An ice cube of mass 10g at -10C is added to the beaker containing 150mL of water at 88.5C. Assuming no heat is lost to the surrounding; calculate the equilibrium temperature for the liquid after the ice melts.(Heat of fusion for H2O = 6.01 kJ/mol. Heat of vaporization 40.67kJ/mol. Density of H2O = 1.0g/mL.
Given Table
H2O(s) = 37.1 J/mol^-1/K^-1
H2O(l) = 75.6 J/mol^-1/K^-1
H2O(g) = 33.6J/mol^-1/K^-1
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To calculate the equilibrium temperature for the liquid after the ice melts, we need to consider the heat exchanged during the phase change from solid to liquid and the subsequent temperature change.
First, let's calculate the heat required to raise the temperature of the ice from -10°C to its melting point (0°C):
Heat for temperature change of ice = mass × specific heat capacity × temperature change
Since we have the mass of the ice (10g) and the specific heat capacity of ice (37.1 J/mol^-1/K^-1), we can convert the mass to moles:
Molar mass of H2O = 18 g/mol
Number of moles = mass / molar mass
Number of moles = 10g / 18 g/mol = 0.556 mol
Now, we can calculate the heat required for temperature change:
Heat for temperature change of ice = number of moles × specific heat capacity × temperature change
Heat for temperature change of ice = 0.556 mol × 37.1 J/mol^-1/K^-1 × (0°C - (-10°C))
Next, let's calculate the heat required for the phase change from solid to liquid:
Heat for phase change = number of moles × heat of fusion
Heat for phase change = 0.556 mol × 6.01 kJ/mol = 6.01 × 10^3 J
Now, let's calculate the heat required to raise the temperature of the water from its initial temperature (88.5°C) to the equilibrium temperature (Tf):
Heat for temperature change of water = mass × specific heat capacity × temperature change
We have the mass of water (150g) and the specific heat capacity of water (75.6 J/mol^-1/K^-1), but we need to convert the mass to moles:
Number of moles = mass / molar mass
Number of moles = 150g / 18 g/mol = 8.33 mol
Finally, we can calculate the heat required for temperature change:
Heat for temperature change of water = number of moles × specific heat capacity × temperature change
Heat for temperature change of water = 8.33 mol × 75.6 J/mol^-1/K^-1 × (Tf - 88.5°C)
To find the equilibrium temperature, we set the heat gained by the water equal to the heat lost by the ice:
Heat for temperature change of ice + Heat for phase change = Heat for temperature change of water
0.556 mol × 37.1 J/mol^-1/K^-1 × (0°C - (-10°C)) + 0.556 mol × 6.01 × 10^3 J + 8.33 mol × 75.6 J/mol^-1/K^-1 × (Tf - 88.5°C) = 0
Now, we can solve the above equation to find the equilibrium temperature (Tf).
Note: In this calculation, we assumed no heat loss to the surroundings. In reality, some heat will be lost, but this assumption allows us to find an approximate equilibrium temperature.