Question

At ${\text{27}}{{\text{ }}^{\text{o}}}{\text{C}}$ latent heat of fusion of a compound is ${\text{2930 J/mol}}$. Entropy change is
(1) ${\text{9}}{\text{.77 J/mo}}{{\text{l}}^{\text{ - }}}{\text{K}}$
(2) ${\text{10}}{\text{.77 J/mo}}{{\text{l}}^{\text{ - }}}{\text{K}}$
(3) ${\text{9}}{\text{.07 J/mo}}{{\text{l}}^{\text{ - }}}{\text{K}}$
(4) ${\text{0}}{\text{.977 J/mo}}{{\text{l}}^{\text{ - }}}{\text{K}}$

Answer 1

Hint: The amount of energy used by the substance in order to change its state from solid to liquid without any increase in the temperature is called the latent heat of fusion. Entropy is inversely proportional to temperature.

Complete step by step answer:
Entropy is described as the measure of disorder. Consider 2 small solids composed of 6 atomic bonds each. In case of a glass filled with ice and the glass filled with water, the glass with water has more entropy when compared to ice. The reason is that in ice the molecules of water are close enough together, either because of low temperature or very high pressure, that the lowest entropy state is a solid form.
Heat brings changes in the state of matter. The quantity of heat utilized by a substance to change from solid state to liquid state without rise in its temperature is called Latent heat of fusion.
Entropy change is given by a formula
${{\Delta }}{{\text{S}}_{{\text{system}}}}{\text{ = }}\dfrac{{{{\text{q}}_{{\text{rev}}}}}}{{\text{T}}}$
From the given data temperature is ${\text{27 + 273}}{\text{.15 = 300}}{\text{.15 K}}$
On substituting
${{\Delta }}{{\text{S}}_{{\text{system}}}}{\text{ = }}\dfrac{{{\text{2930}}}}{{{\text{300}}{\text{.15}}}}{\text{ = 9}}{\text{.76 J/molK}}$

So,the correct answer is option 1.

Additional information:
Factors that affect the entropy of the system are temperature, physical state, dissolving a solid or gas, dissolving a gas and atomic size. These factors may either increase or decrease the entropy of the system. Transition from more to less condensed phase increases the entropy. When a solid or a liquid is dissolved in a solvent then there is an increase in entropy and if gas is dissolved in a solvent then there is decrease in entropy.

Note: With the increase in temperature the latent heat of vaporization becomes zero. Entropy mainly increases with the increase in temperature, molecular weight and with the decrease in pressure and concentration entropy increases.