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A Goodyear blimp typically contains 4770 m3 of helium (He) at an absolute pressure of 1.10 x 105 Pa. The temperature of the helium is 274 K. What is the mass (in kg) of the helium in the blimp?

This is just a case of applying the ideal gas law,

n = PV/RT.

You know the volume (V), pressure (P) and temperature (T) and can compute the number of moles of he contained, n. Each mole of heliim weighs 4.00 grams.

The gas law constant, R is
R = 8.317 Newton-meter-mole/K. If you have P in units of Pascals and T in degrees K, you will get n in moles/m^3.

To solve for the mass of the helium in the blimp, we need to follow these steps:

Step 1: Convert the pressure from Pascals to atmospheres.
1 atmosphere (atm) = 101325 Pascals (Pa)

Given: Absolute pressure (P) = 1.10 x 105 Pa

Convert P from Pa to atm:
P (atm) = 1.10 x 105 Pa / 101325 Pa/atm ≈ 1.085 atm

Step 2: Convert the temperature from Kelvin to Celsius.
The ideal gas law constant (R) is usually given in units of m^3 * Pa / (mol * K), which requires the temperature to be in Kelvin.

Given: Temperature (T) = 274 K

Convert T from K to °C:
T (°C) = 274 K - 273.15 ≈ 0.85 °C

Step 3: Calculate the number of moles of helium gas (n) using the ideal gas law equation.
The ideal gas law equation is: n = PV / RT

Given: Volume (V) = 4770 m^3
Pressure (P) = 1.085 atm
Temperature (T) = 0.85 °C ≈ 273.85 K (converted back to Kelvin)

n = (1.085 atm) * (4770 m^3) / (8.317 m^3 * Pa / (mol * K) * 273.85 K) ≈ 227.2 mol

Step 4: Calculate the mass of the helium gas using the molar mass of helium.
Given: Molar mass of helium (He) = 4.00 g/mol

Mass (m) = n * molar mass
Mass (m) = 227.2 mol * 4.00 g/mol ≈ 908.8 g

Step 5: Convert the mass from grams to kilograms.
Mass (m) = 908.8 g / 1000 ≈ 0.909 kg

Therefore, the mass of the helium in the blimp is approximately 0.909 kg.