Question

(a) A piston at 5.5 atm contains a gas that occupies a volume of 3.5 L. What pressure would have to be placed on the piston to force the volume to adjust to 0.73 L? atm (b) A piston at 46.0°C contains a gas that occupies a volume of 2.5 L. To what temperature would the gas have to be heated to increase the volume to 5.4 L at constant pressure? °C (c) A piston at 2795 torr contains a gas that occupies a volume of 4.7 L. What pressure would have to be placed on the piston to force the volume to adjust to 0.96 L?

Answer 1

(a)

Initial pressure, P₁ = 5.5 atm

Initial volume, V₁ = 3.5 L

Let us say that the final pressure = P₂

Final volume, V₂ = 0.73 L

Now, from Boyle's law (assuming at constant T)

P₁V₁ = P₂V₂

or, 5.5 x 3.5 = 0.73 x P₂

or, P₂ = 26.4 atm

Therefore, the pressure that has to be placed on top of piston = 26.4 atm

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(b)

Initial temperature, T₁ = 46.0 ^oC = (46 + 273.15) = 319.15 K

Initial volume, V₁ = 2.5 L

Final volume, V₂ = 5.4 L

Let us say that the final temperature = T₂

From Charles' law,

V₁/T₁ = V₂/T₂

or, 2.5/319.15 = 5.4/T₂

or, T₂ = (5.4 x 319.15)/2.5

          = 689.36 K

          = (689.36 - 273.15)

          = 416.21 ^oC

Therefore, the gas have to be heated to 416.21 ^oC.

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(c)

Initial pressure, P₁ = 2795 torr

Initial volume, V₁ = 4.7 L

Let us say that the final pressure = P₂

Final volume, V₂ = 0.96 L

Now, from Boyle's law (assuming at constant T)

P₁V₁ = P₂V₂

or, 2795 x 4.7 = 0.96 x P₂

or, P₂ = (2795 x 4.7)/0.96

or, P₂ = 13684 torr

Therefore, the pressure that has to be placed on top of piston = 13684 torr