# How do I determine the amount of water in a sealed container to create a given pressu

#### bigbear312

I have a sealed container with a volume of 1 liter. I want to go from an initial pressure of p1=1 atm and an initial temperature of T1=298 to a final pressure of p2=10 atm and a final temperature of T2=453 K.

I want to to use water to create the pressure. But I do not know how to determine the amount of water, how would I do that?

Thanks.

Last edited:

#### ChipB

PHF Helper
You can set up two equations in two unknowns:

1. For the initial condition you have gaseous air plus liquid water in the container. The number of moles of air from the Ideal Gas law is:

$$\displaystyle n_{a} = \frac {P_1 V_{a}}{RT_1}$$

where $$\displaystyle n_a$$ is the number of moles of air and $$\displaystyle V_{a}$$ is the volume of air in the container. The volume of water at this stage is then

$$\displaystyle V_{w} = V - \rho_{w} n_w$$

where V = size of the container or 1 liter and $$\displaystyle \rho_w$$ is the density of water in terms of liter/mole.

Combining these two equations:

$$\displaystyle n_a = \frac {P_1(V-\rho_w n_w)}{R T_1}$$

2. The second equation is at the higher temperature, when the water has turned to gaseous steam. From the Ideal Gas law:

$$\displaystyle n_a + n_w = \frac {P_2 V}{R T_2}$$

So now you have two equation with unknowns $$\displaystyle n_a$$ and $$\displaystyle n_w$$.