MCQ
The enthalpy change on freezing of $1\, mol$ of water at $5\,^oC$ to ice at $-5\,^oC$ is .....$ kJ\, mol^{-1}$

(Given ${\Delta _{fus}}H = 6\, kJ\, mol^{-1}$ at $0\,^oC$,

$C_p(H_2O, l) =75.3\, J\, mol^{-1} \, K^{-1}$ ,

$C_p(H_2O, s) = 36.8\, J\, mol^{-1} \, K^{ -1}$ )

  • A
    $5.44$
  • B
    $5.81$
  • $6.56$
  • D
    $6$

Answer

Correct option: C.
$6.56$
c
In order to calculate the enthalpy change for $H_2O$ at $5\,^oC$ to ice at $-\,5\,^oC$ , we need to calculated the enthalpy change of all the transformation involved in the process.

$(a)$ Energy change of $1\,mol$, $H_2O\,(l)$, at $5\,^oC$

$\to \,1\,mol$, $H_2O\,(l)$ , $0\,^oC$

$(b)$ Energy change of $1\,mol$, $H_2O\,(l)$, at $0\,^oC$

$\to \,1\,mol$, $H_2O\,(s)$ (ice) , $0\,^oC$

$(c)$ Energy change of $1\,mol$, Ice $(s)$, at $0\,^oC$

$\to \,1\,mol$, Ice $(s)$ , $-5\,^oC$

Total $\Delta H$

$ = \,{C_P}\,[{H_2}O\,(l)]\,\,\Delta T\,\, + \,\Delta H$ freezing $ + \,\,{C_P}\,[{H_2}O\,(s)]\,\,\Delta T$

$ = \,(75.3\,\,J\,\,mo{l^{ - 1}}\,{K^{ - 1}})\,( - 5)\,K\, + ( - \,6\, \times \,{10^3}\,\,J\,mo{l^{ - 1}}\,{K^{ - 1}})$ $+ \,(36.8\,\,J\,mo{l^{ - 1}}\,{K^{ - 1}})\,( - 5)\,K$

$\Delta H\,\, = \,\, - \,6.56\,\,kJ\,mo{l^{ - 1}}$ (exothermic process)

So, $\Delta H\,\, = \,\,6.56\,\,kJ\,mo{l^{ - 1}}$

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