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: CO_{2}(*s*)→CO_{2}(*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 Δ*H*º_{f} for CO_{2}(*s*) is -427.4 kJ/mol, and for CO_{2}(*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.

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, T_{1} represents the initial temperature and T_{2} 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.

Step 2

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

Step 3

The heat lost by water is calcul...

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