a cylinder with a moveable piston contains 198 ml of nitrogen gas at a pressure of 1.22 atm and a…

a cylinder with a moveable piston contains 198 ml of nitrogen gas at a pressure of 1.22 atm and a temperature of 302 k. what must the final volume be for the pressure of the gas to be 1.52 atm at a temperature of 370 k?\na 194 ml\nb 200 ml\nc 196 ml\nd 195 ml

a cylinder with a moveable piston contains 198 ml of nitrogen gas at a pressure of 1.22 atm and a temperature of 302 k. what must the final volume be for the pressure of the gas to be 1.52 atm at a temperature of 370 k?\na 194 ml\nb 200 ml\nc 196 ml\nd 195 ml

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 respectively, and $P_2$, $V_2$, $T_2$ are the final pressure, volume and temperature respectively.

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 $P_1 = 1.22$ atm, $V_1=198$ mL, $T_1 = 302$ K, $P_2 = 1.52$ atm, $T_2 = 370$ K. $V_2=\frac{1.22\times198\times370}{302\times1.52}$ $V_2=\frac{1.22\times198\times370}{459.04}$ $V_2=\frac{1.22\times73260}{459.04}$ $V_2=\frac{89377.2}{459.04}\approx194$ mL

Answer:

A. 194 mL