A nebula's a region of the galaxy where new stars are forming contains a very tenuous gas with 128 #a t o m s##/cm^3#. This gas is heated to #7459 K# by ultraviolet radiation from nearby stars. What is the gas pressure?

Question

Anna Armstrong · Accepted Answer

Pressure = #1.318 imes10^{-11}" Pa"#.

Use the Ieal Gas Law to get this answer.

Instead of using the customary molar basis, we render the Ideal Gas Law on an atomic basis for this purpose: (Pressure)# imes#(Volume) = (Boltzmann's constant)# imes#(No. of atoms)# imes#(Absolute temprerature) Volume = #1 imes10^{-6}" m"^3# Boltzmann's constant = #1.3806 imes10^{-23}" J/K"# No. of atoms = #128# Absolute temperature = #7459" K"# Thus (Pressure)# imes(1 imes10^{-6}" m"^3) = (1.3806 imes10^{-23}" J/K") imes(128) imes(7459" K")# Pressure = #1.318 imes10^{-11}" J/m"^3=1.318 imes10^{-11}" Pa"#

Audrey Arnold · Answer

undefined The ideal gas law can be used to calculate the gas pressure as follows: $$P = nRT/V$$
Where: - $P$ is the pressure; - $n$ is the number of moles of gas; - $R$ is the ideal gas constant (8.314 J/(mol·K)); - $T$ is the temperature in Kelvin; - $V$ is the volume.
Given: - $n = 128$ atoms/cm³, - $T = 7459$ K.
The number of moles ($n$) can be calculated using Avogadro's number and the volume of the gas (which is not provided): $$n = N/V$$
Where: - $N$ is the number of atoms or molecules; once the volume is known, the gas pressure ($P$) can be calculated using the ideal gas law.