Answer to Question #109190 in General Chemistry for Joyce

Question

Suppose four 30g ice are added to a glass containing 200cm3 of juice at 20degree Celsius. The juice has a density of 1gcm3, specific heat of 4.184J/g-K and heat of fusion of 333J/g. Determine whether or not the ice will melt. If your findining is that some ice will be left in the juice, calculate what mass of ice will be present the moment when thermal equilibrium is reached.

Answer 1

You need to understand 3 concepts to solve this answer.

Firstly, You have to use the principle of calorimetry (measuring heat content of a system) to get the answer for this question.

The principle goes like this:

heat gained by a system(ice) = heat given by a system (water).

That means the heat absorbed by ice will be equal to the heat given by the water.

Secondly,now since you know the principle, next step is to know the formula of heat given or taken, that is

Q= m*c*(t2-t1)

where,

m=mass of the substance

c=heat capacity of substance (ice=2.1kJ/kgK, water=4.2kJ/kgK)

t2-t1=change in temperature of the substance

Now the last but not the least concept, you must know what is latent heat, you see while there is a change of state that is when solid converts to liquid or liquid to water there is no change in temperature with the absorption of heat and that value for ice to water is 336kJ/kg.

So this is the process is which is gonna happen, as the ice comes in contact with water, its temperature will rise upto 0 deg celsius. At that temperature which is the melting point of ice, it converts into water without any change in temperature. After complete conversion it again absorbs heat to reach a state where the converted ice and the water are at same temperatures (thermal equillibrium).

So your final formula would be:

Heat given by water = heat absorbed by ice + latent heat + heat absorbed by water (melted ice)

mw*cw*(tw-T) = mice*cice*(tice-0) +336 +mmw*cmw*(T-0)

The only unknown here is T =mixture temperature.