A 1.5 litre sample of a gas having density 1.25 kg/m³ at 1.0 atm and 0°C was compressed to 575 atm resulting in a gas volume of 3.92 cm³ in violation of Boyle's law. What is the final density of this gas?
A) 568.3 kg/m³
B) 478.3 kg/m³
C) 278.3 kg/m³
D) 378.3 kg/m³
Answer (2)
To find the final density of the gas, we first need to consider the relevant concepts of gases and densities.
Initially, the gas has these properties:
Volume: V 1 = 1.5 L
Density: ρ 1 = 1.25 kg/m³
After compression, the gas has new properties:
Volume: V 2 = 3.92 cm³
We're tasked with finding the new density, ρ 2 .
Step-by-Step Solution:
Convert Initial Volume to m³: V 1 = 1.5 L = 1.5 × 1 0 − 3 m 3
Convert Final Volume to m³: V 2 = 3.92 cm 3 = 3.92 × 1 0 − 6 m 3
Understand Mass Conservation:
Density ( ρ ) is defined as mass ( m ) per unit volume ( V ) .
Mass of gas remains constant unless there's a leak, thus: m = ρ 1 × V 1 = ρ 2 × V 2
Calculate Initial Mass of Gas: m = ρ 1 × V 1 = 1.25 kg/m 3 × 1.5 × 1 0 − 3 m 3 = 1.875 × 1 0 − 3 kg
Determine the Final Density:
Re-arranging the mass equation: ρ 2 = V 2 m = 3.92 × 1 0 − 6 m 3 1.875 × 1 0 − 3 kg
ρ 2 = 478.3 kg/m 3
Hence, the final density of the gas is 478.3 kg/m³ .
Correct Option: B) 478.3 kg/m³
In this problem, changes in volume result from compressing the gas to a much smaller space. Despite violating Boyle's law (which assumes ideal conditions), the calculations here apply properties such as constant mass to determine new density.
The final density of the gas after compression is 478.3 kg/m³. This is calculated by first determining the mass of the gas based on its initial conditions and then using that mass to find the density with the new, smaller volume. Thus, the correct answer is option B) 478.3 kg/m³.
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