Question

A cylinder with a movable piston contains 2.00 g of helium, He, at room temperature. More helium was added to the cylinder and the volume was adjusted so that the gas pressure remained the same. How many grams of helium were added to the cylinder if the volume was changed from 2.00 L to 3.50 L ? (The temperature was held constant.)

Answer 1

Given :-

Mass of Helium(m1) = 2.0 gm

Temperature remains same ie (T) is constant

Pressure remains same ie. (P) is constant

Volume (V1) = 2.0 L

Volume (V2) = 3.50 L

According to Ideal gas law,

  PV = n RT                               (where R is a constant)

  PV/nT = constant

P1V1 / n1T1 = P2V2 / n2T2                                    (P is constant & T is constant)

V1 / n1 = V2 / n2

since n = mass / mw

V1 / (mass 1 / mw) = V2 / (mass 2 / mw)

and since molecular mass = constant

V1 / mass 1 = V2 / mass 2

mass 2 = V2 x mass 1 / V1

= 3.50L x 2.00 g / 2.00 L

mass 2 = 3.50 g

=mass 2 - mass 1

= 3.50 g - 2.00 g

=1.50 g

ANSWER : 1.50 g of He was added.