According to Boyle's gas law, the volume of a gas is inversely proportional to the pressure when the temperature and mass are constant. Mathematically, this can be expressed as:
P₁ * V₁ = P₂ * V₂
where P₁ and V₁ represent the initial pressure and volume, and P₂ and V₂ represent the final pressure and volume.
In this case, we know that the initial volume, V₁, is 196 liters at a pressure of 1 atmosphere (P₁ = 1 atm). Let's denote the final pressure as P₂ and the final volume as V₂.
Plugging in the given values into the equation, we have:
1 atm * 196 L = P₂ * 26 L
Simplifying the equation:
196 = 26 * P₂
To find P₂, we divide both sides of the equation by 26:
P₂ = 196 / 26
P₂ = 7.54
Therefore, a pressure of approximately 7.54 atmospheres (rounded to two decimal places) would compress the gas volume to 26 liters, assuming the temperature and mass remain constant.