Basic Homework Help: Solving Problems with Compressed Air and Diffusion

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To solve the first problem, use the ideal gas law (PV = nRT) to calculate the initial and final number of moles of air in the tank, converting pressure to the appropriate units. The difference in moles will give the number of air molecules released when the pressure drops from 40 atm to 23 atm. For the second problem, the time it takes for a perfume molecule to diffuse 7.00 m in still air can be estimated using the diffusion equation, which incorporates the diffusion constant. The diffusion constant provided is 1.00 x 10^-5 m^2/s, allowing for the calculation of time based on the distance and diffusion properties. These calculations will yield the required answers for both problems.
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Can anyone help me solve these two problems?
1. A tank of compressed air of volume 1.0 m^3 is pressurized to 40 atm at T= 273. A valve is opened and air is released until the pressure in the tank is 23.0 atm. How many air molecules were released?

2. About how long will it take a perfume molecule to diffuse a distance of 7.00 m in one direction in a room if the diffusion constant is 1.00 x 10^-5 m^2/s? Assume that the air is perfectly still- there are no air currents.
 
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Originally posted by merrymanjane
Can anyone help me solve these two problems?
1. A tank of compressed air of volume 1.0 m^3 is pressurized to 40 atm at T= 273. A valve is opened and air is released until the pressure in the tank is 23.0 atm. How many air molecules were released?

Use the formula
PV = nRT

P is pressure (pascals or kilopascals, I can't remember), V is volume in litres, n is the number of moles, R is the gas constant, T is temperature in kelvin
Figure out how many moles of air molecules were there at start then how much after. Just subtract the two.
 
P should be in atmospheres.
 
Depends which R you use.
 
Use Pascals and 8.31 for R
 
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