[earthnation112]

Q2. From the data below calculate H at 25 °C and 65 °C for the reaction.

H2 (g)  +  Br2 (g)  →  2 HBr (g)

Compound      Hf / kJ mol-1      Cp / J K-1 mol-1

H2 (g)         0.0            28.8
Br2 (g)         30.9            36.0
HBr (g)         -36.3            29.1

I am able to calculate delta H for a given temperature, but normally when this question is presented I am given two Cp/ JK^-1 mol^-1 rows. Is it possible to answer this question for two different temperatures when only given one row of data for Cp/ JK^-1 mol^-1?

[mjc123]

To be pedantic, it's a column not a row.
If C_p is constant with temperature (which is a fair assumption over this narrow temperature range) then you only need one value. How does H vary with temperature?

[earthnation112]

Just reading off my notes it says:
 
“In all of the above calculations we have calculated enthalpy changes at 298 K. The majority of reactions carried out in real life are performed at other temperatures. Therefore we need to understand how the enthalpy of reaction changes with temperature. It is related to the heat capacity of the reactants and products and is described by Kirchoff’s equation”

This basically says that the variation in the change in enthalpy with temperature is equal to the change in heat capacity for the reaction. So you use an integrated form of Kirchoff’s equation.
So I understand from that to work out the enthalply change


This is my attempt at the question:

To work out the change in enthalpy at 25c(298K) I simply minis the heat formation of the product minus the reactants producing:
-72.6 – 0 – 30.9 = -103.5kj mol^-1

Then to work out the enthalpy change of at 65(999k) = enthalpy change at 298K + change in heat capacity x (999 - 298).

To work out the change in heat capacity equals products minus reactants:
change in heat capacity = 58.2 – 28.8 – 36.0 = -6.6.7jk^1 mol^-1

Then rearranging the second equation produces:
999k = -103500jmol^-1 + -6.6 (999 - 298)
         = -103500 -3925.6 = -107425.6 j mol ^-1
Is the following answer correct?

[mjc123]

Is 65°C 999K?
You're complicating things; T₂ - T₁ has the same value whether you work in °C or K.

[earthnation112]

Sorry made a mistake by coverting 65c to kelvin, like you mentioned as long as the same unit is used for both t1 and t2 the value will be the same. I have made the adjustments in my calculations:

To work out the change in enthalpy at 25c(298K) I simply minis the heat formation of the product minus the reactants producing:
-72.6 – 0 – 30.9 = -103.5kj mol^-1
Then to work out the enthalpy change of at 65c = enthalpy change at 298K + change in heat capacity x (65 - 25).

To work out the change in heat capacity equals products minus reactants:
change in heat capacity = 58.2 – 28.8 – 36.0 = -6.6.7jk^1 mol^-1

Then rearranging the second equation produces:
65C = -103500jmol^-1 + -6.6 (65 - 25)
         = -103500 -264 = -103764 j mol ^-1
Is the following now correct or have I made other errors? Thanks

[mjc123]

Looks correct to me. Although, since your ΔH_f values are only given to 1 dp of kJ/mol, your answer can't really be more precise than -103.8 kJ/mol.