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?

May 26, 2017

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 $F e$ (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:
$\textcolor{w h i t e}{a} \textcolor{red}{\text{mol Fe}} = \frac{4.5 \textcolor{w h i t e}{a} \textcolor{red}{\cancel{\textcolor{b l u e}{g r a m}}}}{55.85 \textcolor{w h i t e}{a} \frac{\textcolor{red}{\cancel{\textcolor{b l u e}{g r a m}}}}{\textcolor{b l u e}{m o l}}} = 0.081$

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)"
$\textcolor{w h i t e}{a a} 1 \textcolor{w h i t e}{a a a a a a} : \textcolor{w h i t e}{a a a a a a a} 14.9$
$\textcolor{w h i t e}{a a a a a a a a a} \cancel{\textcolor{b l a c k}{\setminus}}$
color(white)(aa)0.081color(white)(aaa):color(white)(aaaaaaa)?

To calculate the energy needed we use the ratio (the cross) and calculate:
$\frac{0.081 \times 14.9}{1} = 1.20$ kJ

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