The pressure of 6.0 L of an ideal gas in a flexible container is decreased to one-eighth of its original pressure, and its absolute temperature is decreased to one-seventh of the original. What is the final volume of the gas?

To find the final volume of the gas, we can use the combined gas law, which relates the initial and final conditions of pressure, volume, and temperature of a gas.

The combined gas law equation is as follows:

(P₁V₁) / T₁ = (P₂V₂) / T₂

Where:
- P₁ and P₂ are the initial and final pressures, respectively,
- V₁ and V₂ are the initial and final volumes, respectively, and
- T₁ and T₂ are the initial and final absolute temperatures, respectively.

Given:
- P₁ is the initial pressure
- V₁ is the initial volume
- T₁ is the initial temperature
- P₂ is one-eighth of the initial pressure (i.e., P₂ = P₁ / 8)
- T₂ is one-seventh of the initial temperature (i.e., T₂ = T₁ / 7)

We are asked to find V₂, the final volume.

We can substitute the given values into the combined gas law equation and solve for V₂.

(P₁V₁) / T₁ = (P₂V₂) / T₂

Substituting the given values:

(P₁ * V₁) / T₁ = ((P₁ / 8) * V₂) / (T₁ / 7)

We can simplify the equation by canceling out common factors:

7P₁V₁ = (P₁V₂) / 8

To solve for V₂, we'll rearrange the equation:

V₂ = (7P₁V₁ * 8) / P₁

V₂ = 56V₁

Therefore, the final volume of the gas would be 56 times the initial volume (V₁).