Respuesta :
Answer:
3696.83715 kJ
Explanation:
The following phase changes will be happening as:
SO₂ at -73 °C melts (Q₁) to form liquid which goes to temperature -10 °C (Q₂) and which evaporates to gas (Q₃) and further goes to temperature at 60 °C (Q₄).
m is the mass of SO₂ = 5.750 kg = 5750 g (as 1 kg = 1000 g)
Q₁ is the enthalpy of fusion for the given mass of SO₂ .
Thus, Q₁ = m×ΔH fusion
ΔH fusion is the enthalpy of fusion = 8.619 kJ/mol
Also, 1 mole of SO₂ = 64 g and 1 kJ = 1000 J
So,
ΔH fusion is the enthalpy of fusion = 8.619×1000 J / 64 g = 134.6719 J/g
Q₂ is the heat released in the temperature change from -73 °C to -10 °C.
Thus, Q₂ = C liquid×ΔT
Where,
C liquid is the specific heat of the liquid SO₂ = 0.995 J/g .K
ΔT = -10 - (-73) = 63 °C
Since this is a difference of temperature, so,
ΔT = 63 K
Q₃ is the enthalpy of vaporization for the given mass of SO₂ .
Thus, Q₃ = m×ΔH vaporization
ΔH vaporization is the enthalpy of vaporization = 25.73 kJ/mol
Also, 1 mole of SO₂ = 64 g and 1 kJ = 1000 J
So,
ΔH vaporization is the enthalpy of vaporization = 25.73 kJ/mol = 25.73 ×1000 J / 64 g = 402.0313 J/g
Q₄ is the heat released in the temperature change from -10 °C to 60 °C.
Thus, Q₄ = C gas×ΔT'
Where,
C gas is the specific heat of the gas SO₂ = 0.622 J/g · K
ΔT = 60 - (-10) = 70 °C
Since this is a difference of temperature, so,
ΔT = 70 K
So,
Q = Q₁ + Q₂ + Q₃ + Q₄
The total heat will be released = m ( ΔH fusion + C liquid×ΔT + ΔH vaporization + C gas×ΔT')
Applying the values as:
Total heat = 5750 ( 134.6719 + 0.995×63 + 402.0313 + 0.622×70) J
= 3696837.15 J
Also 1 J = 10⁻³ kJ
So,
Heat required = 3696.83715 kJ
Based on the data provided, the quantity of Heat required to convert 5.750 kg of solid SO₂ at the melting point to a gas at 60.0°C is 3696.83715 kJ
What is change of state?
Change of state occurs when a substance changes from one phase to another.
Heat is either absorbed or evolved during change of state.
From the data provided, the phase changes that occur and the corresponding quantities of heat involved are as follows:
- SO₂ at -73 °C melts (Q₁) to form liquid
- liquid SO₂ at -73°C heats to liquid at -10 °C (Q₂)
- liquid SO₂ at -10 °C changes to gas at -10°C (Q₃)
- gaseous SO₂ heats up to gas at 60 °C (Q₄).
mass of SO₂ = 5.750 kg = 5750 g
Q₁ is the quantity of Heat required to a given mass of solid SO₂ to liquid.
- Q₁ = m×ΔHf
ΔHf is enthalpy of fusion = 8.619 kJ/mol
1 mole of SO₂ = 64 g and 1 kJ = 1000 J
Therefore,
ΔH fusion is the enthalpy of fusion = 8.619 × 1000 J / 64 g
ΔHf = 134.6719 J/g
Q₂ is heat absorbed by the liquid in the temperature change from -73 °C to -10 °C.
- Q₂ = m× Cliquid ×ΔT
Where,
- Cliquid is the specific heat of the liquid SO₂ = 0.995 J/g .K
- ΔT = -10 - (-73) = 63 °C
Q₃ is the quantity of Heat required to a given mass of liquid SO₂ to gas.
- Q₃ = m×ΔHvap
ΔHvap is the enthalpy of vaporization = 25.73 kJ/mol
1 mole of SO₂ = 64 g and 1 kJ = 1000 J
Thus;
ΔHvap = 25.73 ×1000 J / 64 g
ΔHvap = 402.0313 J/g
Q₄ is the heat absorbed by the gas in the temperature change from -10 °C to 60 °C.
- Q₄ = mass × Cgas×ΔT
Where,
Cgas is the specific heat of the gas SO₂ = 0.622 J/g · K
ΔT = 60 - (-10) = 70 °C
Therefore, the total heat required Q is given as:
- Q = Q₁ + Q₂ + Q₃ + Q₄
Q = m ( ΔHf + Cliquid × ΔT + ΔHvap + Cgas× ΔT)
Substituting the values :
Q = 5750 ( 134.6719 + 0.995 × 63 + 402.0313 + 0.622×70) J
Q = 3696837.15 J
Converting to kJ using 1 J = 10⁻³ kJ
Total Heat required = 3696.83715 kJ
Therefore, the quantity of Heat required to convert 5.750 kg of solid SO₂ at the melting point to a gas at 60.0°C is 3696.83715 kJ
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