I need help with part b I already know how to do part a. Dry ice is solid carbon dioxide. Instead of melting, solid carbon dioxide sublimes according to the equation: CO2(s)→CO2(g). When dry ice is added to warm water, heat from the water causes the dry ice to sublime more quickly. The evaporating carbon dioxide produces a dense fog often used to create special effects. In a simple dry ice fog machine, dry ice is added to warm water in a Styrofoam cooler. The dry ice produces fog until it evaporates away, or until the water gets too cold to sublime the dry ice quickly enough. Suppose that a small Styrofoam cooler holds 15.0 L of water heated to 86 °C. The specific heat of water is 4.184 J/g·°C.  a) Use standard enthalpies of formation to calculate the change in enthalpy for dry ice sublimation. (The ΔHºf for CO2(s) is -427.4 kJ/mol, and for CO2(g) is –393.5 kJ/mol) Answer: 33.9 kj b) Calculate the mass of dry ice that should be added to the water so that the dry ice completely sublimes away when the water reaches 13 °C. Assume no heat loss to the surroundings.

Question
Asked Oct 18, 2019

I need help with part b I already know how to do part a.

 

Dry ice is solid carbon dioxide. Instead of melting, solid carbon dioxide sublimes according to the equation: CO2(s)→CO2(g). When dry ice is added to warm water, heat from the water causes the dry ice to sublime more quickly. The evaporating carbon dioxide produces a dense fog often used to create special effects. In a simple dry ice fog machine, dry ice is added to warm water in a Styrofoam cooler. The dry ice produces fog until it evaporates away, or until the water gets too cold to sublime the dry ice quickly enough. Suppose that a small Styrofoam cooler holds 15.0 L of water heated to 86 °C. The specific heat of water is 4.184 J/g·°C.  

a) Use standard enthalpies of formation to calculate the change in enthalpy for dry ice sublimation. (The ΔHºf for CO2(s) is -427.4 kJ/mol, and for CO2(g) is –393.5 kJ/mol)

 

Answer: 33.9 kj

 

b) Calculate the mass of dry ice that should be added to the water so that the dry ice completely sublimes away when the water reaches 13 °C. Assume no heat loss to the surroundings.

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Expert Answer

Step 1

The heat lost or gained by a substance is related to the change in temperature as given in equation (1), in which, q represents the heat transferred, m is the mass of the substance, c represents the specific heat of the substance, T1 represents the initial temperature and T2 represents the final temperature.

The density of a substance is the ratio of its mass and volume. It is a measure of mass per unit volume. It is given by expression (2), in which, d is the density, m is the mass, and V is the volume of the substance.

The number of moles of a species is calculated by expression (3), in which, n is the number of moles, m is the mass, and M is the molar mass of the species.

9 3 me (T, - Т,)
(1)
(2)
(3)
м
|
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9 3 me (T, - Т,) (1) (2) (3) м |

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Step 2

The mass of the water present in the cooler is calculated by using equation (2),

m
1000 g/L
15.0 L
m 1500 g
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m 1000 g/L 15.0 L m 1500 g

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Step 3

The heat lost by water is calcul...

q1500 g x 4.184 J/g°C(86-13) °C
=4.58x 10 J
=4.58x 102 kJ
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q1500 g x 4.184 J/g°C(86-13) °C =4.58x 10 J =4.58x 102 kJ

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