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drtg45
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For a chemical reaction we have, ΔH=-114.1kJ and ΔS=-146.4J/K ---> ΔS=-146.4·10[itex]^{-3}[/itex]kJ/K.
Question: Determine the temperature range at which the reaction is spontaneous.
A reaction is spontaneous when ΔG is negative in the equation ΔG=ΔH-TΔS, so I do:
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 , so this tells us that the T must be greater than 780K in order for the reaction to be spontaneous, but then when I check my answer in the original equation:
ΔG=ΔH-TΔS
ΔG=-114.1kJ-(900K)(-146.4·10[itex]^{-3}[/itex]kJ/K) ---> ΔG=18kJ , My inequality answer I suppose is wrong because if T is greater than 780K (in this example I used 900K) then ΔG is positive and the reaction is non spontaneous.
ΔG=-114.1kJ-(200K)(-146.4·10[itex]^{-3}[/itex]kJ/K) ---> ΔG=-85kJ , In here if we use a T lower than 780K the reaction is spontaneous.
I know I made a mistake somewhere because these results are not in accordance with each other, I'm guessing I made the mistake in the inequality while solving for T but I'm honestly not seeing it!, Where did I mess up?
Question: Determine the temperature range at which the reaction is spontaneous.
A reaction is spontaneous when ΔG is negative in the equation ΔG=ΔH-TΔS, so I do:
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 , so this tells us that the T must be greater than 780K in order for the reaction to be spontaneous, but then when I check my answer in the original equation:
ΔG=ΔH-TΔS
ΔG=-114.1kJ-(900K)(-146.4·10[itex]^{-3}[/itex]kJ/K) ---> ΔG=18kJ , My inequality answer I suppose is wrong because if T is greater than 780K (in this example I used 900K) then ΔG is positive and the reaction is non spontaneous.
ΔG=-114.1kJ-(200K)(-146.4·10[itex]^{-3}[/itex]kJ/K) ---> ΔG=-85kJ , In here if we use a T lower than 780K the reaction is spontaneous.
I know I made a mistake somewhere because these results are not in accordance with each other, I'm guessing I made the mistake in the inequality while solving for T but I'm honestly not seeing it!, Where did I mess up?