5.6_P - Chemistry: Molecular Nature Of Matter And Change

Question

On a cool, rainy day, the barometric pressure is 730 mmHg. Calculate the barometric pressure in centimeters of water (cmH₂O) (d of Hg = 13.5 g/mL; d of H₂O = 1.00 g/mL).

Step-by-Step Solution

Answer

The barometric pressure of water is 985.5 cmH₂O.

Step 1: Barometric pressure

Barometric pressure is the atmospheric pressure at certain point.

Step 2: Determination of barometric pressure of water

The ratio of the liquid columns is related to the densities,

 $\frac{{\mathrm{h}}_{{\mathrm{H}}_2\mathrm{O}}}{{\mathrm{h}}_{\mathrm{Hg}}}=\frac{{\mathrm{d}}_{{\mathrm{H}}_2\mathrm{O}}}{{\mathrm{d}}_{\mathrm{Hg}}}$

 

Height of Hg = 730 mm = 73.0 cm

 

Now, the barometric pressure of water is,

 $\begin{array}{rcl}{\mathrm{h}}_{{\mathrm{H}}_2\mathrm{O}}& =& \frac{{\mathrm{d}}_{{\mathrm{H}}_2\mathrm{O}}}{{\mathrm{d}}_{\mathrm{Hg}}}\times {\mathrm{h}}_{\mathrm{Hg}}\\ & =& \frac{13.5\mathrm{g}/\mathrm{ml}}{1.00\mathrm{g}/\mathrm{ml}}\times 73.0 \mathrm{cm}\\ & =& 985.5 \mathrm{cm}\end{array}$

 

Thus, the barometric pressure of water is 985.5 cmH₂O.