Question

How much energy is needed to change 1 g of ice at 0°C to water at 0°C?

Answer 1

If you think about it for a moment---and it should be intuitive, you should recognize that ice changing into water is a melting event.

Melting is the opposite of fusion, or freezing.

Hence, we should consider "latent heat of fusion", or enthalpy of fusion, `DeltaH_"fus"`. Or, the molar enthalpy of fusion, `DeltabarH_"fus"`. For that we have the reference value:

`color(green)(DeltabarH_("fus","H"_2"O") = "6.02 kJ/mol")`

A natural melting event occurs at a constant temperature and constant pressure.

At a constant pressure, `DeltaH = q_p`, where `q` is the heat flow through the system, and `q_p` is that at constant pressure.

The "energy" you speak of is `q_p`. Therefore, we should solve for `q_p`:

`\mathbf(n_("H"_2"O")DeltabarH = q_p)`

where `n` is the number of `"mol"`s and `q_p` is in `"kJ"`.

The `"H"_2"O"` in the system technically does not change in quantity while it melts, only in form, so we have:

`n_("H"_2"O") = 1 cancel("g H"_2"O") xx ("1 mol H"_2"O")/(18.015 cancel("g H"_2"O"))`

`= "0.0555 mol H"_2"O"`

Thus:

`color(blue)(q_p) = "0.0555 mol H"_2"O" xx "6.02 kJ/mol"`

`= "0.3342 kJ" = color(blue)("334.2 J")`

Since we have to supply heat energy into the system to melt the ice, the system absorbs energy. Thus, the sign of this answer should be positive.