a cylinder with a moveable piston contains 3.5 l of gas at 310 k and 2.5 atm. if the temperature increases…

a cylinder with a moveable piston contains 3.5 l of gas at 310 k and 2.5 atm. if the temperature increases to 350 k and the pressure drops to 1.5 atm, what is the new volume of the system?

a cylinder with a moveable piston contains 3.5 l of gas at 310 k and 2.5 atm. if the temperature increases to 350 k and the pressure drops to 1.5 atm, what is the new volume of the system?

Answer

Explanation:

Step1: Identify the combined - gas law formula

The combined - gas law is $\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$, where $P_1$, $V_1$, $T_1$ are the initial pressure, volume and temperature, and $P_2$, $V_2$, $T_2$ are the final pressure, volume and temperature.

Step2: Rearrange the formula to solve for $V_2$

$V_2=\frac{P_1V_1T_2}{T_1P_2}$

Step3: Substitute the given values

Given $P_1 = 2.5$ atm, $V_1=3.5$ L, $T_1 = 310$ K, $P_2 = 1.5$ atm, $T_2 = 350$ K. $V_2=\frac{2.5\times3.5\times350}{310\times1.5}$ $V_2=\frac{2.5\times3.5\times350}{465}$ $V_2=\frac{3062.5}{465}\approx6.6$ L

Answer:

$6.6$ L