Two 20.0-g ice cubes at –10.0 °C are placed into 275 g of water at 25.0 °C. Assuming no energy is transferred to or from the surroundings, calculate the final temperature of the water after all the ice melts.
heat capacity h2o (S)=37.7 j/mol*k
heat capacity h2o (l)=75.3 j/mol*k
enthalpy of fusion of h2o= 6.01 kj/mol
see below
To calculate the final temperature of the water after all the ice melts, we need to determine the amount of heat exchanged during the process.
First, let's calculate the heat released by the ice cubes as they warm up from -10.0 °C to 0 °C.
Q1 = m1 * c1 * ΔT1
Where:
m1 = mass of ice cubes = 2 * 20.0 g = 40.0 g = 0.04 kg
c1 = specific heat capacity of ice = 2.09 J/g°C (specific heat capacity of water)
ΔT1 = change in temperature = 0 °C - (-10.0 °C) = 10.0 °C
Plugging in the values:
Q1 = 0.04 kg * 2.09 J/g°C * 10.0 °C
Q1 = 8.36 J
Next, we calculate the heat absorbed by the water as it cools down from 25.0 °C to 0 °C.
Q2 = m2 * c2 * ΔT2
Where:
m2 = mass of water = 275 g = 0.275 kg
c2 = specific heat capacity of water = 4.18 J/g°C
ΔT2 = change in temperature = 0 °C - 25.0 °C = -25.0 °C
Plugging in the values:
Q2 = 0.275 kg * 4.18 J/g°C * (-25.0 °C)
Q2 = -287.65 J
Now, we calculate the heat required to melt the ice cubes at 0 °C:
Q3 = m3 * ΔH_fusion
Where:
m3 = mass of ice cubes = 2 * 20.0 g = 40.0 g = 0.04 kg
ΔH_fusion = enthalpy of fusion of water = 6.01 kJ/mol = 6.01 × 10^3 J/mol
Note: We'll assume that all the ice melts.
Plugging in the values:
Q3 = 0.04 kg * (6.01 × 10^3 J/mol)
Q3 = 240.4 J
Finally, we can calculate the total heat exchanged during the process:
Q = Q1 + Q2 + Q3
Q = 8.36 J + (-287.65 J) + 240.4 J
Q = -38.89 J
Since we know that no energy is transferred to or from the surroundings, the total heat exchanged must be equal to zero.
Q = 0
-38.89 J = 0
Now, let's calculate the final temperature of the water.
Q = m2 * c2 * ΔT
Where:
m2 = mass of water = 275 g = 0.275 kg
c2 = specific heat capacity of water = 4.18 J/g°C
ΔT = change in temperature
Plugging in the values and solving for ΔT:
0 = 0.275 kg * 4.18 J/g°C * ΔT
ΔT = 0 °C
Therefore, the final temperature of the water is 0 °C after all the ice melts.