It is possible to make a barometer using a liquid other than mercury.What would be the height (in meters)of a column of dichloromethane at a pressure of 0.830 atm,given that 0.830 atm is equal to a 0.63522 m column of mercury and the densities of mercury and dichloromethane are 13.5 g/cm³ and 1.33 g/cm³,respectively. A)6.4641 m B)0.156 m C)0.0621 m D)0.838 m E)1.19 m

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Quizplus · Accepted Answer

The height of the dichloromethane column can be calculated using the principle that the pressure exerted by a column of fluid is given by $P = \rho gh$, where $P$ is the pressure, $\rho$ is the density of the fluid, $g$ is the acceleration due to gravity, and $h$ is the height of the fluid column. Given that the pressure is the same for both mercury and dichloromethane, we can set up a ratio of the heights based on the inverse ratio of their densities, since $h \propto \frac{1}{\rho}$. Given the height of the mercury column is 0.63522 m and its density is 13.5 g/cm³, and the density of dichloromethane is 1.33 g/cm³, the height of the dichloromethane column can be calculated as follows:$$h_{\text{DCM}} = h_{\text{Hg}} \times \frac{\rho_{\text{Hg}}}{\rho_{\text{DCM}}} = 0.63522 \times \frac{13.5}{1.33} \approx 6.4641 \, \text{m}$$This calculation shows that the height of the dichloromethane column under the same pressure would be significantly taller than that of mercury due to its much lower density.

It Is Possible to Make a Barometer Using a Liquid