Let's analyze the given equilibrium reaction:
[tex]\[ 2NO_{2(g)} \rightleftharpoons N_2O_4{(g)} \][/tex]
and the observation that moving the mixture to a higher temperature causes it to turn darker brown.
1. Forward Reaction is Exothermic:
If the forward reaction were exothermic, it would release heat. According to Le Chatelier's principle, increasing the temperature would shift the equilibrium to favor the endothermic reaction (the backward reaction, in this case) to absorb the added heat. This would result in more [tex]\( NO_{2} \)[/tex] being formed (darker brown color), which aligns with the observation. Therefore, this conclusion is reasonable.
2. Backward Reaction has a Negative Net Enthalpy:
The backward reaction is the reverse of the forward reaction. If the forward reaction is exothermic, the backward reaction is endothermic, meaning it absorbs heat and has a positive net enthalpy. Hence, this statement does not align with the assumption about the reaction's exothermic nature.
3. The Colorless Gas has a Higher Enthalpy than the Brown Gas:
If the [tex]\( N_2O_4 \)[/tex] gas (colorless) has a higher enthalpy than [tex]\( NO_{2} \)[/tex] (brown), it means the endothermic process would convert [tex]\( N_2O_4 \)[/tex] to [tex]\( NO_{2} \)[/tex], absorbing heat to form more [tex]\( NO_{2} \)[/tex]. This fits with the observation that at higher temperatures, more [tex]\( NO_{2} \)[/tex] is present, and the mixture turns darker brown. So this conclusion could also be true.
4. The Equilibrium Between the Two Forms of the Gas is Disturbed at High Temperatures:
Increasing the temperature of the system causes the equilibrium to shift. According to Le Chatelier's principle, if a system at equilibrium is subjected to a change in temperature, the equilibrium position will shift in the direction that counteracts the change. In this case, higher temperatures shift the equilibrium to produce more [tex]\( NO_{2} \)[/tex], which aligns with the observation. This conclusion is reasonable.
Conclusion:
From the analysis, the valid conclusions about the mixture are:
- The forward reaction is exothermic.
- The colorless gas ([tex]\( N_2O_4 \)[/tex]) has a higher enthalpy than the brown gas ([tex]\( NO_{2} \)[/tex]).
- The equilibrium between the two forms of the gas is disturbed at high temperatures.
Thus, all statements except for "The backward reaction has a negative net enthalpy" can be considered true based on the given observation.
