[Four-digit Integer] A cylinder contains 64 g of an ideal gas (M = 64) at 27°C and 3 atm. In transpo — States of Matter and Gaseous State Chemistry Question
Question
[Four-digit Integer] A cylinder contains 64 g of an ideal gas (M = 64) at 27°C and 3 atm. In transportation, the cylinder fell down and a dent was created, i.e., the effective volume of the cylinder decreases. But the valve attached to the cylinder cannot keep the pressure greater than 3 atm, so 8 g of gas leaked out. The volume of the cylinder before and after the dent was a l and b l, respectively. If the valve were pretty strong, the pressure of gas in the cylinder after dent were cd/7 atm. Temperature remained constant during this process. The value of abcd is
💡 Solution & Explanation
Initial: $n_1=64/64=1$ mol, $P=3$ atm, $T=300$ K, $V_1=n_1RT/P=100R$ L. After leak: $n_2=56/64=0.875$ mol, $P=3$ atm, $V_2=87.5R$ L. Decrease $=12.5\%$. If no leak at new vol: $P_{no\ leak}=24/7$ atm. Book codes ($abcd$): $a=8,\ b=7,\ c=2,\ d=4$, giving answer $\boxed{8724}$