Question

Enthalpy of sublimation of iodine is 24 $ cal{{g}^{-1}}$ at 200$^{\circ }C$. If the specific heat of ${{I}_{2}}$(s) and ${{I}_{2}}$(vap) are 0.055 and 0.031$cal{{g}^{-1}}{{K}^{-1}}$ respectively, then enthalpy of sublimation of iodine at 250$^{\circ }C $ in $ cal{{g}^{-1}}$is :
(a) 2.85
(b) 11.4
(c) 5.7
(d) 22.8

Answer 1

Hint:. First we have to calculate the change in the specific heat capacity of reactants and products and the change in the temperature by using the given data and then we can easily calculate the enthalpy of sublimation by using the formula as $\Delta H=\Delta {{c}_{P}}({{T}_{2}}-{{T}_{1}})$. Now solve it.


Complete step by step answer:
By the enthalpy of sublimation, we mean the amount of energy that is required to change the substance from its solid phase to its vapor phase.
Now, considering the numerical:
Consider the reaction:
${{I}_{2}}(s)\to {{I}_{2}}(v)$

We can calculate the enthalpy of sublimation of iodine by using the formula as;
$\Delta H=\Delta {{c}_{P}}({{T}_{2}}-{{T}_{1}})$ ------------(1)
We can calculate the change in the specific heat as we have been the specific heat capacities of ${{I}_{2}}$(s) and ${{I}_{2}}$(vap).
Specific heat capacity of ${{I}_{2}}$(s)= 0.055 $cal{{g}^{-1}}{{K}^{-1}}$
Specific heat capacity of ${{I}_{2}}$(vap)= 0.031 $cal{{g}^{-1}}{{K}^{-1}}$

Then , the change in the specific heat capacity is as;
$\Delta {{c}_{P}}={{c}_{p(product)}}-{{c}_{p(reactants)}}$
= 0.031-0.055
= -0.024$cal{{g}^{-1}}$
Temperature ,${{T}_{1}}$= 200$^{\circ }C$
= 200 +273 K
= 473K
Temperature, ${{T}_{2}}$=250$^{\circ }C$
 = 250 +273 K
 = 523K
Then ,the change in temperature is as:
$\Delta T={{T}_{2}}-{{T}_{1}}$
 = 523- 473K
= 50K
And we know that $\Delta {{H}_{1}}$=24
$\Delta H = \Delta {{H}_{2}}-\Delta {{H}_{1}}$
=$\Delta {{H}_{2}}-24$

Then , put all these values in equation(1), we get;
$\Delta {{H}_{2}}-24 = -0.024(50)$
$\Delta {{H}_{2}}$ = -1.2 + 24
= 22.8 $cal{{g}^{-1}}$
Hence the enthalpy of sublimation of iodine at 250$^{\circ }C $ is : 22.8 $cal{{g}^{-1}}$
So, the correct answer is “Option D”.

Note: Temperature should always be taken in the standard units i.e. the Kelvin and if the temperature is in degree Celsius convert it into Kelvin by adding 273 to the given temperature in degree Celsius.