The concept related to this exercise to solve this problem is the ideal Gas law which establishes
[tex]PV = nRT[/tex]
P= Pressure
V= Volume
n = Number of moles
R= Gas ideal Constant
T= Temperature
Our values are given as,
[tex]V =5400m^3 \\P = 1.1*10^5Pa\\T = 295K \\M_m =4.0026g\\R = 8.3145J\cdot mol^{-1}K^{-1}\\[/tex]
From the ideal gas equation then we rearrange the equation to obtain the number of moles, then
[tex]PV=nRT\\n = \frac{PV}{RT}\\n= 242174.43[/tex]
By definition the molecular mass (n) is expressed in terms of the mass and molecular weight therefore
[tex]n = \frac{m}{M_m}[/tex]
[tex]m = n*M_m[/tex]
[tex]m = (242174.43)(4.0026)n[/tex]
[tex]m = 969327.37[/tex]
[tex]m = 968.327Kg[/tex]
Therefore the mass of the helium in the blimp is 968.327Kg
