A cube of ice is taken from the freezer at -9.0°C and placed in a 71-g aluminum calorimeter filled with 261g of water at room temperature of 20.0°C. The final situation is observed to be all water at 13.4°C. What was the mass of the ice cube (in grams)?
To find the mass of the ice cube, we can use the concept of heat transfer.
First, let's calculate the heat gained by the water in the calorimeter (Qw). We can use the formula:
Qw = mw * cw * ΔTw
Where:
mw = mass of water = 261 g
cw = specific heat capacity of water = 4.184 J/g°C
ΔTw = change in temperature of water = final temperature - initial temperature = 13.4°C - 20.0°C = -6.6°C
Plugging in the values:
Qw = 261 g * 4.184 J/g°C * -6.6°C
Qw = -7038.8 J (since the water lost heat, the result is negative)
Next, let's calculate the heat lost by the ice cube (Qi). We can use the formula:
Qi = mi * ci * ΔTi
Where:
mi = mass of ice cube (what we are trying to find)
ci = specific heat capacity of ice = 2.09 J/g°C (the same as water below 0°C)
ΔTi = change in temperature of ice = final temperature - initial temperature = 13.4°C - (-9.0°C) = 22.4°C
Plugging in the values:
Qi = mi * 2.09 J/g°C * 22.4°C
Qi = 46.976 mi J
Now, according to the principle of conservation of energy, the heat lost by the ice cube (Qi) is equal to the heat gained by the water (Qw). So, we can equate the two equations:
-7038.8 J = 46.976 mi J
Solving for mi:
mi = -7038.8 J / 46.976 J/g
mi ≈ 148.90 g
Therefore, the mass of the ice cube is approximately 148.90 grams.