Question

A certain gas is present in a 12.0 L
cylinder at 3.0 atm
pressure. If the pressure is increased to 6.0 atm
the volume of the gas decreases to 6.0 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 by entering the numerical values for ki
and kf
in the space provided.

Answer 1

Boyle's law states that for a given amount of gas at constant temperature, the pressure and volume of the gas are inversely proportional. This relationship can be expressed as:

PiVi = PfVf

where Pi and Vi are the initial pressure and volume of the gas, and Pf and Vf are the final pressure and volume of the gas.

Given:
Pi = 3.0 atm
Vi = 12.0 L
Pf = 6.0 atm
Vf = 6.0 L

Using the formula above, we can find the initial value of k (ki) and the final value of k (kf) as follows:

ki = PiVi = 3.0 atm * 12.0 L = 36.0 atm·L
kf = PfVf = 6.0 atm * 6.0 L = 36.0 atm·L

Therefore, ki = 36.0 and kf = 36.0.

Since ki = kf, the gas obeys Boyle's law in this case.