The latent heat of fusion for ice is 6.0 kJ/mole. In order to melt 36 g of ice (solid $H_2O$) at 0°C, how much energy is required?

Md Ariful Islam

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Md Ariful Islam

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The molar latent heat of fusion, which is an alternative name given to the of fusion, tells you how much heat is required in order to convert a specific amount of a given substance, either a gram or a mole, from solid at its melting point to liquid at its melting point.

Ice is said to have a molar enthalpy of fusion equal to

$DeltaH_"fus" = "6.0 kJ mol"^(-1)$

This means that in order to melt $1$ mole of ice at its normal melting point of $0^@"C"$, you must supply it with $"6.0 kJ"$ of heat.

Now, your sample of ice has a mass of $"36 g"$, so the first thing to do here is to convert it to moles by using the molar mass of water

$36 color(red)(cancel(color(black)("g"))) * ("1 mole H"_2"O")/(18.015color(red)(cancel(color(black)("g")))) = "1.998 moles H"_2"O"$

You can now use the molar enthalpy of fusion as a conversion factor to help you figure out how much heat must be supplied to your sample

$1.998 color(red)(cancel(color(black)("moles ice"))) * "6.0 kJ"/(1color(red)(cancel(color(black)("mole ice")))) = color(darkgreen)(ul(color(black)("12 kJ")))$

The answer is rounded to two .

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