Question

A certain gas is present in a 13.0 L cylinder at 1.0 atm pressure. If the pressure is increased to 2.0 atm , the volume of the gas decreases to 6.5 L . Find the two constants ki, the initial value of k, and kf, the final value of k, to verify whether the gas obeys Boyle’s law.

Answer 1

Answer:

The gas obeys the Boyle's law

Explanation:

• According to Boyle's law, the volume of a fixed mass of a gas and the pressure are inversely proportional at constant absolute temperature.
• That is; $P\alpha\frac{1}{V}$
• Therefore, $k=PV$, where k is a constant
• At varying volume and pressures while keeping absolute temperature constant; k = P1V1 =P2V2

In this case, we are given;

Initial Volume of 13.0 L at initial pressure of 1.0 atm

New volume of 6.5 L at new pressure of 2.0 atm

But, K = PV

Therefore,

k1 = P1V1

   = 1.0 atm × 13.0 L

  = 13 atm.L

k2 = P2V2

    = 2.0 atm × 6.5 L

    = 13 atm.L

Thus, k1=k2

Thus, the gas obeys the Boyle's law