Question

g A high altitude balloon is filled with 1.41 x 104 L of hydrogen gas (H2) at a temperature of 21oC and a pressure of 745 torr. What is the volume of the balloon at a height of 20 km, where the temperature is -48oC and the pressure is 63.1 torr

Answer 1

1.27 × 10⁵ L

Step-by-step explanation:

Step 1: Given data

• Initial pressure (P₁): 745 Torr

• Initial volume (V₁): 1.41 × 10⁴ L

• Inital temperature (T₁): 21 °C

• Final pressure (P₂): 63.1 Torr

• Final volume (V₂): ?

• Final temperature (T₂): -48 °C

Step 2: Convert the temperatures to the Kelvin scale

We will use the following expression.

K = °C + 273.15

K = 21 °C + 273.15 = 294 K

K = -48 °C + 273.15 = 225 K

Step 3: Calculate the final volume of the balloon

We will use the combined gas law.

P₁ × V₁ / T₁ = P₂ × V₂ / T₂

V₂ = P₁ × V₁ × T₂/ T₁ × P₂

V₂ = 745 Torr × 1.41 × 10⁴ L × 225 K/ 294 K × 63.1 Torr

V₂ = 1.27 × 10⁵ L