem to be focusing on the crazy in-laws and the rotten things they have done to you and I get that - I swear I do. I have my own set of in-laws that I've been dealing with for nearly 26 years. You need to let go of the anger and hatred. I'm not saying that you become friends with these people or that you will all of a sudden like them - in fact I hope that you keep their contact with your family to a minimum but, for your sake...for your childrens sake, you need to let it go. Its unfortunate that your dream of the perfect extended family isn't going to happen but most of us have to accept that our families aren't all that we may have dreamed about as children. Focus on what you do have, your husband and your children. That is what's important. Create an extended family within your friends and ward members. I honestly don't thing moving away is the answer. You need to set boundaries and do not accept any of them stepping outside those boundaries. You can be tough and no nonsence without being filled with anger and hate. One thought that has helped me in times of my life when I've been dealing with forgiveness and anger is thinking about "what would Jesus do?" And I don't mean that in a stupid little pop culture catch phrase way but I mean for you to actually think about it.... what do you think Jesus would do if faced with this same situation? Of course you aren't perfect and you're bound to struggle more than He would but I think... who else can give you a better example of forgiveness than Him? Also of course you can pray for grace and peace and He will help you reach a point where you can truly get rid of that anger and hate that fills you. Be thankful for the wonderful family that you have and let go of what will never be.

Kinborough Kinborough
undemanding sillyhil who's gonna answer you mate why cant you pop in the library for a sec and verify some books or study your notes and follow the examples. no you may still have given you this question in case you have no longer been taught mate. dont be aggravated ladybird that's the actuality mate
👍 50 | 👎 -4

Kinborough Originally Answered: What are the laws on pulling the plug?
It depends on what is stopped by pulling the plug and the policies of the hospital involved. Some measures are considered "basic sustenance" such as feeding and hydration tubes, while others such as intubation and mechanical ventilation are not. Generally, the next of kin or holder of the medical power of attorney can make those decisions unimpeded. But not always. As an example, a cancer patient is admitted to a Catholic hospital. The patient's doctor wants to try a round of chemotherapy, but prior to that, a feeding tube will have to be inserted to boost the patient's nutritional status. The patient agrees, with the stipulation the feeding tube be removed if the chemotherapy is unsuccessful. The doctor agrees, however the hospital does not as their policies state that once a feeding tube is inserted, it cannot be removed at the patient's discretion or with the family's wishes. ---------------- Happened to my father and took me by surprise. I've been an RN for years.
Kinborough Originally Answered: What are the laws on pulling the plug?
Varies by state, by hospital policy, and by specific situation. Any competent person can refuse any medical treatment - hydration, food, medicine, surgery, etc. If the patient is not able to make a decision, first check whether he had a prior medical directive. Whatever he directed happen (or not happen) as far as treatment options should be honored by the hospital, and by the person he chooses. The patient can designate anyone he wants; need not be family. A common medical directive is called a DNR. Research that. If patient is not able to make a decision and did not have a medical directive, the decision belongs to the patient's spouse. If not married, then typically to another family member. Obviously, there are going to be problems if the unmarried patient has children and the children disagree. Go read up on Terri Schiavo. She was still married at the time of death, and thus the decision to withdraw support was her husband's - not Ms. Schiavo's parents. That is a good place to start for a research paper. Just a kind FYI :) - we are talking about life and death. "Pulling the plug" is slang and inappropriate.

If you have your own answer to the question how to write an equation with a slope of 0, then you can write your own version, using the form below for an extended answer.