Measurements show that the energy of a mixture of gaseous reactants decreases by 190.kJ during a certain chemical reaction, which is carried out at a constant pressure. Furthermore, by carefully monitoring the volume change it is determined that −170.kJ of work is done on the mixture during the reaction.Calculate the change in enthalpy of the gas mixture during the reaction. Be sure your answer has the correct number of significant digits. kJ
Question
Measurements show that the energy of a mixture of gaseous reactants decreases by 190.kJ during a certain chemical reaction, which is carried out at a constant pressure. Furthermore, by carefully monitoring the volume change it is determined that −170.kJ of work is done on the mixture during the reaction.Calculate the change in enthalpy of the gas mixture during the reaction. Be sure your answer has the correct number of significant digits. kJ
Solution
The change in enthalpy (ΔH) of a system can be calculated using the first law of thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (q) minus the work done by the system (w). This can be written as:
ΔU = q - w
In this case, we know that the energy of the system decreases by 190 kJ, so ΔU = -190 kJ. We also know that -170 kJ of work is done on the system, so w = -170 kJ.
We can rearrange the first law of thermodynamics equation to solve for q:
q = ΔU + w
Substituting the given values:
q = -190 kJ + (-170 kJ) = -360 kJ
The heat added to the system is -360 kJ. However, because the reaction is carried out at constant pressure, the change in enthalpy of the system is equal to the heat added to the system. Therefore, the change in enthalpy of the gas mixture during the reaction is -360 kJ.
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