Understanding the Combined Gas Law

The combined gas law relates the pressure (P), volume (V), and temperature (T) of a gas:

(P₁V₁)/T₁ = (P₂V₂)/T₂

Where:

* P₁ and V₁ are the initial pressure and volume

* T₁ is the initial temperature in Kelvin (K)

* P₂ and V₂ are the final pressure and volume

* T₂ is the final temperature in Kelvin (K)

Solving the Problem

1. Convert temperatures to Kelvin:

* T₁ = 227°C + 273.15 = 500.15 K

* T₂ = 27°C + 273.15 = 300.15 K

2. Identify the knowns:

* P₁ = 580 mm Hg

* T₁ = 500.15 K

* T₂ = 300.15 K

3. Assume the volume is constant (not stated in the problem). This means V₁ = V₂

4. Substitute the known values into the combined gas law equation:

(580 mm Hg * V₁)/500.15 K = (P₂ * V₁)/300.15 K

5. Simplify the equation by canceling out V₁:

(580 mm Hg)/500.15 K = (P₂)/300.15 K

6. Solve for P₂:

P₂ = (580 mm Hg * 300.15 K) / 500.15 K

P₂ ≈ 348 mm Hg

Therefore, the new pressure of the gas in the balloon when the temperature drops to 27°C is approximately 348 mm Hg.