Question

Hikers have noticed that a sealed bag of potato chips puffs up when taken to the top of a mountain. Suppose that at the valley floor below, the air pressure is 1.0 atm, temperature is 25°C, and the volume of the chip bag is 0.985 L. At the top of the mountain, the temperature is 22°C and the chip bag has puffed up to 1.030 L. What is the air pressure on top of the mountain?

Answer 1

Answer is: the pressure on the top of the mountain is 0.945 atm.

p₁ = 1.0 atm; pressure at the valley.

T₁ = 25°C = 298.15 K; temperature at the valley.

V₁ = 0.985 L; volume at the valley.

p₂ = ?

T₂ = 22°C = 295.15 K; temperature at the top of the mountain.

V₂ = 1.030 L; volume at the top of the mountain.

Use combined gas law - the volume of amount of gas is proportional to the ratio of its Kelvin temperature and its pressure.  

p₁V₁/T₁ = p₂V₂/T₂.

1 atm · 0.985 L ÷ 298.15 K  = p₂ · 1.030 L ÷ 295.15 K.

0,0033 atm·L/K = 0.00349p₂.

p₂ = 0.945 atm.

Answer 2

The air pressure on top of the mountain is 0.947 atm

Data obtained from the question

• Initial pressure (P₁) = 1 atm
• Initial temperature (T₁) = 25°C = 25 + 273 = 298 K
• Initial volume (V₁) = 0.985 L
• Final temperature (T₂) = 22°C = 22 + 273 = 295 K
• Final volume (V₂) = 1.030 L

• Final pressure (P₂) = ?

How to determine the final pressure

The final pressure (i.e pressure on top of the mountain) can be obtained by using the combined gas equation as illustrated below:

P₁V₁ / T₁ = P₂V₂ / T₂

(1 × 0.985) / 298 = (P₂ × 1.030) / 295

Cross multiply

298 × P₂ × 1.030 = 0.985 × 295

306.94 × P₂ = 290.575

Divide both side by 306.94

P₂ = 290.575 / 306.94

P₂ = 0.947 atm

Learn more about gas laws:

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