How Do You Calculate the Initial Number of Gaseous Molecules in a Closed System?

[tunabeast]

Homework Statement

In a closed system shown in the Figure below (http://i18.tinypic.com/7x1r8mo.jpg"), the piston is freely moving without friction and the system is initially filled with gaseous molecules A only. The mass of a piston is 100 g, its area is 10 cm2 and it is 10 cm from the bottom in the initial state of equilibrium. The pressure outside the system is 1 atm; temperature inside the system is 900 ºC.

a) Calculate the initial number of molecules in the system;
b) Write the equation describing the initial rate of decrease in the number of gaseous
molecules if it is known that molecules A stick to the surface of the piston upon
collision with it (molecules do not stick to any other surfaces; the processes when
gaseous molecules react with a hot substrate surface are the basis of the chemical
vapour deposition technology). Obtain numerical value of the initial rate.

Homework Equations

The Attempt at a Solution

I'm really struggling with where to start on this. I'v been handed a large physical chemistry book and basically been left to my own devices. I understand the problem relates to molecular theory of gasses but could you please steer me in the right direction.

 

[chemisttree]

You can start by determining the pressure exerted by the piston on the confined "Molecules A, 900 C". The external pressure is 1 atm but the piston has mass as well.

 

[Blueshift5]

I would first start by identifying the key information and variables given in the problem. These include: the closed system with a freely moving piston, the initial state with only gaseous molecules A present, the mass and area of the piston, the distance of the piston from the bottom, the outside pressure, and the inside temperature.

Next, I would use the ideal gas law (PV = nRT) to solve for the initial number of molecules (n) in the system. This equation relates pressure (P), volume (V), number of moles (n), gas constant (R), and temperature (T). In this case, we know the pressure, temperature, and volume (since it is a closed system with the piston initially at a specific position). We can also calculate the volume using the area and distance of the piston from the bottom.

Once we have the initial number of molecules, we can use the information given about the sticking of molecules A to the surface of the piston to write an equation for the rate of decrease in the number of molecules. This would involve taking into account the number of collisions between the molecules and the piston, as well as the probability of the molecules sticking upon collision.

From there, we can obtain a numerical value for the initial rate of decrease by plugging in the appropriate values into our equation.

It may also be helpful to research more about chemical vapor deposition technology to gain a better understanding of the process and how it relates to the problem at hand.

Overall, the key to solving this physical chemistry problem would be to identify and utilize the relevant equations and principles, and to carefully consider the given information and variables in order to find a solution.