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Chapter 6: Problem 147

Explain why the height of the mercury column in a barometer is independent of the diameter of the barometer tube.

Short Answer

Expert verified
The height of the mercury column in a barometer is independent of the diameter of the barometer tube because the height is determined by atmospheric pressure and the equilibrium it reaches with the gravitational force exerted on the mercury, not by the tube's width.

Step by step solution

01

Understand the Working of a Barometer

In a barometer, the atmospheric pressure is calculated by balancing it against the gravitational pull on a column of mercury. The height of the mercury column is proportional to the atmospheric pressure. When the pressure is high, the mercury is pushed higher into the column. When the pressure is low, less force is exerted on the mercury, and it doesn't rise as high.
02

Understanding Pressure Equilibrium

In a column of mercury within the tube, gravitational force pulls the mercury down. This force is balanced by the atmospheric pressure pushing down on the mercury in the reservoir. It is the equality of these two forces that determines the height of the mercury column.
03

Explain why Diameter Doesn't Matter

The diameter of the tube does not affect the height of the mercury column. Even though a wider tube would contain more mercury, this does not change the mass per unit of base area (which is the actual pressure) exerted at the tube's bottom. Therefore, regardless of the tube's diameter, the height of the mercury column remains the same for a given atmospheric pressure.

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Most popular questions from this chapter

An \(89.3 \mathrm{mL}\) sample of wet \(\mathrm{O}_{2}(\mathrm{g})\) is collected over water at \(21.3^{\circ} \mathrm{C}\) at a barometric pressure of \(756 \mathrm{mmHg}\) (vapor pressure of water at \(21.3^{\circ} \mathrm{C}=19 \mathrm{mmHg}\) ). (a) What is the partial pressure of \(\mathrm{O}_{2}(\mathrm{g})\) in the sample collected, in millimeters of mercury? (b) What is the volume percent \(\mathrm{O}_{2}\) in the gas collected? (c) How many grams of \(\mathrm{O}_{2}\) are present in the sample?

In the reaction of \(\mathrm{CO}_{2}(\mathrm{g})\) and solid sodium peroxide \(\left(\mathrm{Na}_{2} \mathrm{O}_{2}\right),\) solid sodium carbonate \(\left(\mathrm{Na}_{2} \mathrm{CO}_{3}\right)\) and oxy- gen gas are formed. This reaction is used in submarines and space vehicles to remove expired \(\mathrm{CO}_{2}(\mathrm{g})\) and to generate some of the \(\mathrm{O}_{2}(\mathrm{g})\) required for breathing. Assume that the volume of gases exchanged in the lungs equals \(4.0 \mathrm{L} / \mathrm{min},\) the \(\mathrm{CO}_{2}\) content of expired air is \(3.8 \% \mathrm{CO}_{2}\) by volume, and the gases are at \(25^{\circ} \mathrm{C}\) and \(735 \mathrm{mmHg}\). If the \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\mathrm{O}_{2}(\mathrm{g})\) in the above reaction are measured at the same temperature and pressure, (a) how many milliliters of \(\mathrm{O}_{2}(\mathrm{g})\) are produced per minute and \((\mathrm{b})\) at what rate is the \(\mathrm{Na}_{2} \mathrm{O}_{2}(\mathrm{s})\) consumed, in grams per hour?

The Haber process is the principal method for fixing nitrogen (converting \(\mathrm{N}_{2}\) to nitrogen compounds). $$\mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NH}_{3}(\mathrm{g})$$ Assume that the reactant gases are completely converted to \(\mathrm{NH}_{3}(\mathrm{g})\) and that the gases behave ideally. (a) What volume of \(\mathrm{NH}_{3}(\mathrm{g})\) can be produced from 152 \(\mathrm{L} \mathrm{N}_{2}(\mathrm{g})\) and \(313 \mathrm{L}\) of \(\mathrm{H}_{2}(\mathrm{g})\) if the gases are measured at \(315^{\circ} \mathrm{C}\) and 5.25 atm? (b) What volume of \(\mathrm{NH}_{3}(\mathrm{g}),\) measured at \(25^{\circ} \mathrm{C}\) and\(727 \mathrm{mmHg},\) can be produced from \(152 \mathrm{L} \mathrm{N}_{2}(\mathrm{g})\) and \(313 \mathrm{L} \mathrm{H}_{2}(\mathrm{g}),\) measured at \(315^{\circ} \mathrm{C}\) and \(5.25 \mathrm{atm} ?\)

A 12.8 L cylinder contains \(35.8 \mathrm{g} \mathrm{O}_{2}\) at \(46^{\circ} \mathrm{C}\). What is the pressure of this gas, in atmospheres?

A sample of \(\mathrm{O}_{2}(\mathrm{g})\) has a volume of \(26.7 \mathrm{L}\) at 762 Torr. What is the new volume if, with the temperature and amount of gas held constant, the pressure is (a) lowered to 385 Torr; (b) increased to 3.68 atm?
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