Consider a sample of 20g of water at -20*C and 1.0 atm. Determine the amount of energy required to raise the temperature of this water to 120*C. (Sice=2.1 Jg-1C-1; Swater= 4.184Jg-1C-1; Ssteam=1.7Jg-1C-1; ΔHfus 6.01 kJ/mol; ΔHvap=40.7 kJ/mol)
q1 = heat needed to raise T from -20 to zero.
q1 = mass ice x specific heat ice x (Tfinal-Tinitial)
q2 = heat needed to melt ice at zero to liquid water at zero C.
q2 = mass ice x heat fusion
q3 = heat needed to raise T of liquid water at zero C to 100 C.
q3 = mass H2O x specific heat H2O x (Tfinal-Tinitial)
q4 = heat needed to boil H2O at 100 C to steam at 100 C
q4 = mass H2O x heat vaporization
q5 = heat needed to raise T of steam at 100 C to steam at 120 C.
q5 = mass steam x specific heat steam x (Tfinal-Tinitial)_
Total Q = q1+q2+q3+q4+q5
To solve this problem, we need to break it down into a series of steps and calculate the energy required for each step:
1. Calculate the energy required to raise the temperature of the water from -20°C to 0°C.
2. Calculate the energy required to melt the ice at 0°C to water at 0°C.
3. Calculate the energy required to raise the temperature of the water from 0°C to 100°C.
4. Calculate the energy required to vaporize the water at 100°C to steam at 100°C.
5. Calculate the energy required to raise the temperature of the steam from 100°C to 120°C.
Let's now calculate the energy for each step:
1. Calculate the energy required to raise the temperature of the water from -20°C to 0°C:
Energy = mass (g) × specific heat capacity (J/g°C) × temperature change (°C)
Energy = 20 g × 2.1 J/g°C × (0°C - (-20°C))
Energy = 20 g × 2.1 J/g°C × 20°C
Energy = 840 J
2. Calculate the energy required to melt the ice at 0°C to water at 0°C:
Energy = moles × molar enthalpy of fusion (kJ/mol)
First, we need to calculate the moles of water:
Moles = mass (g) / molar mass (g/mol)
Moles = 20 g / 18.015 g/mol (molar mass of water)
Moles = 1.1106 mol
Energy = 1.1106 mol × 6.01 kJ/mol
Energy = 6.676 kJ
3. Calculate the energy required to raise the temperature of the water from 0°C to 100°C:
Energy = mass (g) × specific heat capacity (J/g°C) × temperature change (°C)
Energy = 20 g × 4.184 J/g°C × (100°C - 0°C)
Energy = 20 g × 4.184 J/g°C × 100°C
Energy = 8,368 J
4. Calculate the energy required to vaporize the water at 100°C to steam at 100°C:
Energy = moles × molar enthalpy of vaporization (kJ/mol)
Energy = 1.1106 mol × 40.7 kJ/mol
Energy = 45.287 kJ
5. Calculate the energy required to raise the temperature of the steam from 100°C to 120°C:
Energy = mass (g) × specific heat capacity (J/g°C) × temperature change (°C)
Energy = 20 g × 1.7 J/g°C × (120°C - 100°C)
Energy = 20 g × 1.7 J/g°C × 20°C
Energy = 680 J
Now, add up the energies from each step to get the total energy required:
Total Energy = Energy step 1 + Energy step 2 + Energy step 3 + Energy step 4 + Energy step 5
Total Energy = 840 J + 6.676 kJ + 8,368 J + 45.287 kJ + 680 J
Therefore, the amount of energy required to raise the temperature of the water from -20°C to 120°C is 61.851 kJ.