What amount of heat is required to completely melt a 29.95-gram sample of #H_2O#(s) at 0° C?

1 Answer
Jan 27, 2016

Answer:

#"9.990 kJ"#

Explanation:

The question wants you to determine how much heat will be required in order to get a #"29.95-g"# sample of ice to undergo a solid #-># liquid phase change at its melting point of #0^@"C"#.

So, in essence, all you need to know in order to answer this question is the value of water's enthalpy of fusion, #DeltaH_"fus"#.

The enthalpy of fusion essentially tells you one thing from two different perspectives

  • how much heat is needed in order to melt one gram of a substance at its melting point
  • how much heat is released when one gram of a substance freezes at its freezing point

In your case, water is going from solid to liquid, so #DeltaH_"fus"# will be positive. For water, you have

#DeltaH_"fus" = "333.55 J g"^(-1)#

https://en.wikipedia.org/wiki/Enthalpy_of_fusion

So, if you need #"333.55 J"# in order to get #"1 g"# of ice at #0^@"C"# to go to liquid water at #0^@"C"#, it follows that #"29.95 g"# of ice would require

#29.95 color(red)(cancel(color(black)("g"))) * overbrace("333.55 J"/(1color(red)(cancel(color(black)("g")))))^(color(blue)(DeltaH_"fus")) = "9989.8 J"#

Rounded to four sig figs, the answer will be

#"heat required " = color(green)(" 9990. J")#

Expressed in kilojoules, you will have

#"heat required " = color(green)(" 9.990 kJ")#