Answer :
Final answer:
The initial density of the neon gas is 0.437 kg/m³. According to Boyle's Law, when the pressure decreases, the volume of the gas increases, hence the final volume is 3.73 m³. The final density of the neon gas is then 0.35 kg/m³.
Explanation:
The subject of this problem is the behavior of gases and the related principles, namely in this case, Boyle's Law and density calculations. Boyle's Law states that the pressure and volume of a gas have an inverse relationship when the temperature is held constant. In terms of calculating density, it is obtained by dividing the mass of the substance by its volume.
First, we find the initial density, which is m/V, giving us 1.31 kg / 3.00 m³ = 0.437 kg/m³. Since we're assuming an isothermic process (temperature remains constant), according to Boyle's law, the final volume** V2 should be V1*(P1/P2), where P1 & V1 are the initial pressure and volume, and P2 is the final pressure. V2 thus becomes 3.00 m³ * (121 kPa / 97.4 kPa) = 3.73 m³. The final density is then m/V2, which is 1.31 kg / 3.73m³ = 0.35 kg/m³.
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