Question

Two ideal gases have the same mass density and the same absolute pressure. One of the gases is helium (He), and its temperature is 175 K The other gas is neon (Ne). What is the temperature of the neon?

Answer 1

Answer:

Temperature of neon gas = 875 K

Explanation:

Using Ideal gas equation as:

PV=nRT

Where,

P is the pressure of the gas

V is the volume of the gas

n is the number of moles

R is the gas constant

T is the temperature

Also,

$moles=\frac{Mass(m)}{Molar\ mass (M)}$

$Density (\rho)=\frac{Mass(m)}{Volume(V)}$

The ideal gas equation can be written as:

$P=\frac{Mass(m)}{Molar\ mass (M)\times Volume(V)}\times RT$

Thus,

$P=\frac{Density (\rho)}{Molar\ mass (M)}\times RT$

$P\times M=Density (\rho)\times RT$

As Density and Pressure is constant , We only consider molar mass and Temperature which are directly proportional according to the equation above as:

$\frac {M_1}{T_1}=\frac {M_2}{T_2}$

Data given for He:

Temperature (T₁) = 175 K

Molar mass of He (M₁)= 4 g/mol

For Ne:

Temperature (T₂)= ?

Molar mass of He (M₂)= 20 g/mol

Applying in the equation,

$T_2=\frac {M_2}{T_1} \times {M_1}$

$T_2=\frac {20 g{mol}^{-1}}{175 K} \times {4 g{mol}^{-1}}$

$T_2=875 K atm$

Temperature of neon gas = 875 K