## No problem! I can help you solve this problem step-by-step.

To find the mass of the helium in the blimp, we can use the Ideal Gas Law equation you provided:

PV = NkT

Where:

P = Pressure of the gas in Pascals (Pa)

V = Volume of the gas in cubic meters (m^3)

N = Number of gas molecules

k = Boltzmann constant (1.38 × 10^-23 J/K)

T = Temperature of the gas in Kelvin (K)

We are given:

P = 1.10 x 10^5 Pa

V = 4770 m^3

T = 274 K

First, let's calculate the value of N using the equation you provided:

N = PV / (kT)

N = (1.10 x 10^5 Pa) * (4770 m^3) / ((1.38 × 10^-23 J/K) * 274 K)

N = 1.913 x 10^27 molecules of helium

Now, we know the number of helium molecules in the blimp, but we need to find the mass of the helium. We know that the mass of one helium atom is approximately 4u, where 1u is the atomic mass unit (1u = 1.66 x 10^-27 kg).

The mass of one helium atom is approximately 4u = 6.642 x 10^-27 kg.

Now, we can find the total mass of the helium in the blimp:

Total mass = mass of one helium atom * number of helium atoms

= 6.642 x 10^-27 kg * 1.913 x 10^27 molecules

≈ 1.267 kg

Therefore, the mass of the helium in the blimp is approximately 1.267 kg.