Rate Law Equation: Solving for m & k

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Discussion Overview

The discussion revolves around solving for the reaction order (m) and the rate constant (k) in the rate law equation for a hydrochloric acid reaction. Participants explore mathematical approaches to analyze the provided concentration and reaction rate data, focusing on the application of logarithmic transformations and graphical methods.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents a rate law equation r=k[H+]m and expresses uncertainty about how to start solving for m and k using the given data.
  • Another participant suggests converting the rate law equation into a linear form (y=mx+a) to facilitate calculations for m and k.
  • A participant shares their progress, indicating they have derived a logarithmic relationship and calculated a value for k, but expresses uncertainty about the units for k.
  • One participant inquires about the expected outcome of plotting log(r) against log([H+]), hinting at potential relationships in the data.
  • Another participant challenges the need for a plot of the fit to assess the quality of the data and questions the meaning of certain terms and units used in the discussion.
  • A participant asks if there is a way to manipulate the given rate data to align with the rate law, indicating a search for alternative approaches.

Areas of Agreement / Disagreement

The discussion contains multiple competing views and approaches to solving the problem, with no consensus reached on the best method or the correctness of the calculations presented.

Contextual Notes

Participants express uncertainty regarding the interpretation of units and the appropriateness of the data used in the calculations. There are unresolved questions about the method of fitting the data and the implications of the logarithmic transformations.

Who May Find This Useful

This discussion may be useful for students or individuals interested in chemical kinetics, particularly those working on rate laws and data analysis in a homework or experimental context.

TheExibo
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Homework Statement



Concentration of Hydrochloric Acid (mol/L)

3

2

1.5

1

0.5

Reaction Rate (s/M)

1.333

13.30

38.67

73.00

1466

Homework Equations



r=k[H+]m (r is rate in M/s, k is constant, [ ] is concentration, m is order of reaction)

The Attempt at a Solution



I'm not entirely sure how to start off this problem. Using the concentration as the "x" value and the rate of reaction as the "y" value, I need to figure out m, the exponent, and if possible: k, which is the constant. How do I start?
 
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Can you think of a mathematical way of converting the r=k[H+]m equation to the y=mx+a form (where m is the exponent you are looking for, and all other things - x, y, a - are easy to calculate from the given data?
 
Borek said:
Can you think of a mathematical way of converting the r=k[H+]m equation to the y=mx+a form (where m is the exponent you are looking for, and all other things - x, y, a - are easy to calculate from the given data?

I am trying that right now. Here is where I've gotten so far:

*using line of best fit slope of the recordings (0.024s-1/M)
log(1/r)=(0.024s-1/M)[H+]+logk
*using random value in the recordings
log0.065=(0.024s-1/M)log3M+logk
-1.19854=logk
k=0.063

I'm also not sure how to get the units for k.
 
What would you expect to get if you plotted log(r) vs log(H+)?

Chet
 
To stop this being a very scholastic exercise please show the plot of your fit. We have no idea how good it is nor whether there are any systematic trends away from your line.
Also no one would be treating data of a reaction that he didn't know what it was, and what ws in the reaction mixture, so please tell us.
Does s/M mean the numbers in the second table are reciprocals of the reaction rate?
What does Log3M mean?
 
Is there any way you could manipulate the given rate to fit the rate law?
 

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