Answer :
Final answer:
The heat energy required to convert 98.1 g of liquid sulfur dioxide at 200 K to gaseous SO₂ at 263 K is 46.832956 kJ.
Explanation:
To determine the heat energy required to convert liquid sulfur dioxide (SO₂) at 200 K to gaseous SO₂ at 263 K, we can use the equation:
Q = m × ΔHvap + m × Cp × ΔT
Where Q is the heat energy, m is the mass of the substance, ΔHvap is the molar heat of vaporization, Cp is the specific heat capacity, and ΔT is the change in temperature.
Let's calculate it step by step:
- Calculate the heat energy required for the phase change using the molar heat of vaporization:
Q₁ = n × ΔHvap = m/M × ΔHvap - Calculate the heat energy required for the temperature change using the specific heat capacity:
Q₂ = m × Cp × ΔT - Add the two heat energies together to get the total heat energy: Q = Q₁ + Q₂
Now let's plug in the values:
Mass of SO₂ = 98.1 g
Molar heat of vaporization of SO₂ = 24.9 kJ/mol
Specific heat capacity of liquid SO₂ = 1.36 J g⁻¹ °C⁻¹
Change in temperature = 263 K - 200 K = 63 K
First, calculate Q₁:
Q₁ = (98.1 g / 64.06 g/mol) * 24.9 kJ/mol = 38.11 kJ
Then, calculate Q₂:
Q₂ = 98.1 g * 1.36 J g⁻¹ °C⁻¹ * 63 K = 8722.956 J
Now, convert Q₂ to kJ:
Q₂ = 8722.956 J / 1000 = 8.722956 kJ
Finally, calculate the total heat energy:
Q = Q₁ + Q₂ = 38.11 kJ + 8.722956 kJ = 46.832956 kJ
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