Question

A large balloon contains 5400 m3 of He gas that is kept at a temperature of 280 K and an absolute pressure of 1.10 x 105 Pa. Find the mass of He inside the balloon. (Molar mass of He : 4.002 g/mol)

Answer 1

Answer:

1.02 × 10⁶ g

Explanation:

Step 1: Given data

• Volume of the balloon (V): 5400 m³

• Temperature (T): 280 K

• Absolute pressure (P): 1.10 × 10⁵ Pa

• Molar mass of He (M): 4.002 g/mol

Step 2: Convert "V" to L

We will use the conversion factor 1 m³ = 1000 L.

5400 m³ × 1000 L/1 m³ = 5.400 × 10⁶ L

Step 3: Convert "P" to atm

We will use the conversion factor 1 atm = 101325 Pa.

1.10 × 10⁵ Pa × 1 atm / 101325 Pa = 1.09 atm

Step 4: Calculate the moles of He (n)

We will use the ideal gas equation.

P × V = n × R × T

n = P × V / R × T

n = 1.09 atm × 5.400 × 10⁶ L / 0.08206 atm.L/mol.K × 280 K

n = 2.56 × 10⁵ mol

Step 5: Calculate the mass of He (m)

We will use the following expression.

m = n × M

m = 2.56 × 10⁵ mol × 4.002 g/mol

m = 1.02 × 10⁶ g