An unspecified quantity of an ideal gas was at initial pressure of 5 atm and temperature of 303 K. T — States of Matter and Gaseous State Chemistry Question
Question
An unspecified quantity of an ideal gas was at initial pressure of 5 atm and temperature of 303 K. The gas is expanded at 303 K until the volume has increased by 60% of the initial value. Next, the quantity of the gas in the vessel is increased by 20% of the initial value while the volume is maintained constant. Finally, the temperature is adjusted at constant volume until the gas pressure is again 5 atm. What is the final temperature, in kelvin?
💡 Solution & Explanation
Initial state: $P_1 = 5\text{ atm}$. Expansion increases volume by 60%, so $V_2 = 1.6 V_1$. Isothermal expansion means $P_2 = P_1 / 1.6 = 5 / 1.6 = 3.125\text{ atm}$. Gas quantity increased by 20%, so $n_3 = 1.2 n_1$. Pressure is proportional to moles at constant V and T, so $P_3 = 3.125 \times 1.2 = 3.75\text{ atm}$. Final state targets $P_4 = 5\text{ atm}$ at constant V and n. Thus $T_4 = T_3 \times (P_4 / P_3) = 303 \times (5 / 3.75) = 303 \times (4/3) = 404\text{ K}$. Therefore, correct answer is 0404.