Question

The specific heat capacity of silver is 0.235 J/g ∙ K. Its melting point is 962 °C, and its enthalpy of fusion is 11.3 kJ/mol. What quantity of energy, in joules, is required to change 9.70 g of silver from a solid at 25 °C to a liquid at 962 °C?

Answer 1

Answer: The total heat required for the conversion process is 1228.5 J

Explanation:

The processes involved in the given problem are:  

$1.)Ag(s)(25^oC,298K)\rightarrow Ag(s)(962^oC,1235K)\\2.)Ag(s)(962^oC,1235K)\rightarrow Ag(l)(962^oC,1235K)$

• For process 1:

To calculate the amount of heat absorbed, we use the equation:

$q_1=m\times C_{p,l}\times (T_{2}-T_{1})$

where,

$q_1$ = amount of heat absorbed = ?

$C_{p,s}$ = specific heat capacity = 0.235 J/g.K

m = mass of silver = 9.70 g

$T_2$ = final temperature = 1235 K

$T_1$ = initial temperature = 298 K

Putting all the values in above equation, we get:

$q_1=9.70g\times 0.235J/g.K\times (1235-298)K=213.6J$

• For process 2:

To calculate the amount of heat released, we use the equation:

$q_2=m\times L_f$

where,

$q_2$ = amount of heat absorbed = ?

m = mass of silver = 9.70 g

$L_f$ = latent heat of fusion = 11.3 kJ/mol = $\frac{11300J/mol}{108g/mol}=104.63J/g$   (Conversion factor:  1 kJ = 1000 J; Molar mass of silver = 108 g/mol)

Putting all the values in above equation, we get:

$q_2=9.70g\times 104.63J/g=1014.9J$

Total heat required for the conversion = $q_1+q_2$

Total heat required for the conversion = $[213.6+1014.9]J=1228.5J$

Hence, the total heat required for the conversion process is 1228.5 J