How much heat is released when 75.0 g of steam at 100.0C is cooled to ice at -15.0C?
To calculate the amount of heat released, we need to consider the energy required to cool the steam to its freezing point and then to convert it into ice.
1. Determine the heat energy required to cool the steam to its freezing point:
The heat energy released during this phase is determined by the equation:
q = m * c * ΔT,
where:
q = heat energy released (in joules),
m = mass of the substance being cooled (in grams),
c = specific heat capacity of the substance (in J/g°C), and
ΔT = change in temperature (in °C).
The specific heat capacity of steam is about 2.03 J/g°C, so we use this value.
ΔT = 100.0°C - 0.0°C (since steam is at 100°C)
m = 75.0 g
Substituting the values into the formula:
q₁ = 75.0 g * 2.03 J/g°C * 100.0°C.
2. Determine the heat energy required for the phase change from steam to liquid water:
During this phase change, the heat energy required can be calculated using the equation:
q₂ = m * ΔHf,
where:
q₂ = heat energy released during phase change (in joules),
m = mass of the substance (in grams), and
ΔHf = heat of fusion (in J/g).
The heat of fusion for water is 334 J/g.
Substituting the values into the formula:
q₂ = 75.0 g * 334 J/g.
3. Determine the heat energy required to cool the liquid water to its freezing point:
Using the same method as step 1, calculate q₃:
q₃ = m * c * ΔT,
where:
q₃ = heat energy released (in joules),
m = mass of the substance being cooled (in grams),
c = specific heat capacity of the substance (in J/g°C), and
ΔT = change in temperature (in °C).
The specific heat capacity of liquid water is approximately 4.18 J/g°C, so we use this value.
ΔT = 0.0°C - (-15.0°C),
m = 75.0 g.
Substituting the values into the formula:
q₃ = 75.0 g * 4.18 J/g°C * 15.0°C.
4. Total the heat energy:
The total heat energy released is the sum of q₁, q₂, and q₃:
q_total = q₁ + q₂ + q₃.
Calculate the values of q₁, q₂, q₃, and q_total using the formulas and values given, and perform the necessary calculations to find the final answer for the amount of heat released.