Question

A balloon is filled at 0°C to a volume of 3.45L. The balloon then expands to 4.25L when placed in a 44°C room at a pressure of 0.97 atm. At what pressure was the balloon originally?

Answer 1

1.0 atm

Step-by-step explanation:

Step 1: Given data

• Initial pressure (P₁): ?

• Initial volume (V₁): 3.45 L

• Initial temperature (T₁): 0°C

• Final pressure (P₂): 0.97 atm

• Final volume (V₂): 4.25 L

• Final temperature (T₂): 44°C

Step 2: Convert the temperatures to the Kelvin scale

We will use the following expression.

K = °C + 273.15

T₁: K = 0°C + 273.15 = 273 K

T₂: K = 44°C + 273.15 = 317 K

Step 3: Calculate the initial pressure of the balloon

We will use the combined gas law.

P₁ × V₁ / T₁ = P₂ × V₂ / T₂

P₁ = P₂ × V₂ × T₁ / T₂ × V₁

P₁ = 0.97 atm × 4.25 L × 273 K / 317 K × 3.45 L = 1.0 atm