Please, show the steps. Thank you. The figure at the right shows your experiment

Question

Please, show the steps. Thank you.

The figure at the right shows your experimental setup for estimating the triple point of CO_2 Carefully mark off your capillary tube in ten I-cm segments, and note the position of the drop of dye solution when the capillary is inserted in the open plastic tube. When the top of the plastic tube is sealed, the pressure inside will increase as the CO_2 sublimes, and the drop of dye will be forced up the capillary, compressing the air inside it. Note the position of the drop of dye when liquid CO_2 starts to form. The pressure inside the capillary should then correspond to the pressure at the triple point of CO_2. You can calculate the pressure from a modification of Boyle's law, P_1V_1 = P_2 V_2: The volume of the capillary = hA where h is the height and A is the cross-sectional area, which is constant. Boyle's law therefore reduces to P_1h_1= P_2h_2. Where P_1 is the pressure in the open tube, hi is the distance of the drop from the top of the capillary in the open tube. h_2 is the distance of the drop from thetop of the capillary in the closed tube, and P_2 is the pressure in the closed tube, the pressure at the triple point. What are the heights of the air columns in the two capillaries to the right? (Measure from the top of the dye droplet.) Height of column in the open tube (h_1): Height of column in the closed tube (h_2): Calculate the pressure in the closed tube, assuming the pressure in the open tube is 1.0 atm.

Explanation / Answer

solution

From the figure we can measure

the height of column in the open tube (h1) = 10 cm = 0.1 m

the height of column in the open tube (h2) = 2.2 cm = 0.022 m

here, pressure in open tube (P1) = 1 atm = 101325 N/m2

so, the pressure in closed tube (P2) can be find by the equation

P1h1 = P2h2

   P2 = P1h1 / h2

= 101325 X 0.1 / 0.022

   = 460568.18 N/m2

= 4.54 atm

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