What's the final temperature in bomb calorimeter if 1.785 grams of benzoic acid (##HC7H5O2##) is combusted in a calorimeter with heat capacity of 5.02 Kj/C and initial temperature of 24.62 degree Celsius? Heat of combustion for benzoic acid is -26.42 Kj/g.

The final temperature of the calorimeter is 34.0 °C.

Two heats are involved:

a. the heat released by the combustion reaction, ##q_1##. b. the heat gained by the calorimeter as it warms up, ##q_2##.

##q_1 + q_2## = 0

##mΔH_"c" + C_"cal"ΔT = 0##

##∆T = T_"f" –T_"i"##, (where ##"f"## and ##"i"## stand for final and initial

##"1.785 g × (-26.42 kJ·g"^-1) + "5.02 kJ°C"^-1 × "(T"_"f" – "24.62) °C = 0"##

##"-47.16 kJ + 5.02 kJ°C"^-1 × "T"_"f" - "123.59 kJ = 0"##

##"5.02 °C"^-1 × T_"f" = 123.59 + 47.16 = 170.75"##

##T_"f" = 170.75/"5.02 °C"^-1 = "34.0 °C"##

The final temperature is 34.0 °C.

Note: The answer can have only three , because that is all you gave for the heat capacity of the calorimeter.. If you need more precision, you will have to recalculate.