A gas occupies 1 dm3 at 2 atm pressure; what will its new volume be if the pressure is raised to 6 atm at constant temperature?
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Answer: B. 1/3dm3
Explanation
Applying Boyle's law shows that tripling the pressure from two to six atmospheres reduces volume threefold. Initial pressure multiplied by initial volume equals final pressure multiplied by final volume at constant temperature. Solving the equation yields a final volume of one-third of a cubic decimeter. Boyle's law establishes that the product of pressure and volume remains constant for a fixed gas mass. An increase in pressure forces gas molecules closer together, resulting in a proportional decrease in space. Mathematical calculations using inverse proportionality are essential for solving quantitative gas law problems.
Scuba divers must understand pressure-volume calculations to prevent lung injuries during ascent from deep water. Engineering designs for compressed gas cylinders rely heavily on accurate gas law mathematical models. Laboratory experiments involving gas syringes utilize these calculations to determine molar volumes. A volume of one-half cubic decimeter would incorrectly imply a pressure increase by a factor of two. A volume of one-fourth cubic decimeter represents an incorrect calculation inconsistent with inverse proportion. Two-thirds of a cubic decimeter fails to reflect the true threefold increase in applied gas pressure.
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