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?

Question

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?

Madeline Arroyo · Accepted Answer

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#.

Cooper Ann · Answer

undefined 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