Respuesta :
Answer:
Heat required to convert 2.500 kg of solid SO₂ at the melting point to a gas at 60˚C is 1,589.724 kilo joules.
Explanation:
Heat required to melt sulfur dioxide solid -73˚C = [tex]q_1[/tex]
Latent heat melting of sulfur dioxide = [tex]\Delta H^o_{fus}=8.169 kJ/mol=8169 J/mol[/tex]
Mass of sulfur dioxide solid , m= 2.500 kg = 2500 g
Moles of sulfur dioxide solid ,n= [tex]\frac{2500 g}{64 g/mol}=39.062 mol[/tex]
[tex]q_1=n\times \Delta H^o_{fus}[/tex]
[tex]q_1=39.062 mol\times 8169 J/mol=319,097.48 J=319.097 kJ[/tex]
Heat required to raise the temperature of liquid sulfur dioxide from -73˚C to -10˚C = [tex]q_2[/tex]
-10˚C = 263.15 K, -73˚C = 200.15 K
Mass of sulfur dioxide liquid, m= 2.500 kg = 2500 g
Specific heat of liquid sulfur dioxide = [tex]C_1=0.995 J/g K[/tex]
Change in temperature =[tex]\Delta T_1=(263.15 K-200.15 K)=63 K[/tex]
[tex]q_2=m\times C_1\times \Delta T_1[/tex]
[tex]q_2=2500 g\times 0.995 J/g K\times 63 K=156,712.5 J=156.712 kJ[/tex]
Heat required to vaporize sulfur dioxide liquid at -10˚C= [tex]q_3[/tex]
Latent heat melting of sulfur dioxide = [tex]\Delta H^o_{vap}=25.73 kJ/mol=25730 J/mol[/tex]
Mass of sulfur dioxide liquid, m= 2.500 kg = 2500 g
Moles of sulfur dioxide solid ,n= [tex]\frac{2500 g}{64 g/mol}=39.062 mol[/tex]
[tex]q_3=n\times \Delta H^o_{vap}[/tex]
[tex]q_3=39.062 mol\times 25.73 kJ/mol=1,005.065 kJ[/tex]
Heat required to raise the temperature of liquid sulfur dioxide from -10˚C to 60˚C = [tex]q_4[/tex]
-10˚C = 263.15 K, 60˚C = 333.15 K
Mass of sulfur dioxide liquid, m= 2.500 kg = 2500 g
Specific heat of gas sulfur dioxide = [tex]C_2=0.622 J/g K[/tex]
Change in temperature =[tex]\Delta T_2=(333.15 K-263.15 K)=70 K[/tex]
[tex]q_4=m\times C_2\times \Delta T_2[/tex]
[tex]q_4=2500 g\times 0.622 J/gK\times 70 K=108,850 J=108.850 kJ[/tex]
Heat required to convert 2.500 kg of solid SO₂ at the melting point to a gas at 60˚C = Q
[tex]Q=q_1+q_2+q_3+q_4[/tex]
[tex]Q=319.097 kJ+156.712 kJ+1,005.065 kJ+108.850 kJ=1,589.724 kJ[/tex]
