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A reaction has produced 5 moles of water vapor and 10 liter bone dry air at 27ºC and 15 atm, what is the humidity?
- a)24%
- b)49%
- c)83%
- d)106%
Correct answer is option 'C'. Can you explain this answer?
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A reaction has produced 5 moles of water vapor and 10 liter bone dry a...
Calculating Humidity:
To calculate the humidity, we need to first determine the amount of water vapor in the air and then compare it to the maximum amount of water vapor the air can hold at that temperature and pressure.
Step 1: Calculate the mole fraction of water vapor:
Given that 5 moles of water vapor are produced, the mole fraction of water vapor can be calculated as:
Mole fraction of water vapor = (moles of water vapor) / (moles of water vapor + moles of dry air)
Mole fraction of water vapor = 5 / (5 + 10) = 5 / 15 = 1/3
Step 2: Calculate the partial pressure of water vapor:
Since the total pressure is 15 atm, the partial pressure of water vapor can be calculated using Dalton's Law of Partial Pressures:
Partial pressure of water vapor = Mole fraction of water vapor * Total pressure
Partial pressure of water vapor = (1/3) * 15 = 5 atm
Step 3: Calculate the saturation pressure of water vapor:
Using a steam table at 27°C, we find that the saturation pressure of water vapor is approximately 6.25 atm.
Step 4: Calculate the humidity:
Humidity = (Partial pressure of water vapor / Saturation pressure of water vapor) * 100%
Humidity = (5 / 6.25) * 100% = 80%
Therefore, the humidity of the air is 80%, which is closest to option C (83%).
To calculate the humidity, we need to first determine the amount of water vapor in the air and then compare it to the maximum amount of water vapor the air can hold at that temperature and pressure.
Step 1: Calculate the mole fraction of water vapor:
Given that 5 moles of water vapor are produced, the mole fraction of water vapor can be calculated as:
Mole fraction of water vapor = (moles of water vapor) / (moles of water vapor + moles of dry air)
Mole fraction of water vapor = 5 / (5 + 10) = 5 / 15 = 1/3
Step 2: Calculate the partial pressure of water vapor:
Since the total pressure is 15 atm, the partial pressure of water vapor can be calculated using Dalton's Law of Partial Pressures:
Partial pressure of water vapor = Mole fraction of water vapor * Total pressure
Partial pressure of water vapor = (1/3) * 15 = 5 atm
Step 3: Calculate the saturation pressure of water vapor:
Using a steam table at 27°C, we find that the saturation pressure of water vapor is approximately 6.25 atm.
Step 4: Calculate the humidity:
Humidity = (Partial pressure of water vapor / Saturation pressure of water vapor) * 100%
Humidity = (5 / 6.25) * 100% = 80%
Therefore, the humidity of the air is 80%, which is closest to option C (83%).
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Community Answer
A reaction has produced 5 moles of water vapor and 10 liter bone dry a...
Moles of bone dry air = 6, ⇒ humidity = 5/6*100 = 83%.
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A reaction has produced 5 moles of water vapor and 10 liter bone dry air at 27ºC and 15 atm, what is the humidity?a)24%b)49%c)83%d)106%Correct answer is option 'C'. Can you explain this answer?
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