# Difference between ideal gas law and saturated vapor pressure

Little bit confused on what each of these concepts are. So far i understand that the ideal gas law tells us how much pressure an amount of gas exerts on the walls of a container. I also understand that the saturated vapor pressure is the pressure applied on the container from a substance in liquid/vapor equilibrium. What i dont get is whether these two concepts are related. Like are the pressures the same? If I use the ideal gas law equation to calculate the pressure would that be the same as the pressure of the saturated vapor pressure?

The ideal gas law strictly applies only to ideal gases, which do not condense to form a liquid. This means that there is no vapor pressure associated with ideal gases, which are used to represent real gases that are at a temperature that is very much higher than their condensation temperature.

Regarding vapor pressure, practically every liquid contains atoms or molecules that have enough velocity to escape into the vapor phase. In a closed and evacuated container that initially contains only a liquid such as water, these molecules will move into the vapor phase at a rate that depends on the temperature of the liquid. With no outside heat source, such a liquid will lose temperature as this happens, so heat input to this system is required to hold the liquid temperature at a specified value as water evaporates.

As more and more molecules enter the vapor space, there will be water molecules that strike the liquid surface and re-condense. Thus, there is a rate at which water in the container evaporates and a rate at which water in the container condenses. Assuming a constant temperature, and a constant rate of water evaporation, the water vapor density rises with time, as does the rate of water vapor molecules striking the water surface and re-condensing. At equilibrium, the rate of water evaporation and water condensation are equal.

Water vapor molecules in the vapor space of the container are also striking the surfaces of the container, producing pressure as a result. At the equilibrium point, the pressure that is produced is the vapor pressure of the liquid. This vapor pressure is related to the liquid temperature via the Antoine equation. For much more information, see https://en.wikipedia.org/wiki/Antoine_equation

No, they are really different. You seem to be very confused.

We've got two substances here: dry air and water vapour.

If we consider them both as ideal gases, then EACH one will satisfy the ideal gas law, separately.

Plus, Dalton's law says that "total pressure = sum of partial pressures", i.e. $P_{Tot}=P_d + P_w$.

So you can always apply ideal gas law to find your desired variable. Knowing P, V, T allows you get $n$, or whatever other example.

Now, saturation vapour pressure is, as you said, the pressure for which liquid water and vapour water are in equilibrium.

If there's enough liquid water available, it will vaporize until water vapor is the maximum allowed, that is, such that $P_w=P_{sat}$.

If there isn't liquid water enough, the air will have $P_w<P_{sat}$; in fact we define the relative humidity as $RH=\frac{P_w}{P_{sat}}\cdot 100\%$.

And the saturation vapor pressure depends on temperature through Clapeyron's equation. This is the tool to get $P_{sat}$ (or also consulting tables).

• Still a bit confused. If water inside a closed system evaporates, and turn into vapour then it would have a saturated vapour pressure. Also wouldn't that mean that we can also use the ideal gas law to calculate the partial pressure of just the water vapour, which is the same? Apr 2, 2018 at 23:18
• Many points there. 1) Water evaporates until $P_w=P_s$. In abundance of liquid water, you'll reach $P_w=P_s$ (100% humidity). If water is scarce, you won't reach $P_s$ and so $HR$ will be $<100%$. Apr 3, 2018 at 13:12
• 2) Yes, you can use the ideal gas law for any ideal gas. Both dry air and water vapor use to be considered ideal gases. You don't have to think about vapor and dry air, just "gas 1" and "gas 2". It's just a mixture of two gas substances, after all. Apr 3, 2018 at 13:14