### Time-Temperature Calculation #2:

Solid Water Melting to Liquid

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72.0 grams of solid water is 0.0 °C. It is going to melt AND stay at zero degrees Celsius. This is an important point. While the ice melts, its temperature will remain the same. We need to calculate the energy needed to do this.

This summarizes the information needed:

ΔH_{fus} = 6.02 kJ/mol

The mass = 72.0 g

The molar mass of H_{2}O = 18.0 gram/mol

The calculation needed, using words & symbols is:

q = (moles of water) (ΔH_{fus})

We can rewrite the moles of water portion and make the equation like this:

q = (grams water / molar mass of water) (ΔH_{fus})

Why is this equation the way it is?

Think about one mole of ice. That amount of ice (one mole or 18.0 grams) needs 6.02 kilojoules of energy to melt. Each mole of ice needs 6.02 kilojoules. So the (grams water / molar mass of water) in the above equation calculates the amount of moles.

I hope that helped.

With the numbers in place, we have:

q = (72.0 g / 18.0 g mol¯^{1}) (6.02 kJ / mol)

So we calculate and get 24.08 kJ. We won't bother to round off right now since there are three more calculations to go. We're doing the second step now. When all five are done, we'll sum them all up.

One warning before going on: three of the calculations will yield J as the unit on the answer and two will give kJ. When you add the five values together, you MUST have them all be the same unit.

In the context of this problem, kJ is the preferred unit.

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