What amount of heat is required to melt $"300 g"$ of ice at its freezing point if the enthalpy of fusion is $"6.02 kJ/mol"$?

Md Ariful Islam

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Md Ariful Islam

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For a phase transition, we assume a constant temperature (and also, pressure). So, the heat flow $q$ into a substance is equal to the change $DeltaH$.

$bb(q_P)$

$= bb(mDeltaH)$, if $DeltaH$ is in $"J/g"$, or
$= nDeltaH = bb(m/(M_m)DeltaH)$, if $DeltaH$ is in $"J/mol"$,

where:

  • $m$ is the mass of the ice in $"g"$.
  • $n$ is the $bb("mol")$s of the ice.
  • $M_m$ is the molar mass of the ice in $"g/mol"$.
  • $DeltaH$ is the enthalpy of fusion, which is about $"6.02 kJ/mol"$ for ice at $0^@ "C"$ and $"1 atm"$.

So, simply solve for the heat flow required to melt $"300 g"$ of ice:

$color(blue)(q_P) = (300 cancel"g" xx cancel"1 mol"/(18.015 cancel"g"))("6.02 kJ"/cancel"mol")$

$=$ $color(blue)("100. kJ")$

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