Question

Calculate the quantity of energy, in joules, required to raise the temperature of 486 g tin from room temperature, 25.0 °C, to its melting point, 231.9 °C, and then melt the tin at that temperature. (The specific heat capacity of tin is 0.227 , and the enthalpy of fusion of this metal is 59.2 J/g.)

Answer 1

Since you are only going to the melting point, you need to know the Heat of Fusion not 'Vaporization'. This is the value you have given 59.2J/g

First, change all the temps to their K equivalents by adding 273.

(rounding)
231.9C = 505K
25C = 298K

Now get the difference in temps by subtraction: 207 deg K
This is the amount the tin warmed before melting.

To get the quantity of heat required to do this, use Q = S x M x dT
Where dT is "delta temperature, or the "change in temperature", 207 deg K; Q is the amount of heat in Joules; S is the specific heat; and M is the mass of tin.

Q = 0.227J/g*K x 486g x 207K...... 22.836 J

At the melting point, additional heat goes in to change the tin from solid to liquid, but does NOT raise the temperature. Here you simply use the Heat of Fusion and the mass of tin to determine how much heat was required to do all that melting:

Q = hF x M, or 59.2J/g x 486g = 28.77J

Adding the two values calculated gives you the total heat needed to raise the mass of tin from solid at 25C to liquid at 231.9C


22.836 J + 28.77J = 51.606 J or 51.6 kiloJoules