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A nebula—a region of the galaxy where new stars are forming—contains a very tenuous gas with 100atoms/cm3 . This gas is heated to 7500K by ultraviolet radiation from nearby stars. What is the gas pressure in atm?

Short Answer

Expert verified

The gas pressure is1.02×10-16atm

Step by step solution

01

: Given information and Formula used 

Given : A nebula contains gas with : 100atoms/cm3.

Temperature : 7500K

Heated by : Ultraviolet radiation

Theory used :
The number density is given by NV

The ideal gas law is given by PV=nRT
Rewriting ideal gas law for Vintheform:localid="1648796492843" V=nRTp
If we know the number of molecules N, we obtain the number of moles nby using Avogadro's number :

n=NNAn=nNA

02

Finding the gas pressure .

Now substitute the expressions for NandVinto number density formula to get the form of the number density Numberdensity=NAρRT
We obtain the number density by 100/cm³=0.01x10-6/m³.

We solve the above equation forp to get the pressure in Pascal.
Now we substitute the values for N₁, P, R and T into the equation to get the number density
p=RTNA
We substitute the values forR,T,NAand the number density to obtain
p=(8.314J/molK)(7500K)(6.023x1025molecules/mol)(100x10m³)=1.035x10-11Pa
Convert the pressure from pascal to atm into the form

p=(1.035×10-11Pa)1atm1.013x105Pa=1.02X10-16atm

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