A stumper for you physics gurus can you solve this?

Question

If a certain sample of an ideal gas has a temperature of 104 degrees C and exerts a pressure of 2.3 x 10^4 Pa on the walls of it's container, how many gas molecules are present in each cm^3 of volume? assume that the gas is ideal. The gas constant is R=8.314 J/mol K and avagadro's number is NA=6.022 x 10^23 molecules/mol

???

can you show work to prove to it??

Is the volume of the container or the moles of gas provided? Nope! that is what threw me for a loop

I end up getting 4.4X10^23??

Answer 1

The Ideal Gas Law is

PV = nRT

which we will rewrite as

n / V = P / RT

You know R, T (convert from Celcius to Kelvins), and P; solve for n / V ( moles / unit volume ). Convert into cubic centimeters if necessary and multiply by Avagadro's number to get the number of molecules per cubic centimeter.

Answer 2

Is the volume of the container or the moles of gas provided?

Answer 3

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From ideal gas equation of state,the pressure P, volume V ,number of moles n , Universal gas constant R and absolute temperature T are related as

PV =nRT

PV = (m/M)RT

where m is mass of N molecules of gas and M is molecular weight or mass of Avogadro number(NA) of molecules

PV=(N / NA)RT

N/V=P(NA)/RT

Number of gas molecules in each m^3 of volume=N/V

Number of gas molecules in each m^3 of volume=P(NA)/RT

Pressure = P = 2.3 x 10^4 Pa

Temperature =T= 104 +273 =377 K

NA = 6.022 x 10^23 molecules/mol

R=8.314 J/mol K

Number of gas molecules in each m^3 of volume=2.3 x 10^4 *6.022 x 10^23 /8.314*377

Number of gas molecules in each m^3 of volume = 4.4189*10^24

1 m^3 =10^6 cm^3

Number of gas molecules in each cm^3 of volume = 4.4189*(10^24) /10^6

Number of gas molecules in each cm^3 of volume is 4.4189*(10^18)

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Answer 4

4.4x10^18

Answer 5

Yes. I think I can solve this.

But you did not have to give me Avogadro's number. I knew it, already.

:-)

Answer 6

maybe