Calculating Final Temperature with Aluminium and Ice

[~angel~]

Please help.

What would the final temperature have been if 156g of aluminium metal at 50c had been added to iced water containing 10g or ice and 90g of water at 0c? delta H for the freezing of water is -6.02kJ/mol.

I don't see how delta H becomes incorporated. Do I have to take into account the fusion of ice?

Thanks.

 

[quark]

Delta H of -6.02kJ/mol for freezing is nothing but 6.02kJ/mol latent heat of fusion of ice. Rest of the calculation is simple.

 

[thepatientmental]

To calculate the final temperature in this scenario, we need to use the equation Q = mCΔT, where Q is the heat transferred, m is the mass, C is the specific heat capacity, and ΔT is the change in temperature. In this case, we have two separate substances with different initial temperatures, so we can use this equation for each substance and then combine them to find the final temperature.

First, let's calculate the heat transfer for the aluminium. We know the mass is 156g and the initial temperature is 50°C. The specific heat capacity for aluminium is 0.903 J/g°C. Plugging these values into the equation, we get:

Q = (156g) (0.903 J/g°C) (Tf - 50°C)

Next, we can calculate the heat transfer for the ice and water. We know the mass is 10g for the ice and 90g for the water, and the initial temperature is 0°C. The specific heat capacity for water is 4.18 J/g°C. However, we also need to take into account the heat of fusion for the ice, which is -6.02 kJ/mol. We can convert the mass of ice (10g) to moles (10g/18.02 g/mol = 0.555 mol) and then multiply by the heat of fusion to get the heat transfer for the ice:

Q = (0.555 mol) (-6.02 kJ/mol) + (90g) (4.18 J/g°C) (Tf - 0°C)

Now, we can set these two equations equal to each other and solve for Tf (final temperature):

(156g) (0.903 J/g°C) (Tf - 50°C) = (0.555 mol) (-6.02 kJ/mol) + (90g) (4.18 J/g°C) (Tf - 0°C)

Solving for Tf gives us a final temperature of -2.14°C. This means that the final temperature would be slightly below freezing, as expected since we are adding a relatively large amount of cold aluminium to the ice and water mixture.

To answer your question about delta H, we do not need to incorporate it into this calculation. Delta H represents the enthalpy change for a chemical reaction, and in this scenario, we are not dealing with a chemical reaction.