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.

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; [tex]P\alpha\frac{1}{V}[/tex]
Therefore, [tex]k=PV[/tex], 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