# How many joules does it take to melt 35 g of ice at 0° C?

Apr 29, 2016

It takes 12,000 Joules of energy to melt 35 grams of ice at 0 °C

#### Explanation:

The enthalpy change for melting ice is called the entlaphy of fusion. Its value is 6.02 kj/mol. This means for every mole of ice we melt we must apply 6.02 kj of heat. We can calculate the heat needed with the following equation:

$q = n \times \Delta H$

where:
$q$ = heat
$n$ = moles
$\Delta H$ = enthalpy

In this problem we would like to calculate the heat needed to melt 35 grams of ice at 0 °C. This problem can be broken into three steps:
1. Calculate moles of water
2. multiply by the enthalpy of fusion
3. Convert kJ to J

Step 1: Calculating moles of water

$35 g \times \left(\frac{1 m o l}{18.02 g}\right) = 1.94 m o l s$

Step 2: Multiply by enthalpy of fusion

$q = n \times \Delta H = 1.94 \times 6.02 = 11.678 k J$

Step 3: Convert kJ to J

$11.678 k J \times \left(\frac{1000 J}{1 k J}\right) = 11 , 678 J$

Finally rounding to 2 sig figs (since 34°C has two sig figs) we get

$q = 12 , 000 J$

For more examples on phase changes and enthalpy, see the video below:

One last note, if the temperature were not 0 °C then the ice would have to be heated in addition to melted. This would be a phase change problem combined with a heat capacity problem.