Calculate the total amount of heat absorbed (in kJ) when 2.00 mol of ice at -30.0°C is converted to steam at 140.0°C. (Cp(ice)=2.06 J/g∘C; Cp(water)=4.18 J/g∘C; Cp(steam)=1.87 J/g∘C) (7 pts: Given-1point; Formula-1point; Substitution-1point; Solution-2 points; Final Answer-2points)
I need help
Given:
Number of moles of ice (n) = 2.00 mol
Temperature of ice (T1) = -30.0°C
Temperature of steam (T2) = 140.0°C
Specific heat capacity of ice (Cp(ice)) = 2.06 J/g∘C
Specific heat capacity of water (Cp(water)) = 4.18 J/g∘C
Specific heat capacity of steam (Cp(steam)) = 1.87 J/g∘C
Formula:
Q = (m x Cp x ∆T)
Substitution and Solution:
First, we need to calculate the amount of heat required to raise the temperature of ice from -30.0°C to 0°C, using the specific heat capacity of ice:
Q1 = (2.00 mol x 18.0 g/mol) x (2.06 J/g∘C) x (0°C - (-30.0°C))
Q1 = 2.00 mol x 18.0 g/mol x 2.06 J/g∘C x 30.0°C
Q1 = 0.3708 kJ
Next, we need to calculate the amount of heat required to melt the ice at 0°C, using the enthalpy of fusion of ice (∆Hfusion):
∆Hfusion = 6.01 kJ/mol
Q2 = (2.00 mol x 6.01 kJ/mol)
Q2 = 12.02 kJ
Then, we need to calculate the amount of heat required to raise the temperature of water from 0°C to 100°C, using the specific heat capacity of water:
Q3 = (2.00 mol x 18.0 g/mol) x (4.18 J/g∘C) x (100°C - 0°C)
Q3 = 2.00 mol x 18.0 g/mol x 4.18 J/g∘C x 100.0°C
Q3 = 15.048 kJ
Next, we need to calculate the amount of heat required to convert the water at 100°C to steam at 100°C, using the enthalpy of vaporization of water (∆Hvaporization):
∆Hvaporization = 40.7 kJ/mol
Q4 = (2.00 mol x 40.7 kJ/mol)
Q4 = 81.4 kJ
Finally, we need to calculate the amount of heat required to raise the temperature of steam from 100°C to 140°C, using the specific heat capacity of steam:
Q5 = (2.00 mol x 18.0 g/mol) x (1.87 J/g∘C) x (140°C - 100°C)
Q5 = 2.00 mol x 18.0 g/mol x 1.87 J/g∘C x 40.0°C
Q5 = 0.26976 kJ
Therefore, the total amount of heat absorbed is:
Total heat absorbed = Q1 + Q2 + Q3 + Q4 + Q5
Total heat absorbed = 0.3708 kJ + 12.02 kJ + 15.048 kJ + 81.4 kJ + 0.26976 kJ
Total heat absorbed = 109.10956 kJ
Final Answer:
The total amount of heat absorbed is 109.11 kJ.
To calculate the total amount of heat absorbed, we need to consider the different stages of the heating process and calculate the heat absorbed in each stage.
1. First, we need to calculate the heat absorbed to raise the temperature of the ice from -30.0°C to 0°C:
Q1 = mass × specific heat capacity × change in temperature
The mass of ice can be calculated using the molar mass of water (18.015 g/mol) and the number of moles (2.00 mol):
mass = number of moles × molar mass
Next, we need to convert the specific heat capacity from J/g°C to J/mol°C by dividing by the molar mass:
Cp(ice, mol) = Cp(ice, g) / molar mass
Substituting the given values:
mass = 2.00 mol × 18.015 g/mol
Cp(ice, mol) = 2.06 J/g°C / 18.015 g/mol
Finally, we can calculate Q1:
Q1 = mass × Cp(ice, mol) × (0 - (-30.0)°C)
2. Next, we need to calculate the heat absorbed to melt the ice at 0°C:
Q2 = mass × heat of fusion
The heat of fusion for water is 334 J/g. We can use the same mass value calculated in step 1 to calculate Q2.
Q2 = mass × 334 J/g
3. After the ice has melted, we need to calculate the heat absorbed to raise the temperature of the water from 0°C to 100°C:
Q3 = mass × Cp(water) × (100 - 0)°C
Substituting the given values:
Q3 = mass × 4.18 J/g°C × (100 - 0)°C
4. Next, we need to calculate the heat absorbed to convert the water at 100°C to steam at 100°C:
Q4 = mass × heat of vaporization
The heat of vaporization for water is 2260 J/g. Again, we can use the same mass value calculated in step 1.
Q4 = mass × 2260 J/g
5. Finally, we need to calculate the heat absorbed to raise the temperature of the steam from 100°C to 140°C:
Q5 = mass × Cp(steam) × (140 - 100)°C
Substituting the given values:
Q5 = mass × 1.87 J/g°C × (140 - 100)°C
Now, we can calculate the total amount of heat absorbed by summing up all the individual heat values:
Total heat absorbed = Q1 + Q2 + Q3 + Q4 + Q5
Finally, we convert the answer to kJ by dividing by 1000:
Total heat absorbed (in kJ) = (Q1 + Q2 + Q3 + Q4 + Q5) / 1000
By substituting the values and performing the calculations, you can determine the total amount of heat absorbed in kJ.