Answer
$6.19\times10^{5}Pa$
Work Step by Step
Let's apply Archimedes' principle to find the mass of He inside the balloon. So we can write,
Buoyant force = total weight of the balloon
$F_{b}=mg=\rho Vg$ ; Let's plug known values into this equation.
$mg=(1.19\space kg/m^{3})(\frac{4}{3}\pi)(1.5\space m)^{3}g$
$m=16.8\space kg$ (Total mass of the balloon)
Therefore,
Mass of the helium = Total mass - mass of the balloon
$m_{he}=16.8\space kg-3\space kg=13.8\space kg$
Now we can find the number of moles of He present in the balloon.
$n=\frac{m_{he}}{Molecular\space mass}=\frac{13.8\space kg}{4.0026\times10^{-3}kg/mol}=3448\space mol$
Let's apply the ideal gas law $PV=nRT$ to find the pressure of Helium.
$PV=nRT=>P=\frac{nRT}{V}$ ; Let's plug known values into this equation.
$P=\frac{3448\space mol(8.31\space J/mol\space K)(305\space K)}{\frac{4}{3}\pi(1.5\space m)^{3}}=6.19\times10^{5}Pa$
