The relative humidity is 55% on a day when the temperature is 30.0°C. Using the graph below, determine the number of moles of water vapor per cubic meter of air.
on the graph, Vapor pressure of water is on the y-axis and temperature on the x-axis 30C cordinates with 4200 Pa of water vapor.
This how i tried to sove it.
Since 30 corresponds to 4200 Pa
T in Kelvin =303
n/v = p/RT
=4200/(8.32 x 303)
= 1.67
the answer is wrong
You read the vapor pressure of water vs temp on the graph. Then you put that in the pvnrt equation. What makes you think that was the partial pressure of the water in the air on that day? If the air had been saturated with water, yes, but this was at 55 percent humidity.
Thank you.
To correctly determine the number of moles of water vapor per cubic meter of air, you need to consider the relative humidity and the partial pressure of water vapor in the air. The relative humidity indicates the percentage of water vapor in the air compared to the maximum amount it can hold at a given temperature.
In this case, the graph provides the vapor pressure of water at a temperature of 30.0°C, which is 4200 Pa. However, you cannot assume that this value directly represents the partial pressure of water vapor in the air on that day because it only represents the vapor pressure of water at that specific temperature.
To calculate the partial pressure of water vapor in the air, you need to use the concept of partial pressure and the formula for calculating partial pressure. The formula is:
P_water_vapor = relative_humidity * saturation_vapor_pressure
The saturation vapor pressure is the maximum vapor pressure of water that the air can hold at a given temperature. It varies with temperature, so you will need to refer to a table or use an equation to determine the saturation vapor pressure at 30.0°C.
Once you have the saturation vapor pressure at 30.0°C, you can substitute it into the equation along with the relative humidity (55%) to calculate the partial pressure of water vapor in the air.
Finally, use the ideal gas law equation, PV = nRT, where P is the partial pressure, V is the volume (1 cubic meter), n is the number of moles, R is the gas constant, and T is the temperature in Kelvin (303 K).
Rearrange the equation to solve for n:
n = PV / RT
Substitute the known values of P (partial pressure of water vapor), V (volume), R (gas constant), and T (temperature in Kelvin) to calculate the number of moles of water vapor per cubic meter of air.
Keep in mind that the actual calculation requires obtaining the saturation vapor pressure at 30.0°C and accurately substituting the values into the equations.