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A region of the galaxy where new stars are forming-contains a very tenuous gas with 100 #a t oms ##/cm^3#. This gas is heated to #7500 K# by ultraviolet radiation from nearby stars. What is the Gas Pressure in ATM?

Answer 1

The pressure of the gas under these conditions would be #1.02xx10^(-16) atm#

An accurate estimate is provided by the ideal gas law at this extremely low pressure.

#PV=nRT#

wherein

#P# is the gas pressure in atmospheres, #n# is the number of moles of gas in the sample, #T# is the Kelvin temperature, #V# is the volume of the sample in litres and #R# is the gas constant, which can have a variety of values, depending on the units chosen for the other variables. I used #R=0.0821# to be consistent with the units given in the problem, and to produce an answer that would be a fraction of normal atmospheric pressure.

First, we must convert #100# atoms per #cm^3# into moles per litre.

Since there are #6.02xx10^23# atoms in a mole, 100 atoms is only

#100-: 6.02xx10^23 = 1.66 xx10^(-22)# moles per #cm^3#.

Next, since there are #1000 cm^3# in a litre, we arrive at the result that

#100 "atoms"/(cm)^3 = 1.66xx10^(-19) "moles"/L#

In the ideal gas law, the above value would represent #n/V#, so if we write the law as

#P=(nRT)/V#

we need only multiply the above value by #R# and by #T# to find the answer

#P=(1.66xx10^(-19))(0.0821)(7500)=1.02xx10^(-16) atm#

The result is in atmospheres of pressure due to the choice made for the value of #R#.

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Answer 2

Cooper Ann

To find the gas pressure in ATM, you can use the ideal gas law equation:

[PV = nRT]

Where:

(P) is the pressure in atmospheres (ATM)
(V) is the volume of the gas in cubic centimeters (cm³)
(n) is the number of moles of gas
(R) is the ideal gas constant ((0.0821 \frac{L \cdot atm}{K \cdot mol}))
(T) is the temperature in Kelvin (K)

Given:

Gas density ((n/V)) = (100) atoms/cm³
Temperature ((T)) = (7500) K

We need to find the pressure ((P)). First, we need to calculate the number of moles of gas using the gas density and volume. Then, we can rearrange the ideal gas law equation to solve for pressure ((P)).

[n = \frac{100}{6.022 \times 10^{23}} \times V]

[P = \frac{nRT}{V}]

Substitute the values and solve for (P):

[P = \frac{\left(\frac{10

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Answer from HIX Tutor

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