Chemistry Calorimetry Question

Question

You order a 16 oz glass of tea (where the mass of Tea is 474 grams) from a local restaurant. The tea is freshly brewed and has an initial temperature of 28.21 °C. You add ice to cool it. If the heat of fusion of ice is 6.020 ^kJ/_mol and each ice cube contains exactly 1 mol of water (assume the ice does not add anymore volume), how many ice cubes are necessary to cool the tea to 0.890 °C? The specific heat of the "tea" is 4.184 ^J/_g°C. Ice cubes (partial cubes allowed) and ignore the heat required to raise the temperature of the melted ice cubes

Answer 1

First, find out how much energy you need to cool down the tea. We can use the equation E = mCdeltaT.

T final is what we want, 0.890C. T initial is what we start with, 28.21C. Recall that deltaT is T final - T initial.

Energy(J) = (474g tea)(4.184J/gC)(0.890C - 28.21C)

Energy(J) = (474g tea)(4.184J/gC)(-27.32C)

Before moving on, check that we have the right units for everything. We want the energy, in a unit like Joules. We have g*J*C/g*C. g and C cancel, so we just have J. Looks good!

Now solving the equation:

Energy(J) = -54200J

I don't like dealing with large numbers, so I'll convert this to kJ. Recall that 1kJ = 1000J.

Energy(kJ) = -54.2kJ

Halfway done. According to the law of conservation of energy, the total change in energy in a closed system should be zero. So if the change in energy from the tea is -54.2kJ, the energy change from something else (the problem mentions ice) should be +54.2kJ to cancel it out.

So now we know Energy(ice cubes) = 54.2kJ. The problem says to ignore temperature change for the ice, so we don't need E = mCdeltaT. They do mention a phase change, melting. So we can use the enthalpy of phase change equation, E = nH

54.2kJ = (n moles ice)(6.020kJ/mol)

Adjusting the equation to solve for moles of ice, we get

n moles ice = 54.2kJ/(6.020kJ/mol)

Check again that we have the right units. We want moles, and kJ/(kJ/mol) gives us mol*kJ/kJ. kJ cancels out, so we just get moles. Perfect.

Now solving, we get 9.00 mol ice. The question asks for number of ice cubes, not moles of ice, so we have one last unit conversion. They tell us 1 ice cube = 1 mol ice. So 9 mol ice * (1 ice cube/1 mol ice) gives us:

9 ice cubes