Question

For which one of the following reactions will the enthalpy change be approximately equal to the internal energy change?

2 NaN₃(s) → 2 Na(s) + 3 N₂(g)

2 H₂O( ℓ ) → 2 H₂(g) + O₂(g)

2 Sb(s) + 3 I₂(g) → 2 SbI₃(s)

Ca(NO₃)₂(aq) + 2 NH₄Cl(aq) → CaCl₂(aq) + 2 NH₄NO₃(aq)

CaCO₃(s) → CaO(s) + CO₂(g)

Answer 1

As we know that ,

∆H= ∆U +P∆V

Or

∆H = ∆U + ∆ngRT

Where , ∆H = enthalpy change

∆U = internal energy change

∆ng = change in no. of moles of gas= no. of gaseous moles in product side - no. of gaseous moles in reactant side

R = gas constant

T = temperature

Now if a reaction has ∆ng = 0 , means it has ∆nRT ( work done) zero or in other words we can say that if ∆ng = 0 then enthalpy change will be equals to internal energy change.

Now for reaction 1 ,

2NaN3 (s) --> 2Na(s) + 3N2(g)

we see that ∆ng = 3 ,thus ∆ngRT will not be zero it means its enthalpy change will be not equals to internal energy change.

For reaction 2 ,

2H2O(l) --> 2H2(g) +O2(g)

again ∆ng = 3 which again indicates that enthalpy change is not equals to internal energy change.

For reaction 3 ,

2Sb(s) +3I2(g)--> 2SbI3(s)

We see that ∆ng = -3 it means it's enthalpy change will be not equals to internal energy change.

For reaction 4 ,

Ca(NO3)2(aq) + 2NH4Cl(aq) --> CaCl2(aq) +2NH4NO3(aq)

we see that ∆ng = 0 , it means it's enthalpy change will be equals to internal energy change.moreover since all species are in aqueous state thus ∆V will also be zero , hence P∆V will be zero , thus enthalpy is approximately equal to change in internal energy

For reaction 5

CaCO3(s) --> CaO(s) + CO2(g)

, we see that ∆ng = 1 which indocates that enthalpy change is not equals to internal energy change.

Thus the correct answer is reaction 4 that is

Ca(NO3)2(aq) + 2NH4Cl(aq) --> CaCl2(aq) + 2NH4NO3(aq)