the relative humidity in a room is 65%. assuming ideal gas behavior. what mass of water vapor is in the air at 25 degrees celsius if the room measures 4m 4m 3m? the vapor pressure of liquid water is 23.8 torr at 25 degrees celsius

The relative humidity in a room (4m  4m  4m) is 65%. Assuming ideal gas behaviour, what

mass of water vapour is present in the room at 25C.

no no no what is it carrying if it's out side!!!!!!!!!!!

To find the mass of water vapor in the air, we need to use the ideal gas law and the concept of relative humidity.

Step 1: Convert the relative humidity value to a decimal:
Relative humidity = 65%
Relative humidity = 0.65

Step 2: Calculate the vapor pressure of water in the air:
Vapor pressure = Relative humidity * Saturation vapor pressure
The saturation vapor pressure of water at 25 degrees Celsius is 23.8 torr. Therefore, the vapor pressure in the air is:
Vapor pressure = 0.65 * 23.8 torr = 15.47 torr

Step 3: Convert the vapor pressure to atmospheres (since we will be using the ideal gas law, which requires pressure in atm):
1 atm = 760 torr
Vapor pressure (in atm) = 15.47 torr / 760 torr/atm = 0.0204 atm

Step 4: Use the ideal gas law to find the number of moles of water vapor:
PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

First, let's convert the temperature to Kelvin:
T = 25 degrees Celsius + 273.15 = 298.15 K

Volume of the room = 4m * 4m * 3m = 48m^3

Now, rearrange the ideal gas law to solve for the number of moles (n):
n = PV / RT

n = (0.0204 atm) * (48m^3) / [(0.0821 L*atm/mol*K) * 298.15 K]
n ≈ 0.381 mol

Step 5: Convert the number of moles of water vapor to grams:
Since the molar mass of water (H2O) is approximately 18 g/mol, the mass of water vapor is:
Mass = 0.381 mol * 18 g/mol ≈ 6.86 g

Therefore, the mass of water vapor in the air at 25 degrees Celsius with a relative humidity of 65% in a room measuring 4m x 4m x 3m is approximately 6.86 grams.

To calculate the mass of water vapor in the air, we need to use the concept of partial pressure and the ideal gas law. Here are the steps to solve this problem:

Step 1: Convert the relative humidity to a decimal form.
Relative humidity is expressed as a percentage, so to convert it to decimal form, divide it by 100. In this case, the relative humidity is 65%, so it becomes 0.65.

Step 2: Calculate the vapor pressure of water at 25 degrees Celsius.
The vapor pressure of water is given as 23.8 torr at 25 degrees Celsius. This is the pressure exerted by water vapor when it is in equilibrium with its liquid phase at that temperature.

Step 3: Calculate the partial pressure of water vapor in the air.
The partial pressure of water vapor is the pressure exerted by water vapor alone in a mixture of gases. To calculate it, multiply the vapor pressure of water by the relative humidity in decimal form. In this case, it would be 23.8 torr * 0.65 = 15.47 torr.

Step 4: Convert the pressure to SI units.
Since the dimensions of the room are given in meters, we need to convert the pressure from torr to pascals (Pa) for consistency in units. The conversion factor is 1 torr = 133.3239 Pa. So, 15.47 torr * 133.3239 Pa/torr = 2062.7246 Pa.

Step 5: Apply the ideal gas law to calculate the mass of water vapor.
The ideal gas law is given by the equation: PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin.

Since we are trying to find the mass of water vapor and not the number of moles, we need to rearrange the equation to solve for mass. The equation becomes:
mass = (PV)/(RT)

The volume of the room is given as 4m * 4m * 3m = 48 m^3.
The temperature is given as 25 degrees Celsius, which we need to convert to Kelvin by adding 273.15. So, the temperature becomes 25 + 273.15 = 298.15 K.

Now we can substitute the known values into the equation:
mass = (2062.7246 Pa * 48 m^3) / (8.314 J/(mol*K) * 298.15 K)

Step 6: Calculate the mass of water vapor.
Using a calculator, evaluate the expression to find the mass of water vapor.

Note: The molar mass of water is approximately 18.015 g/mol. You can use this value to convert moles to grams if needed.

Remember to round your final answer to an appropriate number of significant figures based on the given data and calculations.