[Matt9001]

I have a reactant mixture which is first heated up to a reaction temperature lets say from T atmospheric= 25°c to starting reaction temperature T 1=100°c . Once the reaction has started, I have to maintain this temperature for about t=50 minutes and from 50th minutre onwards till end of reaction there is a linear increase of temperature giving me T 2= 150°c at t=100 minutes. so 1°/min increase rate. I want to calculate the total energy that I have to provide from heating the reactants till end of the reaction.
so what I have untill now is


The reaction lets say is:
                                                   A+ B :rarrow:C+D

The reaction is overall exothermic.
The stichiometric coefficients are all 1

Energy total supplied= Q_heating(25°c to 100°c) + Q_reaction1(at constant 100°c for 50 minute) + Q_reaction2(from 100°c to 150°c)

i know Q_heating= n_A.ΔH_A  + n_B.ΔH_B           
 where ΔH=  ∫[c_p.dT] from 25 to 100°c
 
I am not however sure about how to calculate other Q's .
imo Q_reaction1= n_c.ΔHF_c + n_d.ΔHF_d -n_a.ΔHF_a- n_c.ΔHF_c                    ΔHF= heat of formation at 100°c

ΔHF_i= ΔHF_i°(25°c) + ∫[c_p,i.dT] from 25 to 100°c
 also i am confused if this Q_reaction1 is negative does that mean i remove this heat from my overall  energy supply??

I am not sure however how to calculate the third term as reaction is also occuring while temperature is not constant. I know the amount of  A, B, C, D at all points in the reaction, should i calculate the heat of reaction like in case of Q_reaction1 and what would be the temperature range for temperature (25°c to 150°c??) in cpdt also should i use ΔHF° (25°c) or should  i just calculate the  enthalpy change from (100 to 150°c) not adding the heat of formations?

Thanks

[mjc123]

You can use a Hess's law cycle as enthalpy is a state function and therefore path-independent.
A + B (25°C)  C + D (150°C)   ΔH1
A + B (25°C)  C + D (25°C)   ΔH2
C + D (25°C)  C + D (150°C)   ΔH3
ΔH1 = ΔH2 + ΔH3 = ΣΔHf(25°) +  ∫Cp(C+D)dT
The sign of ΔH is the sign of the energy you have to put in, so if ΔH2 is negative, that reduces the energy input, but ΔH3 is positive so requires input of energy.

[Matt9001]

Hey thanks, i was able to solve it now. Just need one more clarification, i needed to calculate the cost of the overall energy input. But if my overall energy balance comes out to be negative  does that mean it wouldn't cost me anything but i have excess energy at my disposal even though i did use heating source to heat up before and after the 50th minute of reaction.
Thanks

[mjc123]

The above calculation doesn't tell the whole story in the real world. What else are you heating? Flask? Oil bath? (Is there a solvent?) What losses to the surroundings? It's very difficult to quantify these (and hence the cost) without trying it out.
Note that if this is a large scale reaction, you may have to heat it up to get it going, but then the heat released, if it can't escape to the surroundings, may overheat the mixture and cause a dangerous situation, even an explosion. This is called "thermal runaway".

[Enthalpy]

Even if the reaction is exothermic, bringing the reactants to temperature costs heat first. But in a continuous production process, you might use the heat in the reactor or the products to bring the reactants to temperature, once the reaction has started.

About the computation, on a small scale it's highly possible that maintaining +100°C for 50min costs more heat than reaching first the temperature. And if heating is inefficient, then the consumption is hard to evaluate.