The molar heat of fusion of iron is #14.9# kJ/mol. What is the energy (in kJ) needed to melt #4.50g# of iron?

1 Answer
May 26, 2017

Answer:

The energy needed is #1.20# kJ for #4.50# gram iron.

Explanation:

To determine the energy that is needed to melt the iron, we have to calculate the amount of mol #Fe# (iron) we have. This can be done with the molar mass of iron, which is #55.85 u# (look up in the periodic table!)

Now we use the formula:
#mol=("mass" color(white)(a) color(blue)((gram)) )/("molar mass"color(white)(a)color(blue)(((gram)/(mol)))#

We fill the numbers in and we obtain:
#color(white)(a) color(red)("mol Fe")=(4.5color(white)(a)color(red)(cancel(color(blue)(gram))))/(55.85color(white)(a)color(red)(cancel(color(blue)(gram)))/color(blue)(mol))=0.081#

We use the molar heat of iron (#14.9# kJ/mol) to calculate the amount of energy that is needed to melt it.

We make a table:

#color(red)("mol Fe") color(white)(aaaaa)color(red)("Energy needed (kJ)"#
#color(white)(aa)1color(white)(aaaaaa):color(white)(aaaaaaa)14.9#
#color(white)(aaaaaaaaa)cancel(color(black)(\))#
#color(white)(aa)0.081color(white)(aaa):color(white)(aaaaaaa)?#

To calculate the energy needed we use the ratio (the cross) and calculate:
#(0.081xx14.9)/1=1.20# kJ

Therefore to melt down the 4.50 gram of iron we need 1.20 kJ energy.