How Much Ice Melts to Lower Water Temperature from 24°C to 5°C?

[blueskadoo42]

Homework Statement

How much ice (in grams) would have to melt to lower the temperature of 351 ml of water from 24 deg C to 5 deg C? (Assume the density of water is 1.0g/ml .)

Homework Equations

q=mc(deltaT)

The Attempt at a Solution

m=351 g c=4.18J/g*C deltaT=19deg C

q=27.88kJ

then heat of fusion = 6.02kJ/mol

take 27.88/6.02 = 4.631 mol * 18.02g/mol= 83.45 grams.



this is wrong. the only problem i see is where i used the specific heat of water instead of ice. spec heat of ice=2.09. should I use the spec heat of ice instead of water? thanks!

 

[blueskadoo42]

anyone?

 

[Mapes]

Doesn't the water from the ice have to go from 0°C to 5°C?

 

[Bacat]

You should definitely be using the spec heat of ice. It is the ice which is melting, so that is where the heat energy is going and thus where the heat capacity matters. Otherwise, your attempt at a solution looks good to me.

What is the answer supposed to be?

 

[Mapes]

You should definitely be using the spec heat of ice. It is the ice which is melting, so that is where the heat energy is going and thus where the heat capacity matters.

Huh? Specific heat capacity is used to calculate the required energy for a temperature change. The initial temperature of the ice isn't provided, so presumably we should take it to be 0°C. It doesn't change temperature, it just melts!

 

[Bacat]

Mapes, in order for the ice to melt it needs to take heat from somewhere. That heat comes from the water. That's why putting ice in water cools the water (it is heating the ice). It's just thermodynamics.

 

[Mapes]

OK, prove me wrong and write the equation that uses the specific heat of ice, 2.1 J g^-1 °C^-1. You're going to need to multiply it by a temperature to get energy (and that temperature isn't 5°C or 24°C, because ice doesn't exist at those temperatures). Make sure your units match.

 

[Bacat]

The energy required to melt the ice (phase transition) comes from the water that we assume the ice is surrounded by (to avoid taking heat from the air, which would complicate things). So he calculated the amount of heat required to change the temperature of the water by 19 degrees (using heat capacity of water). This heat energy went into melting the ice (not raising the temperature of the ice, but as a phase change). By measuring how much the temperature changed in the water (got colder), and knowing the heat capacity and molar heat of fusion you should be able to calculate how much ice melted to effect that change.

So actually that makes my previous statement wrong. You do need to use the spec heat of water, because it is the water we have temperatures for. Hmm...