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A given mass of air has a volume of 6.0 L at 1 atm. What volume will it occupy at 190 mmHg if the temperature remains unchanged?

This problem is solved using Boyle’s law, a gas law. It gives the relation between volume and pressure of a given mass of a gas at a constant temperature. According to Boyle’s law, volume of a given mass of a gas is inversely proportional to the pressure of the gas, at a given temperature. Hence, if pressure of a gas is increased, the volume of the gas decreases or the gas gets compressed and if the pressure is reduced, the volume of the gas increases or the gas expands. Mathematically the law can be expressed as


P α 1/V


P = constant  x 1/V


Or PV=constant.


Thus if V1 is the volume of a given mass of a gas at pressure P1, and if the pressure is changed to P2, then according to Boyle’s law, the volume of the gas will change to V2 in such a way that


P1V1 =P2V2


This equation can be used to solve the given problem.


Given that the volume of the gas is 6.0 L (V1) under a pressure of 1 atm (P1), when the pressure is changed to 190 mmHg (P2), the new volume can be calculated by first converting 190 mmHg to atm:


190 mmHg x (1 atm / 760 mmHg) = .25 atm


    P1     V1   =      P2      V2


(1 atm)(6 L) = (.25 atm)(V2)


 V2= P1V1 / P2


   V2 = (1atm x 6.0 L) / (.25 atm)


Therefore  V2 = 24.0 L


The new volume of the gas is 24.0 L.

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