So I was brainstorming trying to find what I did wrong in this chemistry problem:(adsbygoogle = window.adsbygoogle || []).push({});

https://www.physicsforums.com/showthread.php?t=627731 (simple algebra no chemistry knowledge required)

And I noticed something peculiar about the process of solving inequalities, let me sum up in a phrase what I found:

"When solving inequalities the VERY FIRST thing we should do is input the known values of all the variables we have in the inequality"

In the problem in the previous link what I did was solve for T first and then at the very end input all the values to get a numerical answer (just as I have been doing all my life with equations), doing it that way I got a wrong answer because there was a change of direction in the inequality sign:

ΔG=ΔH-TΔS

0>ΔH-TΔS

-ΔH>-TΔS

[itex]\frac{-ΔH}{-ΔS}[/itex]<T (the inequality sign changes direction when we multiply or divide both sides by a negative number right?)

[itex]\frac{ΔH}{ΔS}[/itex]<T (signs cancel each other)

[itex]\frac{-114.1kJ}{-146.4·10^-3kJ/K}[/itex]<T (we input the values)

780K<T

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In contrast when I repeat the problem inputting the values first I get the correct answer:

ΔG=ΔH-TΔS

0>ΔH-TΔS

0>-114.1kJ-T(-146.4·10[itex]^{-3}[/itex]kJ/K)

114.1kJ>-T(-146.4·10[itex]^{-3}[/itex]kJ/K)

114.1kJ>T(146.4·10[itex]^{-3}[/itex]kJ/K)

[itex]\frac{114.1kJ}{146.4·10^-3kJ/K}[/itex]>T

780K>T , indeed when the temperature is lower than 780K the inequality 0>ΔG is satisfied, ΔG is negative, and the reaction is spontaneous!

So please someone aware me on this, is the fact that the very first step in solving an inequality is to input the values and then continue with the solving process kind of an unwritten rule or something? Because I never heard of it! then again I don't think I ever solved inequalities with more than one variable.

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# Mmmmmm Something very interesting I found about inequalities

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