Assume that you have an open-end manometer filled with...

Assume that you have an open-end manometer filled with chloroform (density $=1.4832 \mathrm{g} / \mathrm{mL}$ at $20^{\circ} \mathrm{C} )$ rather than mercury (density $=13.546 \mathrm{g} / \mathrm{mL}$ at $20^{\circ} \mathrm{C} )$ What is the difference in height between the liquid in the two arms if the pressure in the arm connected to the gas sample is 0.788 atm and the atmospheric pressure reading is 0.849 atm? In which arm is the chloroform level higher?

Assume that you have an open-end manometer filled with chloroform (density $=1.4832 \mathrm{g} / \mathrm{mL}$ at $20^{\circ} \mathrm{C} )$ rather than mercury (density $=13.546 \mathrm{g} / \mathrm{mL}$ at $20^{\circ} \mathrm{C} )$ What is the difference in height between the liquid in the two arms if the pressure in the arm connected to the gas sample is 0.788 atm and the atmospheric pressure
reading is 0.849 atm? In which arm is the chloroform level higher?

Key Concepts

Manometer Operation

A manometer is an instrument used to measure pressure differences by balancing the weight of a fluid column between two points. It operates based on the principle that pressure is exerted by the weight of the fluid above a given level, and differences in pressure produce corresponding differences in height of the fluid in the two arms of the device.

Hydrostatic Pressure

Hydrostatic pressure refers to the pressure exerted by a static fluid due to the force of gravity. It is calculated as the product of the fluid's density, gravitational acceleration, and the height of the fluid column. This concept allows us to relate a given pressure difference to a specific height difference in a fluid of known density.

Fluid Density

Fluid density is a critical property that determines how much mass exists per unit volume. In the context of manometers, the density of the manometric fluid directly influences the height difference required to balance a given pressure difference; fluids with lower density, such as chloroform compared to mercury, will produce a larger column height for the same pressure differential.

Pressure Differential

The pressure differential in a manometer is the difference between the pressures applied at the two ends of the device, such as between a gas sample and atmospheric pressure. This difference is balanced by the weight of the fluid column, and it is used in conjunction with the equation for hydrostatic pressure to calculate the height difference between the fluid levels in the manometer arms.

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