Two ideal gases have the same mass density and the same absolute pressure. One of the gases is helium (He), and its temperature is 298 K. The other gas is neon (Ne). What is the temperature of the neon?

Molar Density = P/RT

At 298 K and 1 atm, both gases would have the same number or molar density. The MASS density of Ne is 20.2/4.0 = 5.05 times that of He, because of its higher atomic weight. To equal the MASS density of He, the Ne would have to have 5.05 times the absolute temperature of the He, or 1505 K.

Why did the helium and neon go to couples therapy? Because they had a "temperature" problem!

But to answer your question, since the two ideal gases have the same mass density and the same absolute pressure, we can apply the ideal gas law equation: PV = nRT. Since the pressure (P), volume (V), and molar quantity (n) are all the same, we can assume that the temperature (T) should also be the same! So the temperature of the neon gas is also 298 K. Those gases better learn to share the temperature love!

To find the temperature of neon, we need to use the ideal gas law equation: PV = nRT, where P is the absolute pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

Since both gases have the same mass density and the same absolute pressure, we can assume that the volume and number of moles are the same for both gases as well.

We can write the equation for helium as PH * VH = nHe * R * THe, and the equation for neon as PN * VN = nNe * R * TNe, where PH and PN are the absolute pressures, VH and VN are the volumes, nHe and nNe are the number of moles, THe and TNe are the temperatures of helium and neon respectively.

Dividing the two equations, we get:

(PH * VH) / (PN * VN) = (nHe * R * THe) / (nNe * R * TNe)

Since VH and VN are the same for both gases, they cancel out:

PH / PN = (nHe * R * THe) / (nNe * R * TNe)

We know that PH = PN and nHe = nNe, so the equation simplifies to:

1 = THe / TNe

Rearranging the equation, we can solve for TNe:

TNe = THe / 1

Since THe is given as 298 K, the temperature of neon is also 298 K.

To find the temperature of neon, we can assume that both gases follow the ideal gas law. The ideal gas law is given by the equation:

PV = nRT,

where P is the absolute pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.

Since we are comparing two ideal gases with the same mass density and the same absolute pressure, we can write the equation for helium (He) and neon (Ne) as follows:

P_He * V_He = n_He * R * T_He,
P_Ne * V_Ne = n_Ne * R * T_Ne.

Since both gases have the same mass density, we can assume that the volume occupied by each gas is the same, i.e.,
V_He = V_Ne.

We are given that the temperature of helium (T_He) is 298 K. We can now solve for the temperature of neon (T_Ne). Dividing the two equations, we get:

(P_He * V_He) / (P_Ne * V_Ne) = (n_He * R * T_He) / (n_Ne * R * T_Ne).

Canceling out the common terms, we have:

P_He / P_Ne = T_He / T_Ne.

Rearranging the equation, we can solve for T_Ne:

T_Ne = (T_He * P_Ne) / P_He.

Plug in the values for T_He, P_Ne, and P_He to find the temperature of neon.