Dry-ice baths are used in chemistry laboratories to cool substances to temperatures much below the freezing point of water. They are composed of solid carbon dioxide (dry ice) immersed in organic solvents. Because dry ice sublimes at -78.7deg C (i.e., transforms directly from the solid to the vapor phase), a dry-ice cooling bath will stay at -78.7deg C as long as solid carbon dioxide is present in the bath. Organic liquids with a melting point below -78.7deg C, such as isopropanol (m.p. -88.5deg C ) or acetone (m.p. -94.5deg C ), are common liquids used for dry-ice baths.
What is the minimum mass of dry ice (originally stored at the temperature of liquid nitrogen, which is -195.8deg C ) that must be added into a 500mL bath of acetone to cool it from room temperature (25deg C) to the dry-ice sublimation temperature of -78.7deg C ?
Acetone:
C_(P,m)(l)=124.3(J)/(molK),
ho (25deg C)=0.7847(g)/(mL)
Carbon dioxide:
C_(P,m)(s)(-200deg C to -78deg C)=A+B*T+C*
with: A=7.3556(J)/(molK)
B=0.5425(J)/(molK^(2))
C=-2.8813 imes 10^(-3)(J)/(molK^(3))
D=7.0429 imes 10^(-6)(J)/(molK^(4))
ho (-78deg C)=1.62(g)/(mL),Delta H_(sub )=26.1(kJ)/(mol)
Dry-ice baths are used in chemistry laboratories to cool substances to temperatures much below the freezing point of water. They are composed of solid carbon dioxide (dry ice) immersed in organic solvents. Because dry ice sublimes at -78.7 C (i.e., transforms directly from the solid to the vapor phase), a dry-ice cooling bath will stay at -78.7 C as long as solid carbon dioxide is present in the bath. Organic liquids with a melting point below -78.7 C, such as isopropanol (m.p. -88.5 C) or acetone (m.p. -94.5 C), are common liquids used for dry-ice baths.
What is the minimum mass of dry ice (originally stored at the temperature of liquid nitrogen, which is -195.8 C) that must be added into a 500 mL bath of acetone to cool it from room temperature (25 C) to the dry-ice sublimation temperature of -78.7 C?
Acetone:
Cp,m(l) = 124.3 mol K
p (25 C)=0.7847_g mI
Carbon dioxide:
Cp,m(s) (-200 C to -78C)=A+BT+C.T2+DT3
with:A = 7.3556 mol K
J B = 0.5425 - mol K2
C = -2.8813 x 10-3 mol K3 D = 7.0429 10-6 mol K4
p (-78 C) =1.62 _g mL
mol
