[Four-digit Integer] A barometer tube contains a mixture of air and saturated water vapour in the sp β States of Matter and Gaseous State Chemistry Question
Question
[Four-digit Integer] A barometer tube contains a mixture of air and saturated water vapour in the space above the mercury column. If reads 70 cm when the actual atmospheric pressure is 76 cm of Hg. The saturation vapour pressure of water at room temperature is 1.0 cm of Hg. The tube is now lowered in the mercury reservoir till the space above the mercury column is reduced to half of its original volume. The reading of barometer (in cm) is
![Chemistry diagram for: [Four-digit Integer] A barometer tube contains a mixture of air and saturated water vapour in the space above the mercur](https://urywdhpqdpvmqzlenttu.supabase.co/storage/v1/object/public/question-images/nk/ch03_exII_Q8.png)
π‘ Solution & Explanation
Initially: $P_{air,1}=76-70-1=5$ cm Hg in air column $x_1=80-70=10$ cm (tube $L=80$ cm). Lowered 5 cm: new tube length above mercury $=75$ cm; air space $=75-h_2$ cm. Boyle's law: $5\times10=(P_{air,2})(75-h_2)$. Pressure balance: $h_2=75-50/(75-h_2)$. Solve quadratic: $h_2=75-5\sqrt{2}\approx67.9$ cm $\approx679$ mm Hg. Answer: $\boxed{0679}$