If 5.00 moles of [tex]H_2[/tex] react with 5.00 moles of [tex]Cl_2[/tex] to form [tex]HCl[/tex], what is [tex]\Delta U[/tex] (in kJ) for this reaction at 1.0 atm and 25°C? Assume the reaction goes to completion.

Question

17-10-2024
Chemistry

College

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If 5.00 moles of [tex]H_2[/tex] react with 5.00 moles of [tex]Cl_2[/tex] to form [tex]HCl[/tex], what is [tex]\Delta U[/tex] (in kJ) for this reaction at 1.0 atm and 25°C? Assume the reaction goes to completion.

Answer :

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Final answer:

In a reaction where 5 moles of H2 react with 5 moles of Cl2 to form HCl, the change in internal energy (ΔU) at 1 atm and 25°C is approximately -462.5 kJ, assuming ΔU is approximately equal to ΔH.

Explanation:

When 5.00 moles of H2 react with 5.00 moles of Cl2 to form HCl, we can use the enthalpy change of the reaction to determine the change in internal energy, ΔU. From the given data, for the formation of 2 moles of HCl, the energy required to break one mole of H-H bonds (436 kJ/mol) and one mole of Cl-Cl bonds (243 kJ/mol) is needed. Two moles of H-Cl bonds are then formed, releasing 2 x 432 kJ (864 kJ).

The net enthalpy change, ΔH, is the energy released minus the energy required. For the formation of 2 moles of HCl, ΔH is calculated as:

ΔH = Energy released by forming bonds - Energy required to break bonds
= (2 x 432 kJ) - (436 kJ + 243 kJ)
= 864 kJ - 679 kJ
= 185 kJ (for 2 moles of HCl)

To find the ΔH for 5 moles of HCl formed, the ΔH per 2 moles is multiplied by (5 moles / 2 moles):

ΔH for 5 moles of HCl = 185 kJ x (5 moles / 2 moles)
= 462.5 kJ

Since the reaction is carried out at constant pressure (1 atm), the ΔU can be assumed approximately equal to ΔH. Therefore, the change in internal energy for the reaction at 25°C and 1 atm is approximately -462.5 kJ.