Question

Boyle's law is used to calculate atmospheric pressure with a simple glass J-shaped tube. An experiment is done with two different diameter tubes in a laboratory. The smaller diameter tube resulted in a measured atmospheric pressure of 746 mm of Hg. The second tube was twice the diameter of the first tube but no additional mercury was added. Which of the following would be the expected measured value from the second J- tube?
(A) 186.5 mm of Hg
(B) 559 mm of Hg
(C) 746 mm of Hg
(D) 1492 mm of Hg

Answer 1

Hint: A theoretical gas composed of a set of randomly moving particles that interact only elastic collisions is called an ideal gas. The ideal gas concept useful for a simplified equation of a state which obeys the ideal gas laws and is amenable to analysis under statistical mechanics. The mole and volume relationship is Avogadro’s law.

Complete step by step solution:
Ideal gas equation: This equation of the state of a hypothetical ideal gas from the ideal gas law. The ideal gas equation has a good approximation to the behavior of many gases under several conditions and limitations.
$PV=nRT$ - (1)
Boyle’s Law states that the volume of a given mass of gas changes inversely proportional to pressure when the temperature is kept constant.
The volume of the first J- tube = $\pi r_{1}^{2}{{h}_{1}}$ - (2)
The volume of the second J- tube = $\pi r_{2}^{2}{{h}_{2}}$ -(3)
${{r}_{1}}\And {{r}_{2}}$And ${{h}_{1}}\And {{h}_{2}}$ will be the radius and height of the two glass J-shaped tubes respectively.
In the given experiment, no additional mercury was added then both volumes of the tubes will be the same.
Hence, $\pi r_{^{1}}^{2}{{h}_{1}}=\pi r_{2}^{2}{{h}_{2}}$ -(4)
From the atmospheric pressure in the first tube = 746 mm of Hg,
Then, the height of the tube ${{h}_{1}}=746mm$
The second tube was twice the diameter of the first tube, ${{r}_{2}}=2{{r}_{1}}$
Substitute the values in equation (4),
$\pi {{r}_{1}}^{2}(746)=\pi {{(2{{r}_{1}})}^{2}}{{h}_{2}}$
${{h}_{2}}=186.5mm$
Hence, the expected measured value from the second J- tube = 186.5 mm of Hg.

The correct answer is option A.

Note: The ideal gas laws which deal with ideal gases naturally and laws are Boyle’s law, Charles law, and Avogadro’s law. The specific gas constant observed that when a molecular mass of any gas multiplied with R is always the same for all gases. This product is called the universal gas constant.