Question #7a804

1 Answer
Jun 17, 2016

Answer:

#"2650 J"#

Explanation:

Let's assume that your textbook provided you with the molar enthalpy of fusion, #DeltaH_"fus"#, for water

#DeltaH_"fus" = "6.01 kJ mol"^(-1)#

A substance's molar enthalpy of fusion tells you how much is needed in order for one mole of that substance to go from solid to liquid at its melting point.

#color(purple)("solid")color(white)(a) "at melting point " stackrel(color(blue)(DeltaH_"fus")color(white)(aaa))(->) color(darkgreen)(" liquid") color(white)(a) "at melting point"#

In your case, water's enthalpy of fusion tells you that you need #"6.01 kJ"# of heat in order to convert one mole of ice, which is water in its solid form, to one mole of liquid water at #0^@"C"#.

The problem provides you with the mass of ice, so you must use water's molar mass to convert this to moles of ice

#7.93 color(red)(cancel(color(black)("g"))) * ("1 mole H"_2"O")/(18.015color(red)(cancel(color(black)("g")))) = "0.4402 moles H"_2"O"#

So, if you need #"6.01 kJ"# of heat to melt #1# mole of ice at its melting point, it follows that #0.4402# moles will require

#0.4402 color(red)(cancel(color(black)("moles"))) * overbrace("6.01 kJ"/(1color(red)(cancel(color(black)("mole")))))^(color(blue)(= DeltaH_"vap")) = "2.6456 kJ"#

Rounded to three sig figs and expressed in joules, #"1 kJ" = 10^3"J"#, the answer will be

#"amount of heat needed" = color(green)(|bar(ul(color(white)(a/a)color(black)("2650 J")color(white)(a/a)|)))#