Sulfur dioxide is produce din enormous amounts for sulfuric acid production. It melts at -73 degrees C and boils at -10 degrees C. Its heat of fusion is 8.619 kJ/mol and its heat of vaporation is 25.73 kJ/mol. The specific heat capacities of the liquid and gas are .995 j/g*K and .622 j/g*K, respectively. How much heaat is required o conver 2.500 kg of solid SO2 at the melting point to a gas at 60 degrees C.
Here is how you do this. I suggest you make a table showing T in one column and the transition in the other; i.e. solid to liquid, melting point, liquid to gas, boiling point, etc.
Then as long as you are in one phase, th3 formula is
q = mass x specific heat x (Tfinal-Tinitial).
At the phase transitions the formula is
q = mass x heat fusion at the melting point.
q = mass x heat vaporization at the boiling point.
Then add all of the q amounts together to arrive at the total q.
1605kJ
To calculate the amount of heat required to convert 2.500 kg of solid SO2 at the melting point to a gas at 60 degrees C, we need to consider the following steps:
1. Determine the heat required to raise the temperature of the solid SO2 to its boiling point.
2. Calculate the heat required for the phase change from solid to liquid.
3. Determine the heat required to raise the temperature of the liquid SO2 to its boiling point.
4. Calculate the heat required for the phase change from liquid to gas.
5. Calculate the heat required to raise the temperature of the gas SO2 to 60 degrees C.
Let's perform the calculations step by step:
Step 1: Heat required to raise the temperature of solid SO2 to its boiling point:
The temperature change is (-10 degrees C) - (-73 degrees C) = 63 degrees C.
The specific heat capacity of the solid SO2 is not provided, so we cannot directly calculate the heat required for this step.
Step 2: Heat required for the phase change from solid to liquid:
The heat of fusion for SO2 is 8.619 kJ/mol.
First, we need to find the number of moles in 2.500 kg of SO2:
Molar mass of SO2 = 32.07 g/mol + 16.00 g/mol = 48.07 g/mol
Number of moles = 2500 g / 48.07 g/mol ≈ 52.023 moles
Heat required = 8.619 kJ/mol × 52.023 moles = 448.583617 kJ
Step 3: Heat required to raise the temperature of liquid SO2 to its boiling point:
Temperature change = 60 degrees C - (-10 degrees C) = 70 degrees C
Mass of liquid SO2 = 2.500 kg - (52.023 moles × molar mass of SO2 ≈ 2.500 kg - (52.023 moles × 48.07 g/mol) ≈ 0.521 kg
Heat required = mass × specific heat capacity = 0.521 kg × 0.995 j/g*K × 70 degrees C = 36.442 j
Step 4: Heat required for the phase change from liquid to gas:
The heat of vaporization for SO2 is 25.73 kJ/mol.
Heat required = 25.73 kJ/mol × 52.023 moles = 1338.34979 kJ
Step 5: Heat required to raise the temperature of the gas SO2 to 60 degrees C:
Mass of gas SO2 = 2.500 kg - 0.521 kg = 1.979 kg
Heat required = mass × specific heat capacity = 1.979 kg × 0.622 j/g*K × 60 degrees C = 73.76436 j
Total heat required = Step 2 + Step 3 + Step 4 + Step 5
Total heat required = 448.583617 kJ + 36.442 kJ + 1338.34979 kJ + 73.76436 kJ
Therefore, the total heat required to convert 2.500 kg of solid SO2 at the melting point to a gas at 60 degrees C is approximately 1897.14 kJ.
To calculate the amount of heat required to convert 2.500 kg of solid SO2 at its melting point (-73°C) to a gas at 60°C, we need to consider several steps:
1. Heat required to raise the temperature of solid SO2 from -73°C to its melting point (0°C).
2. Heat of fusion required to convert solid SO2 at its melting point to liquid SO2 at its boiling point.
3. Heat required to raise the temperature of liquid SO2 from its boiling point (-10°C) to the desired temperature (60°C).
4. Heat of vaporization required to convert liquid SO2 at its boiling point to gaseous SO2 at the desired temperature (60°C).
Let's calculate each step:
1. Heat required to raise the temperature of solid SO2 from -73°C to 0°C:
The specific heat capacity of the solid is not given, but we can assume it is similar to that of the liquid. So, we can use the specific heat capacity of the liquid, which is 0.995 J/g*K.
The temperature change is 0°C - (-73°C) = 73°C.
The mass of solid SO2 is 2.500 kg, which is equivalent to 2500 g.
Heat = mass * specific heat capacity * temperature change
Heat = 2500 g * 0.995 J/g*K * 73°C
2. Heat of fusion required to convert solid SO2 at its melting point to liquid SO2 at its boiling point:
The heat of fusion is given as 8.619 kJ/mol.
To convert it into J/g, we need to know the molar mass of SO2, which is approximately 64.07 g/mol.
Heat of fusion = 8.619 kJ/mol * (1 mol / 64.07 g) * 2500 g
3. Heat required to raise the temperature of liquid SO2 from -10°C to 60°C:
The specific heat capacity of the liquid SO2 is given as 0.995 J/g*K.
The temperature change is 60°C - (-10°C) = 70°C.
The mass of liquid SO2 is 2.500 kg, which is equivalent to 2500 g.
Heat = mass * specific heat capacity * temperature change
Heat = 2500 g * 0.995 J/g*K * 70°C
4. Heat of vaporization required to convert liquid SO2 at its boiling point to gaseous SO2 at 60°C:
The heat of vaporization is given as 25.73 kJ/mol.
Heat of vaporization = 25.73 kJ/mol * (1 mol / 64.07 g) * 2500 g
To find the total heat required, sum up the results from each step:
Total heat = Step 1 heat + Step 2 heat + Step 3 heat + Step 4 heat
Calculate each step separately and then sum up the values to get the final result.