Question

a certain gas is present in a 12.0 l cylinder at 1.0 atm pressure. if the pressure is increased to 2.0 atm, the volume of the gas decreases to 6.0 l. find the two constants ( k_1 ) and ( k_2 ), the initial value of ( k ) and the final value of ( k ) to verify boyles law by entering the numerical values for ( k_1 ) and ( k_2 ) in the space provided. express your answers to two significant figures separated by a comma.

part d

if a certain gas occupies a volume of 14 l when the applied pressure is 7.0 atm, find the pressure when the gas occupies a volume of 35 l. express your answer to two significant figures and include the appropriate units.

Explanation:

Step1: Recall Boyle's law

Boyle's law states that $P_1V_1 = P_2V_2=k$ (at constant temperature).

Step2: Calculate $k$ for the first - part

For the first situation, $P_1 = 1.0$ atm, $V_1 = 12.0$ L. So $k_1=P_1V_1=1.0\times12.0 = 12$ L - atm.

Step3: Calculate $k$ for the second - part

For the second situation, $P_2 = 2.0$ atm, $V_2 = 6.0$ L. So $k_2=P_2V_2=2.0\times6.0 = 12$ L - atm.

Step4: Solve for the pressure in Part D

We know from Boyle's law $P_1V_1 = P_2V_2$. Given $P_1 = 7.0$ atm, $V_1 = 14$ L, $V_2 = 35$ L. Then $P_2=\frac{P_1V_1}{V_2}=\frac{7.0\times14}{35}=2.8$ atm.

Answer:

$12,12$
$2.8$ atm