A 72.2 g ice cube floats in the Arctic Sea. The temperature and pressure of the system and surroundings are at 1 atm and 0°C. Calculate ΔSsys, ΔSsurr, and ΔSuniv for the melting of the ice cube. (The molar heat of fusion of water is 6.01 kJ/mol.)
To calculate ΔSsys, ΔSsurr, and ΔSuniv for the melting of the ice cube, you can use the equations involving entropy change, temperature, and heat.
First, let's calculate ΔSsys, the entropy change of the system. In this case, the system is the ice cube.
The equation for ΔSsys is given by:
ΔSsys = qsys / T
Where qsys is the heat added to the system and T is the temperature in Kelvin.
To find qsys, we can use the equation:
qsys = n * ΔHfus
Where n is the number of moles of water and ΔHfus is the molar heat of fusion.
To find the number of moles of water, we can use the molar mass of water (18.015 g/mol) and the mass of the ice cube (72.2 g):
n = mass / molar mass
n = 72.2 g / 18.015 g/mol
Now, we can calculate qsys:
qsys = n * ΔHfus
Substituting the values from the question:
qsys = (72.2 g / 18.015 g/mol) * (6.01 kJ/mol)
Also, convert the temperature from Celsius to Kelvin:
T = 0°C + 273.15
Now, we have all the values to calculate ΔSsys:
ΔSsys = qsys / T
Now, let's calculate ΔSsurr, the entropy change of the surroundings. In this case, the surroundings are the Arctic Sea.
The equation for ΔSsurr is given by:
ΔSsurr = -qsys / T
Note that the sign is negative because the heat released by the system (the ice cube) is absorbed by the surroundings.
Finally, ΔSuniv, the entropy change of the universe, can be calculated by summing ΔSsys and ΔSsurr:
ΔSuniv = ΔSsys + ΔSsurr
Plug in the values into the equations to obtain the final values.
Note: Make sure to check the units of all the values and convert them if necessary to maintain consistency throughout the calculations.