Final answer:
The final volume of the ideal gas is 3.64 times the original volume after the pressure is halved and the temperature is reduced to 0.55 of its original value, using the combined gas law.
Step-by-step explanation:
To solve the problem regarding the change in volume of an ideal gas when the pressure is halved and the temperature is reduced to 0.55 of its original value, we use the combined gas law which relates pressure (P), volume (V), and temperature (T) for a fixed amount of gas.
The combined gas law is PV/T = k, where k is a constant.
Let P₁, V₁, and T₁ be the original pressure, volume, and temperature of the gas, and P₂, V₂, and T₂ be the final pressure, volume, and temperature after the change.
Applying the given conditions, P₂ = P₁/2 and T₂ = 0.55T₁, and we want to find V₂/V₁.
Using the combined gas law:
P₁V₁/T₁ = P₂V₂/T₂,
Substituting the given conditions:
P₁V₁/T₁ = (P₁/2)V₂/(0.55T₁).
Simplifying this equation gives the ratio of the final volume to the original volume:
V₂/V₁ = 2/0.55 = 3.64.
Therefore, the final volume is 3.64 times the original volume of the gas.