If 142.38 g of l water at 21.7 degrees C is placed into a syrofoam cup with 174.36 g of ice at -27.5 degrees C what would be the final temperature of the entire contents at equilibrium? If it is partially frozen, how many g of the ice has melted?
given values
cp water = 4.184 j/g degree c
cp ice = 2.114 j/g degree c
heat of fusion of ice is 335 J/g
so far, i have this:
(174.36g)(2.114g)(27.5 C)
= 10247 g to three sig figs = 10200 J
is that i calculate the energy required to raise the ice to 0 degrees C?
now i know that the next steps are to find the enrgy required to melt the ice and the energy reuired to cool the water down to 0 degrees C. how do i do those two calculations?
Yes. Now, you have ice at 0C. How much did the 142 g of water cool to supply this heat?
To calculate the energy required to melt the ice, use the heat of fusion value given for ice. The equation to calculate this is:
Energy = mass of ice * heat of fusion of ice
In this case, the mass of ice is 174.36 g, so the energy required to melt the ice would be:
Energy = 174.36 g * 335 J/g = 58311.6 J
Next, you need to calculate the energy required to cool the water down to 0 degrees Celsius. To do this, use the specific heat capacity of water:
Energy = mass of water * specific heat capacity of water * change in temperature
The mass of water is 142.38 g, the specific heat capacity of water is 4.184 J/g°C, and the change in temperature is (21.7 °C - 0 °C) = 21.7 °C. Plug these values into the equation to find the energy required:
Energy = 142.38 g * 4.184 J/g°C * 21.7 °C = 12529.6 J
Note that these calculations assume there is no energy transfer to or from the surroundings, effectively an isolated system.
To find the final temperature at equilibrium, you need to balance the energy gained by the ice with the energy lost by the water. Use the equation:
Energy gained by ice = Energy lost by water
58311.6 J = 10200 J + 12529.6 J + Energy lost during water cooling
Rearrange the equation to solve for the energy lost during water cooling:
Energy lost during water cooling = 58311.6 J - 10200 J - 12529.6 J = 35582 J
Since the specific heat capacities and masses of the substances are known, you can now calculate the temperature change for the water:
Temperature change = Energy lost during water cooling / (mass of water * specific heat capacity of water)
Temperature change = 35582 J / (142.38 g * 4.184 J/g°C) = 65.52°C
Finally, subtract the temperature change from the initial water temperature to find the final temperature at equilibrium:
Final temperature = Initial water temperature - Temperature change = 21.7 °C - 65.52 °C = -43.82 °C
So, the final temperature of the entire contents at equilibrium is approximately -43.82 °C.
To calculate the amount of ice that has melted, subtract the initial mass of ice from the mass of ice that would exist at equilibrium:
Mass of ice melted = Initial mass of ice - (Energy lost during water cooling / heat of fusion of ice)
Mass of ice melted = 174.36 g - (35582 J / 335 J/g) = 174.36 g - 106.19 g = 68.17 g
Approximately 68.17 g of the ice has melted.