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
(heat to move ice from -10 to zero C) + (heat to melt ice) + (heat to move ice from zero C to final T) + (loss of heat to move water at 88.5 to final T) = 0
[(mass ice*sp.h.ice x (Tfinal-Tinitial)] + [(mass ice x heat fusion)] + [(mass H2O x sp. h liq H2O x (Tfinal-Tinitial)] + [(mass H2O x sp.h. x (Tfinal-Tionitial)] = 0
Solve for Tfinal. I think the answer is approximately 77 C.
To determine the equilibrium temperature for the liquid after the ice melts, we need to consider two processes: heat transfer from water to ice during ice melting and heating of the resulting liquid.
Let's calculate the heat transfer during the melting of the ice and then the heat transfer to increase the temperature of the liquid.
1. Heat transfer during ice melting:
The heat transfer during ice melting can be calculated using the equation:
Q = m * ΔH_fusion,
where Q is the heat transfer, m is the mass of the ice, and ΔH_fusion is the heat of fusion for water.
First, we need to convert the mass of the ice from grams to moles:
moles of ice = mass of ice / molar mass of water.
The molar mass of water (H2O) can be obtained from the periodic table:
molar mass of water (H2O) = 2 * atomic mass of hydrogen + 1 * atomic mass of oxygen.
= (2 * 1.008 g/mol) + (1 * 16.00 g/mol) = 18.016 g/mol.
Substituting the values into the equation:
moles of ice = 10 g / 18.016 g/mol.
Now, we can calculate the heat transfer:
Q_ice = moles of ice * ΔH_fusion.
2. Heat transfer to increase the temperature of the liquid:
The heat transfer to increase the temperature of the liquid can be calculated using the equation:
Q = m * c * ΔT,
where Q is the heat transfer, m is the mass of the liquid, c is the specific heat capacity of water, and ΔT is the change in temperature.
First, we need to calculate the mass of the liquid water in the beaker:
To convert from mL to grams, we use the density of water:
mass of water = volume of water * density of water.
Substituting the values into the equation:
mass of water = 150 mL * 1.0 g/mL.
Now, we can calculate the heat transfer:
Q_water = mass of water * c_water * ΔT.
3. Equilibrium temperature calculation:
At equilibrium, the heat transferred during the melting of the ice (Q_ice) equals the heat transferred to the liquid water (Q_water).
Q_ice = Q_water.
Now we can set up and solve the equation to find the equilibrium temperature:
moles of ice * ΔH_fusion = mass of water * c_water * ΔT.
Substituting the given values and solving the equation will yield the equilibrium temperature for the liquid after the ice melts.