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 83 ∘C.

Question

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 83 ∘C.

Use standard enthalpies of formation to calculate the change in enthalpy for dry ice sublimation. (The ΔH∘f for CO2(s) is -427.4 kJ/mol.)
ΔH∘rxn =
33.9
kJ

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 35 ∘C. Assume no heat loss to the surroundings.
mdryice = _____ g

Answer 1

what reaction is the delta H rxn = 33.9 kJ?

Answer 2

To calculate the change in enthalpy (ΔH∘rxn) for dry ice sublimation, we can use the standard enthalpy of formation (ΔH∘f) of CO2(s), which is -427.4 kJ/mol.

The equation for sublimation of solid carbon dioxide is:
CO2(s)→CO2(g)

Since we need to calculate the change in enthalpy for the reaction, we need to consider the stoichiometric coefficients. The stoichiometric coefficient for CO2(g) is 1, and for CO2(s) it is also 1.

Therefore, the change in enthalpy (ΔH∘rxn) for the reaction is equal to the standard enthalpy of formation (ΔH∘f) of CO2(s) multiplied by the stoichiometric coefficient of CO2(g).

ΔH∘rxn = ΔH∘f(CO2(s)) * stoichiometric coefficient(CO2(g))
= -427.4 kJ/mol * 1
= -427.4 kJ

So, the change in enthalpy for dry ice sublimation is -427.4 kJ.

To calculate the mass of dry ice that should be added to the water, we need to use the concept of molar mass. The molar mass of carbon dioxide (CO2) is approximately 44 g/mol.

We can use the change in enthalpy to calculate the mass of dry ice.

ΔH∘rxn = -427.4 kJ
Molar mass of CO2 = 44 g/mol

The number of moles of CO2 can be calculated using the equation:

ΔH∘rxn = moles * ΔH∘f

Rearranging the equation, we have:

moles = ΔH∘rxn / ΔH∘f

moles = (-427.4 kJ) / (-427.4 kJ/mol)
= 1 mol

Now, to calculate the mass:

mass = moles * molar mass

mass = 1 mol * 44 g/mol
= 44 g

Therefore, you need to add 44 grams of dry ice to the water so that it completely sublimes away when the water reaches 35 ∘C, assuming no heat loss to the surroundings.