Cramster.com - Homework Solutions, Lecture Notes, Exams, and Free Online Homework Help
Sign Up Now! Login Customer Support
McAfee Secure sites help keep you safe from identity theft, credit card fraud, spyware, spam, viruses and online scams
Problem Solved.
    Home    
    Homework Help    
   Answer Board   
    Resources (Beta)    
   
You Are Here: Home > Answer Board > Chemistry > Topic: Given a table of Time vs. Molarity (Conc.) Deduce ord...
Member's Topic Headline:

Given a table of Time vs. Molarity (Conc.) Deduce order of rxn, rate constant, average rate, and instantaneous rate.

Know the answer? Have a better solution? Share it.
Sign Up Now for FREE!
Join the thousands of students
getting ahead in their classes.
Member Testimonials

Question:

Advertisement:
Answer | Ask New Question | Customize Profile | Leaderboards | 
FAQ

Member's Avatar
Guru
Karma Points: 2,688
Respect (97%):
Date Posted: 7/19/2008 11:53:27 AM  Status: Closed
Given a table of Time vs. Molarity (Conc.) Deduce order of rxn, rate constant, average rate, and instantaneous rate.
Course Textbook Chapter Problem
General Chemistry General Chemistry 1 3
Question Details:

Consider the reaction:      A --> B

Below is a table giving the concentration of A at various times.

Time (s)

[A] (M)

 

 

0

2.00 M

5

1.414246924

10

1.000047182

15

0.707156825

20

0.500047183

25

0.353595095

30

0.250035388

35

0.176805889

40

0.125023593

45

0.088407116
a.         What is the order of the reaction? Explain! 
It is a first-order reaction because it only depends on the concentration of one reactant (rate = k[A]).
Please help me confirm or deny this.
b.         What is the rate constant for the reaction? (Include units.) 
rate constant = slope = (ln[A]2-ln[A]1)/(t2-t1) = (ln[2]-ln[0.0884])/(0s-45s) =
 = -1.81x10-2 s-1
Please help me confirm or deny this.
c.         What is the average rate between 35 and 40 seconds? (Include units.) 
-Δ[A]/Δt = -(-0.051782296 M)/5s = +0.0104 M/s
Δt = 40s-35s = 5s
Δ[A] = 0.125023593 M - 0.176805889 M = -0.051782296 M
Please help me confirm or deny this.
d.         What is the instantaneous rate of the reaction at 50 seconds? (Include units.)
Rate = lim/Δt->0 * ((-Δ[A])/t) = -d[A]/dt = ?
Please help me figure this out.
e.         What is the instantaneous rate of the reaction when the concentration of A is 0.100 M? 
 
Please help me figure this out.

 

 
Bonus Point Alert! Earn +4 additional karma points for helping this annual member.

Answers:

Member's Avatar
Sage
Karma Points: 3,332
Date Posted: 7/24/2008 2:03:01 AM  Status: Live
Asker's Rating: Lifesaver   
Response:
First of all what is a first order reaction?

It is a reaction such that the rate depends directly (linearly) on the amount of material currently available.

rate = -k*C, where C is concentration. Seeing as this is a batch process (implications for a chemical engineer), you know that rate is the time derivative of concentration.

rate = dc/dt = -kc

Integration yields. C = C0*exp(-kt), where k is the rate constant, C0 is the initial concentration.

So if you plot, lnC vs t, and a straight line results, you have confirmed that it is a first order reaction. By a linear regression, the slope of that line would be -k (in inverse time)

I think what you did for the average rate is fine.

For instantaneous rate, you would use the k value from the slope of your line and use your concentration equation:
dc/dt = -k*C0*exp(-kt).

Just sub for C0 = 2M, and t = 50s, and k (from slope). Make sure k is in inverse seconds so that the argument of the exponential function is dimensionless.

For e),

you can use C = C0*Exp(-kt). Just plug in for C, and then calculate t.

Use that t and sub into the rate equation I showed earlier (rate  = -k*C0*exp(-kt))

Note, that the reaction order not need be 1st order. (sorry but I don't have a graph/spreadsheet right now).

If rate is second order, you would get completely different equations. But just try if it is first order right now. If not, PM and I will walk you through another way. Namely, you will use dc/dt = -kc^2 for a second order. Integrate for a function of concentration vs. time, and get expressions for rate.


If you want to ensure that your equation is first order (plot ln(C) vs. t. You will know it is linear if the R^2 ~1, which is the square of the correlation coefficient).

Good luck.
Please PM me if you have more questions and don't forget to rate my answer.



By reading or posting messages on these forums, you are agreeing to the Answer Board's Terms of Service and Conduct (TSC).


About Cramster | Terms of Use | Privacy Policy | Contact Us | Press Room | Site Map | Support | Anti-Cheating Policy

Cramster.com is not affiliated with any publisher. Book covers, title and author names appear for reference only.
Copyright © 2008 Cramster, Inc.