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Would more heat be released when 1.00 gram of ch4(g) is burned in excess o2(g) to form co2(g) and h2o(ℓ) in a constantpressure calorimeter or in a constant-volume calorimeter?

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The answer is: the heat of reaction would be the same. This reaction is the combustion of methane gas. There is already an empirical value for heat of reaction. The only difference is how the experiment is carried out. The first one is at constant volume, while the other one is in constant pressure. Whatever the condition is, it will always lead to one theoretical value for heat released.
User Olivierg
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