Ice added to Water (heats of rxn)

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In summary, the problem involves adding 24g of ice at -5C to 50 mL of water at 10C in an isolated system. The heat capacity can be ignored and the system is completely isolated. Using the specific heat capacities of water in its liquid and solid states, and the heat of fusion, the temperature of the system at equilibrium is calculated to be 5.98C. Assumptions were made that the ice would melt and the transfer of heat between the water and ice would cancel out. It is also noted that the energy available before the water reaches 0C is a determining factor in whether the ice will melt or the water will freeze.
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aqwsde
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Homework Statement



If 24g of ice at -5C is added to a isolated dewar containing 50 mL of water at 10C. What would the temperature of the system be at equilibrium if the heat capacity can be ignored and the system is completely isolated.

Homework Equations



sp ht H2O (l) - 4.18 J/(gC)
sp ht H2O(s) = 2.01 J/(gC)

dHfus = 6.01 kJ/mol
Density H2O = 1g/ml

The Attempt at a Solution



I wasn't sure if the water would start to freeze or the ice would melt or if that is necessary to know. I approached the problem with the assumption that the ice melts and also that the transfer of heat from water to ice during melting is equal and opposite the heat transfer out of the surrounding and thus the terms cancel (I don't know if I can make this assumption). With that in mind

qrxn = -qsurr

qrxn = 24 *2.01 *(0 - (-5)) + 24*4.18*(Tf-0)

-qsurr = -50*4.18*(Tf-10)

Solving for Tf = 5.98C

My main question is if my assumptions are valid and also how would I know without it being said if the ice if going to melt of the water is going to freeze, or does it make a difference?
 
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  • #2
Quick check is how much energy is available before the water gets down to 0C (mcT)
If this is more than the energy to melt the ice then it will be water.
 
  • #3




Your approach to the problem is correct. The key assumption you made is that the transfer of heat from water to ice during melting is equal and opposite the heat transfer out of the surrounding. This assumption is valid because the system is completely isolated and there is no external heat source or sink. Therefore, the heat transfer between the water and ice will balance out and the temperature of the system will reach equilibrium.

As for the question of whether the ice will melt or the water will freeze, it is not necessary to know beforehand. In this case, the initial temperatures of the water and ice are such that the final temperature will be between the two. If the initial temperature of the ice was lower than the water, then it would have melted completely. If the initial temperature of the water was lower than the ice, then it would have frozen completely. However, since the initial temperatures are close, both melting and freezing will occur, but the final temperature will be somewhere in between.

Overall, your solution is correct and your assumptions are valid. Keep in mind that this is a simplified approach and in a real-life scenario, other factors such as pressure and non-ideal behavior of the substances may affect the final temperature.
 

1. What is the enthalpy change when ice is added to water?

When ice is added to water, the enthalpy change is negative, meaning it releases heat energy. This is because the process of ice melting and becoming water is exothermic, or heat-releasing.

2. How does the temperature of the water change when ice is added?

When ice is added to water, the temperature decreases due to the endothermic process of melting. This is because the energy from the water is used to break the bonds between the molecules in the ice, resulting in a decrease in temperature.

3. Does the amount of heat released depend on the amount of ice added?

The amount of heat released when ice is added to water does depend on the amount of ice added. The more ice added, the more energy is required to melt it, resulting in a larger enthalpy change.

4. How does the addition of salt affect the enthalpy change when ice is added to water?

The addition of salt to water affects the enthalpy change when ice is added by lowering the freezing point of water. This means that it will take longer for the ice to melt and for the water to reach its freezing point, resulting in a smaller enthalpy change compared to pure water.

5. Can the heat released from melting ice be used for other purposes?

Yes, the heat released from melting ice can be used for other purposes, such as heating a substance or powering a heat engine. This is known as the principle of latent heat, where the heat energy released during a phase change can be harnessed for other uses.

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