How much energy is released when 54.0 g of H2O are condensed from a gas at 115°C to a liquid at 65°C?
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To determine the amount of energy released when water condenses, we can use the formula:
q = m * ΔHf
Where:
q represents the amount of energy released or absorbed (in joules).
m represents the mass of the substance (in grams).
ΔHf represents the heat of fusion for the substance (in J/g).
In this case, we need to find the energy released when 54.0 g of water (H2O) condenses. To do this, we'll need two pieces of information:
1. The specific heat capacity of water:
The specific heat capacity of water is 4.18 J/g°C. This value represents the amount of energy (in joules) required to change the temperature of 1 gram of water by 1 degree Celsius.
2. The heat of fusion of water:
The heat of fusion of water is 334 J/g. This value represents the amount of energy (in joules) required to convert 1 gram of water from a liquid to a solid (or vice versa) at its melting/freezing point, which is 0°C.
Since we are dealing with water condensing from a gas (115°C) to a liquid (65°C), we need to calculate the energy released for two separate processes:
1. Cooling the water vapor from 115°C to 100°C (since that's when it starts to condense):
q1 = m * c * ΔT1
Where:
q1 represents the energy released during the cooling process.
m represents the mass of water (54.0 g).
c represents the specific heat capacity of water (4.18 J/g°C).
ΔT1 represents the change in temperature (final temperature - initial temperature).
2. Condensing the water from 100°C to 65°C:
q2 = m * ΔHf
Where:
q2 represents the energy released during condensation.
m represents the mass of water (54.0 g).
ΔHf represents the heat of fusion of water (334 J/g).
Now, let's calculate the energy released for each process and sum them up to find the total energy released.
For the cooling process:
q1 = m * c * ΔT1
q1 = 54.0 g * 4.18 J/g°C * (100°C - 115°C)
q1 = 54.0 g * 4.18 J/g°C * (-15°C)
q1 = - 11,277.6 J
For the condensation process:
q2 = m * ΔHf
q2 = 54.0 g * 334 J/g
q2 = 18,036 J
Total energy released:
q_total = q1 + q2
q_total = -11,277.6 J + 18,036 J
q_total = 6,758.4 J
Therefore, when 54.0 g of H2O is condensed from a gas at 115°C to a liquid at 65°C, approximately 6,758.4 J of energy is released.