Question

What is the heat of fusion of mercury in $J.k{g^{ - 1}}$ ?

Answer 1

Hint: The heat of fusion is described as the amount of heat required to convert $1gm$ of solid to a liquid at room temperature. It is also known as the latent heat of fusion because it is a latent heat. Since water freezes at a single temperature $\left( {0^\circ C} \right)$ it only has one value: $79.71cal.k{g^{ - 1}}$(rounded to $80cal.k{g^{ - 1}}$). Water fusion has an exceptionally high heat of fusion.

Complete step by step answer:
It is experimented that when solid mercury of \[1.00kg\] at its melting point of $ - 39.0^\circ C$ is placed in a calorimeter which is filled with $1.20kg$of water at $20.0^\circ C$, it is found that the final temperature of the combination is $16.5^\circ C$. The specific heat of liquid mercury is $140.0$$J.k{g^{ - 1}}^\circ {C^{ - 1}}$.

Let’s assume that the heat of fusion of mercury is ${L_m}$.Heat $({Q_1})$ required for the solid mercury of \[1.00kg\]at $ - 39.0^\circ C$ to become liquid mercury by the change of state at $ - 39.0^\circ C$ is $1.00{L_m}J$. Secondly, the temperature of mercury is changing from$ - 39.0^\circ C$to $16.5^\circ C$. Heat required for this-
${Q_2} = mc\Delta T$
$\Rightarrow {Q_2} = 1.00 \times 140.0 \times (16.5 - ( - 39))$
$\Rightarrow {Q_2} = 140.0 \times 55.5$
$\Rightarrow {Q_2} = 7770J$
Net heat gained by the mercury = ${Q_1} + {Q_2}$= $(7770 + {L_m})J$

Assuming that there is no loss or gain of heat in the calorimeter, this heat is supplied by water. Using law of conservation of energy, we get
$(7770 + {L_m})$ = $1.20 \times 4186 \times (20 - 16.5)$
Where $4186J.k{g^{ - 1}}.^\circ {C^{ - 1}}$ is the specific heat of water.
$7770 + {L_m} = 17581.2 \\
\therefore {L_m} = 9811.2J.k{g^{ - 1}} \\ $
Compare well with the value = $11.3\,kJ\,k{g^{ - 1}}$

Note: The amount of heat applied to or extracted from a material to cause a phase change is known as latent heat. This energy is needed to break down the intermolecular attractive forces as well as to expand the device. Latent heat of fusion of mercury is $2.29kJ.mo{l^{ - 1}}$.