Integrating the first order rate law

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Discussion Overview

The discussion revolves around the integration of the first order rate law, specifically the equation -d[A]/dt = k[A]. Participants are examining the steps involved in integrating this equation and the resulting expressions for concentration over time.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant presents the integration steps leading to ln[A] = -kt - ln[A0], questioning where they might be incorrect.
  • Another participant suggests an alternative expression, (ln[A] - ln[A0]) = kt, implying a different interpretation of the integration results.
  • A third participant questions the use of the negative sign in the initial expression.
  • A fourth participant clarifies that the convention is to use final minus initial when performing integrals, suggesting that the integration process should follow this rule.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as there are competing views on the correct form of the integrated equation and the interpretation of the negative sign.

Contextual Notes

There may be limitations related to assumptions about the integration process and the definitions of the variables involved, which remain unresolved in the discussion.

kasse
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-d[A]/dt = k[A]

- Int( d[A]/[A]) = Int (k dt)

- ( ln[A] + ln[A0] ) = kt

ln[A] = -kt - ln[A0]


Where am I wrong?
 
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- ( ln[A] - ln[A0] ) = kt
 
Why "-"?
 
It's always final - initial when doing integrals i.e.

[tex]F(b) - F(a) = \int_{a}^{b} f(x) dx[/tex]

and not +.
 

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