Q5.7P - Chemistry: Molecular Nature Of Matter And Change

Question

A long glass tube, sealed at one end, has an inner diameter of 10.0 mm. The tube is filled with water and inverted into a pail of water. If the atmospheric pressure is 755 mmHg, how high (in mmH₂O) is the column of water in the tube (d of Hg = 13.5 g/mL; d of H₂O = 1.00 g/mL)?

Step-by-Step Solution

Answer

The height of the column of water is 10192.5 mm.

Step 1: Formula used

Density of Hg$\left(d_{Hg}\right)$ = 13.5 g/mL

Density of H₂O  $\left(d_{H_{2}O}\right)$= 1.00 g/mL

Height of the mercury column = 755 mmHg

 Height and density of water and mercury are related by the given equation,

 $\frac{h_{H_{2}O}}{h_{Hg}} = \frac{d_{H_{2}O}}{d_{Hg}}$

Step 2: Determination of height of water

The height of the column of water is,

 $\begin{array}{rcl}{h}_{H_{2}O } & =& \frac{d_{H_{2}O}}{d_{Hg}} \times h_{Hg}\\ & =& \frac{13.5g/ml}{1.00g/ml} \times 755 mm\\ & =& 10192.5 mm\\ & & \end{array}$

Thus, the height of the column of water is 10192.5 mmH₂O.