Question

Determine the specific enthalpy of fusion of water. Mass of Calrimeter is 3.492g, Mass os water is 43.552g. Mass of Ice is 29.276g. Initial water temp is 24 degrees C. Initial Ice is 0 C. Final Calrimeter temp is 1C. What is the q(ice) in joules, and what is the Delta fusion H of ice in J/g and what is the % difference? The accepted enthalpy value for ice is 335J/g.

Answer 1

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First review some concepts: Enthalpy of fusion is the heat absorbed by a substance during a change from solid to liquid (fusion). It is a latent heat, because during the melting process, although the substance absorbs heat, there is no change in temperature. So the temperature remains constant during the whole melting process. When the heat of fusion is referenced to a unit of mass, it is usually called the specific heat of fusion. The symbol usually used to represent it is DHf. We can use the equation:

Experimentally, one way to determine the latent heat of a change of state is the method of mixtures. During the experiment you mix a substance in the two states (solid and liquid) at different temperatures, so that one of them provides the heat which the other absorbs. At the end the temperature reaches the final equilibrium after one of them has changed from solid to liquid (melts). An important condition is that there is no heat loss to the external environment. This is done by placing the mixture in a calorimeter, which makes practically negligible the heat loss to the environment. To correct for any error, we need to take into account the amount of heat absorbed by the calorimeter, through a water equivalent K, determined for the calorimeter.

How to proceed: M is the initial mass of water (43.552 g), in this case the liquid water and m is the mass of the melting ice (29.276 g). K will be the water equivalent of the calorimeter. T₀is the water and calorimeter temperature, before mixing (24 ºC), the final temperature after equilibrium is reached is T. c is the specific heat of liquid water, which we take as (1.0 ± 0.1) cal/g and DHf the specific heat of fusion of water, which we want to determine.

Clearing for DHf:

During the experiment you should have determined the water equivalent of the calorimeter, which is not among the data, but you can easily find from the experiment.

To determine the water equivalent of the calorimeter, you begin by weighing the empty and dry calorimeter, and note the value of the mass obtained Mcal. You already have that (3.492) so you probably did the rest.

1) Add an amount of water and heat to about 10 ºC above the ambient laboratory temperature. Once hot, pour this water in the calorimeter and close it. Now determine the mass of calorimeter with the water, M(cal + water[1]). The added mass of water, Ma, is obtained by difference between the two previous weights

Ma = M(cal + water[1]) - Mcal

2) Next, measure the temperature of the system cal + water and register as T1.

3) Take another amount of water and add a little crushed ice (until about 10 °C below room temperature). Register the second temperature as T2 (should be lower that ambient temperature). The second mass of water Mb is determined from the difference of the final weight subtracting the previous weight.

The equation to find the value K for the calorimeter is:

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