Finding the number of molecules

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In summary, the conversation discussed the use of vacuum technology to achieve a pressure of 1 * 10^-10 mm of Hg and the calculation of the number of molecules in 5.00 cm3 at this pressure and a temperature of 30.0 C. The conversation also explored the atomic number of Hg, the conversion of mm to atmospheres, and the use of the ideal gas law to calculate the number of molecules. There was also a discrepancy in the calculation, which was resolved by using the van der Waals state law.
  • #1
mawalker
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:confused:

Current vacuum technology can achieve a pressure of 1 * 10^-10 mm of Hg. At this pressure, and at a temperature of 30.0 C, how many molecules are in 5.00 cm3 ?

ok so atomic number of Hg = 80

80 * 1.661 * 10^-27 yields 1.33 * 10 ^-25 which is the mass of one molecule

converting from mm to atmospheres i get 1*10^-10 mm = 1.32 * 10 ^-13 atm since 760 mm = 1 atm

T = 303
5 cm3 = 5 ml = 5 * 10 ^ -3

so using pV = nRT
(1.32*10^-13)(5*10^-3) = n(.08206)pressure constant(303)
solving for n... n = 2.6459

n = M(in grams)/M of molecule so :
2.6459 = M/80
which gives me 211.67 grams...

N (number of molecules = M/m = .21167 Kg/1.33 * 10^-25 (mass of one molecule)

which yields me 1.59 * 10^ 24 molecules... this answer is incorrect... any ideas?
 
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  • #2
actually i think that i should be using 201 for the atomic number of mercury... this still ends up yielding 3.99 *10^24 which is still incorrect.
 
  • #3
actually, it yields 1.59 * 10^24...
 
  • #5
I'm not sure why you are going into mass of molecules... if you use PV=nRT, n is the number of moles. You can convert directly from moles to molecules using good ole 6.02E23. According to the IDEAL GAS LAW, the same number of moles of a gas ALWAYS occupy the same volume... regardless of WHAT the gas is.
 
  • #6
Incidentally, Hg (mercury) is a metal, and with metals we never speak about "molecules". In this problem it instructve to use the van der Waals state law, too and compare the 2 results.

Daniel.
 

Related to Finding the number of molecules

What is meant by the number of molecules?

The number of molecules refers to the total count of individual particles that make up a substance. These particles could be atoms, ions, or molecules themselves.

How is the number of molecules calculated?

The number of molecules can be calculated using Avogadro's number, which is approximately 6.022 x 10^23. This number represents the number of particles in one mole of a substance.

What is the relationship between the number of molecules and the amount of substance?

The number of molecules is directly proportional to the amount of substance. This means that as the amount of substance increases, so does the number of molecules, and vice versa.

How can the number of molecules be measured in a laboratory?

The number of molecules can be measured using various techniques such as mass spectroscopy, gas chromatography, or X-ray crystallography. These methods allow for the identification and quantification of individual molecules.

Why is knowing the number of molecules important in scientific research?

Knowing the number of molecules is crucial in understanding the properties and behavior of substances. It allows scientists to make accurate predictions and develop theories about chemical reactions and physical phenomena.

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