Having trouble using the ideal gas law for this problem.

In summary: Are liters correct then? Or should that be in m^3? I converted torr to pascals, and found the molecules to be 2.602914125*10^11, which is still incorrect.In summary, an oil diffusion pump can create a pressure as low as 1 * 10^-8 torr. There are 2568782.388 molecules in 1 cm^3 of a gas at this pressure.
  • #1
lilmul123
40
0

Homework Statement



A pressure as low as 1 * 10^-8 torr can be achieved using an oil diffusion pump. How many molecules are there in 1 cm^3 of a gas at this pressure if its temperature is 371 K?

Homework Equations



PV = nRT = NkT

The Attempt at a Solution



I converted 1*10^-8 torr to atm and got 1.31578947 * 10^-11 atm. Then, I converted 1 cm^3 to liters and got .001L. Then, I plugged all known variables into the ideal gas law. When doing PV = nRT, I got n in molecules to be 2568782.388. This was incorrect. I then tried PV = NkT, and N was also incorrect. Where did I go wrong?
 
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  • #2
lilmul123 said:

Homework Statement



A pressure as low as 1 * 10^-8 torr can be achieved using an oil diffusion pump. How many molecules are there in 1 cm^3 of a gas at this pressure if its temperature is 371 K?


Homework Equations



PV = nRT = NkT


The Attempt at a Solution



I converted 1*10^-8 torr to atm and got 1.31578947 * 10^-11 atm. Then, I converted 1 cm^3 to liters and got .001L. Then, I plugged all known variables into the ideal gas law. When doing PV = nRT, I got n in molecules to be 2568782.388. This was incorrect. I then tried PV = NkT, and N was also incorrect. Where did I go wrong?
Your units are mixed up. Atmospheres are not MKS units. Convert torr to Pascals instead (Newtons/m^2)

AM
 
  • #3
Are liters correct then? Or should that be in m^3? I converted torr to pascals, and found the molecules to be 2.602914125*10^11, which is still incorrect.
 
  • #4
lets see what I get using torrs/atm

volume at stp = 1ml(10^-8/760)*273/371=9.78 x 10-12 ml.

Converting to liters and dividing by 22.4 L/mole I get 4.27 x 10^-16 moles. Multiplying by A's number: 262,837,500 which should be rounded to 2.63 x 10^8. Seems like your answer is off by 1000--maybe liter m^3 conversion?
 
  • #5
lilmul123 said:
Are liters correct then? Or should that be in m^3? I converted torr to pascals, and found the molecules to be 2.602914125*10^11, which is still incorrect.
It is rather difficult to determine where you went wrong if you do not show us your detailed calculations.

n=PV/RT where [itex]P = 10^{-8} Torr = 1.33 \times 10^{-6} Pa[/itex] and [itex]V = 10^{-6} m^3[/itex]

[tex]n = \frac{1.33 \times 10^{-6} \times 10^{-6}}{8.3145 \times 371} = \frac{1.33 \times 10^{-12}}{3.085 \times 10^3} = 4.31 \times 10^{-16} moles[/tex]

Convert the moles to molecules and that is your answer.

AM
 

Related to Having trouble using the ideal gas law for this problem.

1. How do I know when to use the ideal gas law?

The ideal gas law is typically used to calculate the properties of a gas at a constant temperature, pressure, and volume. If these conditions are met, then the ideal gas law can be used to accurately predict the behavior of the gas.

2. Why am I having trouble using the ideal gas law for this problem?

There could be several reasons why you are having trouble using the ideal gas law for a specific problem. It could be due to incorrect input values, not considering all the variables, or using the wrong units. It is important to carefully read and understand the problem before applying the ideal gas law.

3. What are the units for the ideal gas law?

The units for the ideal gas law are pressure (P) in atmospheres (atm), volume (V) in liters (L), temperature (T) in Kelvin (K), and the number of moles (n) in moles (mol). It is important to use consistent units when using the ideal gas law to avoid errors in your calculations.

4. Can I use the ideal gas law for real gases?

The ideal gas law is a simplified equation that assumes gases behave ideally under certain conditions. However, real gases do not always behave ideally and may deviate from the predictions of the ideal gas law. In such cases, more complex equations, such as the van der Waals equation, may be used.

5. How can I check if my calculations using the ideal gas law are correct?

One way to check the accuracy of your calculations is to compare them to experimental data. If the results are similar, then your calculations are likely correct. Additionally, you can check if your final units are consistent with what is expected for the property you are calculating (i.e. pressure in atm, volume in L, temperature in K).

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