If I make an ice pack with 750mL of water, what mass of ammonium chloride must I include to get the temperature to drop from room temperature (20 degrees C) to 5 degrees C?
To determine the mass of ammonium chloride needed to lower the temperature of the water from 20 degrees Celsius to 5 degrees Celsius, you need to consider the specific heat capacity of water, the heat gained or lost during a temperature change, and the heat of dissolution of ammonium chloride.
Let's go step by step on how to calculate it:
1. Determine the heat lost by the water:
The heat lost (q) is given by the equation:
q = m * C * ΔT
Where:
- m is the mass of water
- C is the specific heat capacity of water (approximately 4.18 J/g°C)
- ΔT is the change in temperature (20°C - 5°C = 15°C)
First, convert the volume of water to mass. The density of water is approximately 1 g/cm³ (or 1 kg/L). Therefore, 750 mL of water is equal to 750 grams (or 0.75 kg).
Substituting the values into the equation:
q = 0.75 kg * 4.18 J/g°C * 15°C
2. Determine the heat released by the dissolution of ammonium chloride:
The heat released (q') is given by the equation:
q' = m' * ΔH
Where:
- m' is the mass of ammonium chloride
- ΔH is the heat of dissolution of ammonium chloride (approximately -322 kJ/kg)
Notice that the heat of dissolution is typically provided in kilojoules per kilogram (kJ/kg), so we'll need to convert the units later.
We want the heat released by the ammonium chloride to be equal to the heat lost by the water. Therefore, q' = -q (since the heat lost by the water is heat gained by the ammonium chloride, so they have opposite signs).
Rearranging the equation:
m' * ΔH = -q
3. Calculate the mass of ammonium chloride:
Rearrange the equation from step 2 to solve for m':
m' = -q / ΔH
Substituting the values:
m' = -(0.75 kg * 4.18 J/g°C * 15°C) / (-322000 J/kg)
Convert joules to kilojoules:
m' = -3.14 kJ / -322 kJ/kg
The negatives cancel out:
m' ≈ 0.0097 kg (or 9.7 grams)
Therefore, you would need approximately 9.7 grams of ammonium chloride to lower the temperature of 750 mL of water from 20 degrees Celsius to 5 degrees Celsius.