Graph of ln(A/R) vs 1/T: Arrhenius Equation and Homework Equations

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In summary, this book claims that the graph of ln(k/R) vs 1/T should be a straight line parallel to the x-axis, with a constant y value of ln(k/R) + E/RT. However, the next graph on the page is definitely wrong, and the one for log in which base 10 is not mentioned is also wrong.
  • #1
subhradeep mahata
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Homework Statement


Draw a probable graph of ln (A/R) vs 1/T.

Homework Equations


Arrhenius equation: k= Ae-E/RT

The Attempt at a Solution


Taking natural log on both sides of arrhenius equation :
ln k = ln A - E/RT
ln k - ln R = ln A - E/RT - ln R (subtracting ln R from both sides)
ln (k/R) = ln (A/R) - E/RT
rearranging terms and comparing it with y=mx + c,
c= ln (k/R) and m = E/R
upload_2018-7-16_20-21-51.png

According to me the graph should be like this. In the answers, the graph is a similar one, except that there is no intercept given. I am confused. Any help is appreciated.
 

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  • #2
Are you sure you've got your terms right? A in the Arrhenius equation is a constant independent of T. And you can't write ln(k/R) = c because k certainly varies with T.
 
  • #3
@mjc123
ln(k/R)=c, by 'c' i don't mean constant, i mean the y-intercept.
Regarding the terms, yes i am sure. Though A and R are both independent of T, the graph could also have been straight line parallel to x axis. Any help is appreciated.
 
  • #4
The graph must be a straight line parallel to the x axis, with a constant y value of ln(k/R) + E/RT. But it seems a strange graph to plot anyway.
BTW, c in y = mx + c is a constant. It's not just the value of the y-intercept, it's telling you that the only x-dependence of y is in the term mx.
 
  • #5
Ok, got it. Should i send a screenshot of that page of the book? (for confirmation)
 
  • #6
If it has the text of the question, that would help.
 
  • #7
The question is : Which of the following graphs is correct ?
the answer : fig 8.8 first from left
upload_2018-7-17_20-52-13.png

Even the very next graph is wrong.
log in which base 10 is not mentioned is natural log according to this book.
There were only 3 options, the other two are absolutely wrong, simple arrhenius plots.
 

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  • #8
That's definitely wrong. A is a constant in the Arrhenius expression. If A varied with temperature, you couldn't get E from the slope of the ln k vs. 1/T plot.
 
  • #9
Got it, thanks.
 

1. What exactly is the purpose of plotting ln(A/R) vs 1/T in scientific research?

The graph of ln(A/R) vs 1/T is commonly used in thermodynamics and chemical kinetics to study the relationship between the natural logarithm of the Arrhenius constant (A/R) and the inverse of temperature (1/T). This allows researchers to determine the activation energy of a reaction and make predictions about the rate of a reaction at different temperatures.

2. How is the slope of the ln(A/R) vs 1/T graph related to the activation energy?

The slope of the ln(A/R) vs 1/T graph is directly proportional to the activation energy of a reaction. This means that a steeper slope indicates a higher activation energy, while a flatter slope indicates a lower activation energy. The equation for the slope of this graph is equal to -Ea/R, where Ea is the activation energy and R is the gas constant.

3. Can the ln(A/R) vs 1/T graph be used to predict the rate of a reaction at any temperature?

Yes, the ln(A/R) vs 1/T graph can be used to predict the rate of a reaction at any temperature within the range of temperatures used to plot the graph. By finding the value of ln(A/R) at a specific 1/T value, researchers can use the Arrhenius equation to calculate the rate constant at that temperature and make predictions about the reaction rate.

4. Is it possible for the ln(A/R) vs 1/T graph to have a negative slope?

No, the slope of the ln(A/R) vs 1/T graph cannot be negative. This is because the Arrhenius constant (A) and the gas constant (R) are both positive values. Therefore, the natural logarithm of their ratio (ln(A/R)) will always be a positive value, resulting in a positive slope for the graph.

5. What are the limitations of using the ln(A/R) vs 1/T graph in scientific research?

One limitation of using the ln(A/R) vs 1/T graph is that it assumes a linear relationship between ln(A/R) and 1/T. This may not always be the case, especially for reactions that have a complex mechanism or involve multiple steps. Additionally, the graph may not accurately predict the rate of a reaction at extremely high or low temperatures, as the Arrhenius equation is based on the assumption of a constant activation energy.

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