Question

A J-shaped tube with smaller end closed and longer end was taken. Mercury was added into it till the level of mercury in both the limbs was the same. Volume of air enclosed in the closed end was found to be ${\text{2}} \cdot {\text{4 mL}}$. Now more mercury was added and the air enclosed in the closed end reduced to ${\text{1}} \cdot {\text{9 mL}}$. Now, the difference in the level of the two limbs will be
A) ${\text{43 cm}}$
B) ${\text{5 cm}}$
C) ${\text{10 cm}}$
D) ${\text{20 cm}}$

Answer 1

Hint: The initial volume and the final volume is given which means one can use these values in an equation of ideal gas law and find out the value of pressure. The initial pressure value can be taken as ${\text{760 mmHg}}$ and it is the atmospheric pressure.

Complete step by step answer:
1) First of all we will try to understand what has been given in the question and how to find out the answer. The tube given is J-shaped and the initial volume in the tube is ${\text{2}} \cdot {\text{4 mL}}$. This volume is later reduced to ${\text{1}} \cdot {\text{9 mL}}$ that means there will be a newly formed gap in the tube due to a reduction in volume.
2) Now there is atmospheric pressure is present in the tube which will be as ${\text{760 mmHg}}$ and it later increases to certain pressure due to the decrease in the volume.
3) Now as per the equation of ideal gas law, which is $PV = nRT$. We can get a relation of pressure and volume as,
${P_1}{V_1} = {P_2}{V_2}$
Now as we need the value of ${P_2}$ we can write the equation as,
${P_2} = \dfrac{{{P_1}{V_1}}}{{{V_2}}}$
Now, lets put the values in the above equation,
${P_2} = \dfrac{{760 \times 2 \cdot 4}}{{1 \cdot 9}}$
Now by doing the calculation we get,
${P_2} = \dfrac{{1824}}{{1 \cdot 9}}$
Now by doing the division part we get,
${P_2} = 960{\text{ mmHg}}$
4) Therefore, the pressure will be ${\text{960 mmHg}}$. Now as to calculate the difference in the level of the two limbs we can subtract the value of initial pressure from the final pressure as below,
The difference in the level of the two limbs $ = {P_2} - {P_1} = 960 - 760 = 200{\text{ mmHg}}$
5) Therefore, the difference in the level of the two limbs is ${\text{200 mmHg}}$ which can be written as in centimeters as ${\text{20 cm}}$
Which shows the option D is the correct choice.

Note: The pressure value is in mmHg which is added and it shows the difference in the level of the two limbs. Hence, the pressure difference can be used as a difference in two limbs level and converted into centimeters. In this experiment the number of moles value and temperature value is the same and volume difference is given hence, we can get a relation of pressure and volume as, ${P_1}{V_1} = {P_2}{V_2}$.