Calorimeter - Bomb Calorimeters

Bomb Calorimeters

A bomb calorimeter is a type of constant-volume calorimeter used in measuring the heat of combustion of a particular reaction. Bomb calorimeters have to withstand the large pressure within the calorimeter as the reaction is being measured. Electrical energy is used to ignite the fuel; as the fuel is burning, it will heat up the surrounding air, which expands and escapes through a tube that leads the air out of the calorimeter. When the air is escaping through the copper tube it will also heat up the water outside the tube. The temperature of the water allows for calculating calorie content of the fuel.

In more recent calorimeter designs, the whole bomb, pressurized with excess pure oxygen (typically at 30atm) and containing a weighed mass of a sample (typically 1-1.5 g) and a small fixed amount of water (to saturate the internal atmosphere, thus ensuring that all water produced is liquid, and removing the need to include enthalpy of vapourization in calculations), is submerged under a known volume of water (ca. 2000 ml) before the charge is electrically ignited. The bomb, with the known mass of the sample and oxygen, form a closed system - no gases escape during the reaction. The weighted reactant put inside the steel container is then ignited. Energy is released by the combustion and heat flow from this crosses the stainless steel wall, thus raising the temperature of the steel bomb, its contents, and the surrounding water jacket. The temperature change in the water is then accurately measured with a thermometer. This reading, along with a bomb factor (which is dependent on the heat capacity of the metal bomb parts), is used to calculate the energy given out by the sample burn. A small correction is made to account for the electrical energy input, the burning fuse, and acid production (by titration of the residual liquid). After the temperature rise has been measured, the excess pressure in the bomb is released.

Basically, a bomb calorimeter consists of a small cup to contain the sample, oxygen, a stainless steel bomb, water, a stirrer, a thermometer, the dewar or insulating container (to prevent heat flow from the calorimeter to the surroundings) and ignition circuit connected to the bomb. By using stainless steel for the bomb, the reaction will occur with no volume change observed.

Since there is no heat exchange between the calorimeter and surroundings → Q = 0 (adiabatic) ; no work performed → W = 0 Thus, the total internal energy change ΔU(total) = Q + W = 0

Also, total internal energy change ΔU(total) = ΔU(system) + ΔU(surroundings) = 0 → ΔU(system) = - ΔU(surroundings) = -C_v ΔT (constant volume → dV = 0)

where C_v = heat capacity of the bomb

Before the bomb can be used to determine heat of combustion of any compound, it must be calibrated. The value of C_v can be estimated by C_v (calorimeter) = m (water). C_v (water) + m (steel). C_v (steel)

m (water) and m (steel) can be measured;

C_v(water)= 1 cal/g.K

C_v(steel)= 0.1 cal/g.K

In laboratory, C_v is determined by running a compound with known heat of combustion value: C_v = H_c/ΔT

Common compounds are benzoic acid (H_c = 6318 cal/g) or p-methyl benzoic acid (H_c = 6957 cal/g).

Temperature (T) is recorded every minute and ΔT = T(final) - T(initial)

A small factor contributes to the correction of the total heat of combustion is the fuse wire. Nickel fuse wire is often used and has heat of combustion = 981.3 cal/g

In order to calibrate the bomb, a small amount (~ 1 g) of benzoic acid, or p-methyl benzoic acid is weighed. A length of Nickel fuse wire (~10 cm) is weighed both before and after the combustion process. Mass of fuse wire burned Δm = m(before) - m(after)

The combustion of sample (benzoic acid) inside the bomb ΔH_c = ΔH_c (benzoic acid) x m (benzoic acid) + ΔH_c (Ni fuse wire) x Δm (Ni fuse wire)

ΔH_c = C_v. ΔT → C_v = ΔH_c/ΔT

Once C_v value of the bomb is determined, the bomb is ready to use to calculate heat of combustion of any compounds by ΔH_c = C_v. ΔT