Answer
The net change in energy for the reaction $2Li(s) + 2HCl(g) \rightarrow 2LiCl(s) + H_2(g)$ is -562 kJ.
Work Step by Step
To calculate the net change in energy for the given reaction, we need to use the provided thermochemical data and apply the Hess's law.
The reaction is:
$2Li(s) + 2HCl(g) \rightarrow 2LiCl(s) + H_2(g)$
The steps involved in the calculation are:
1. Calculate the energy required to convert 2 moles of solid lithium (Li(s)) to 2 moles of gaseous lithium (2Li(g)):
Energy of sublimation of Li(s) = 166 kJ/mol
Energy required = 2 × 166 kJ/mol = 332 kJ
2. Calculate the energy required to ionize 2 moles of gaseous lithium (2Li(g)) to form 2 moles of lithium ions (2Li+(g)):
Ionization energy of Li(g) = 520 kJ/mol
Energy required = 2 × 520 kJ/mol = 1040 kJ
3. Calculate the energy released when 2 moles of chlorine atoms (2Cl(g)) gain 2 electrons to form 2 moles of chloride ions (2Cl-(g)):
Electron affinity of Cl(g) = -349 kJ/mol
Energy released = 2 × (-349) kJ/mol = -698 kJ
4. Calculate the energy released when 2 moles of lithium ions (2Li+(g)) and 2 moles of chloride ions (2Cl-(g)) form 2 moles of solid lithium chloride (2LiCl(s)):
Lattice energy of LiCl(s) = -829 kJ/mol
Energy released = 2 × (-829) kJ/mol = -1658 kJ
5. Calculate the energy required to break the bonds in 2 moles of hydrogen chloride (2HCl(g)):
Bond energy of HCl = 427 kJ/mol
Energy required = 2 × 427 kJ/mol = 854 kJ
6. Calculate the energy released when 1 mole of hydrogen gas (H2(g)) is formed:
Bond energy of H2 = 432 kJ/mol
Energy released = 432 kJ/mol
The net change in energy for the overall reaction is the sum of the energies calculated in the previous steps:
Net change in energy = 332 kJ + 1040 kJ - 698 kJ - 1658 kJ + 854 kJ - 432 kJ = -562 kJ
Therefore, the net change in energy for the reaction $2Li(s) + 2HCl(g) \rightarrow 2LiCl(s) + H_2(g)$ is -562 kJ.
