Question

How much heat is produced when $ 2.63gm $ of phosphorus and $ 40gm $ of bromine is allowed to react according to the following equation?
 $ {{\text{P}}_{\text{4}}}\left( {\text{s}} \right){{\; + 6B}}{{\text{r}}_{\text{2}}}\left( {\text{l}} \right) \to 4{\text{PB}}{{\text{r}}_{\text{3}}}\left( {\text{g}} \right),{{\Delta H}} = - 486kJ $
A) $ - 10.30kJ $
B) $ - 20.6kJ $
C) $ - 40.12kJ $
D) $ - 5.63kJ $

Answer 1

Hint: The heat of reaction is the amount of energy that is released or absorbed during the reaction. It is expressed in the unit of joules or kilojoules. When heat is produced, the sign is negative while during the absorption of heat, the sign is positive. The stoichiometric coefficient used in the balanced chemical reaction can be used to calculate the number of moles of the reactants.

Complete Step By Step Answer:
The proposed reaction is - $ {{\text{P}}_{\text{4}}}\left( {\text{s}} \right){{\; + 6B}}{{\text{r}}_{\text{2}}}\left( {\text{l}} \right) \to 4{\text{PB}}{{\text{r}}_{\text{3}}}\left( {\text{g}} \right),{{\Delta H}} = - 486kJ $
As per the reaction, one mole of phosphorus reacts with six moles of bromine to produce four moles of phosphorus tribromide and release $ - 486kJ $ energy.
Now, the mass of reactants involved can be calculated as –
Mass of phosphorus - $ 4X31 = 124gm $
Mass of bromine - $ 6(2X80) = 960gm $
Mass of phosphorus tribromide - $ 4[(80X4) + 31] = 1404gm $
This means that $ 124gm $ of phosphorus requires $ 960gm $ of bromine, so $ 2.63gm $ of phosphorus requires $ \dfrac{{960}}{{124}} \times 2.63 = 20.361gm $ of bromine.
As there is an excess of bromine present in the reaction i.e. $ 40gm $ and the amount of phosphorus is less, so it acts as a limiting agent and will be consumed completely in the reaction while the bromine will be remaining.
Now, as $ 124gm $ of phosphorus produces $ - 486kJ $ of energy or heat, so $ 2.63gm $ of phosphorus will produce $ \dfrac{{ - 486}}{{124}} \times 2.63 = - 10.30kJ $ of heat.
Hence, the produced when $ 2.63gm $ of phosphorous and $ 40gm $ of bromine is allowed to react according to the following equation - $ {{\text{P}}_{\text{4}}}\left( {\text{s}} \right){{\; + 6B}}{{\text{r}}_{\text{2}}}\left( {\text{l}} \right) \to 4{\text{PB}}{{\text{r}}_{\text{3}}}\left( {\text{g}} \right),{{\Delta H}} = - 486kJ $ is $ - 10.30kJ $ .
Hence, option A) is the correct answer.

Note:
Negative heat of reaction indicates the reaction to be exothermic while positive heat of reaction indicates that the reaction is endothermic. Endothermic reactions are the reactions which require heat to complete the reaction while exothermic reactions release the heat. Example of endothermic reaction is photosynthesis while dissolution of limestone is an example of exothermic reaction.