Question

A Goodyear blimp typically contains 5400 m³ of helium (He) at an absolute pressure of 1.10 × 10 5 1.10 × 10 5 Pa. The temperature of the helium is 295 K. What is the mass (in kg) of the helium in the blimp?(The molar mass of Helium is 4.0026 g)

Answer 1

The concept related to this exercise to solve this problem is the ideal Gas law which establishes

$PV = nRT$

P= Pressure

V= Volume

n = Number of moles

R= Gas ideal Constant

T= Temperature

Our values are given as,

$V =5400m^3 \\P = 1.1*10^5Pa\\T = 295K \\M_m =4.0026g\\R = 8.3145J\cdot mol^{-1}K^{-1}$

From the ideal gas equation then we rearrange the equation to obtain the number of moles, then

$PV=nRT\\n = \frac{PV}{RT}\\n= 242174.43$

By definition the molecular mass (n) is expressed in terms of the mass and molecular weight therefore

$n = \frac{m}{M_m}$

$m = n*M_m$

$m = (242174.43)(4.0026)n$

$m = 969327.37$

$m = 968.327Kg$

Therefore the mass of the helium in the blimp is 968.327Kg