If I make an ice pack with 750 mL of water, what mass of ammonium chloride must I include to get the temperature to drop from 20 degrees celsius to 5 degrees celsius. The heat of solution of the water and ammonium chloride is 14.8 kJ/mole. I just need help setting this problem up.
First you must determine how much heat must be removed to make that temperature transition.
q = [mass H2O x specific heat H2O x (Tfinal0Tinitial)].
q should be in J.
Then calculate mols NH4Cl needed to get that q.
14,800 J/mol x # mols = q(in J)
Then convert mols NH4Cl to grams.
To set up this problem, you need to determine the amount of heat that needs to be extracted from the water to lower its temperature from 20 degrees Celsius to 5 degrees Celsius. The heat of solution of ammonium chloride will be used to calculate the heat transfer.
The general equation you can use is:
q = m * ΔT * C
Where:
q is the heat transfer (in joules)
m is the mass of the substance (in grams)
ΔT is the change in temperature (in Celsius)
C is the heat capacity specific to the substance (in J/g·°C)
First, you need to calculate the mass of water in grams. Since the density of water is 1 g/mL, you can convert the volume to grams:
mass_water = volume_water * density_water
mass_water = 750 mL * 1 g/mL = 750 g
Next, calculate the change in temperature:
ΔT = final temperature - initial temperature
ΔT = 5 °C - 20 °C = -15 °C
Now, you need to determine the heat transfer, q. The heat of solution is given in kJ/mole, so you'll need to convert it to joules.
1 kJ = 1000 J
heat_of_solution = 14.8 kJ/mole * 1000 J/kJ = 14800 J/mole
Now, you have all the information needed to set up the problem. Since the heat of solution refers to 1 mole of ammonium chloride, you'll also need to determine the number of moles of ammonium chloride required.
moles_ammonium_chloride = (q) / (heat_of_solution)
Finally, you need to convert the moles of ammonium chloride to grams using its molar mass. The molar mass of ammonium chloride is NH4Cl = 14.0067 g/mol + 4(1.0078 g/mol) + 1.0078 g/mol = 53.4915 g/mol.
mass_ammonium_chloride = moles_ammonium_chloride * molar mass_ammonium_chloride
By plugging in the values and performing the calculations, you can find the mass of ammonium chloride required to lower the temperature of the water.