Question

Question #7a804

Answer 1

`"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)|)))`