Question

The initial volume of a gas cylinder is 750.0 mL, If the pressure of the gas inside the cylinder changes from 840.00 mmHg to 360.00 mmHg, the final volume of the gas will be:
a.) 3.60 L
b.) 4.032 L
c.) 1.750 L
d.) 7.50 L

Answer 1

Hint: According to Boyle’s law, at constant temperature, pressure is inversely proportional to volume. Using the equation ${ V }_{ 2 }=\dfrac { { P }_{ 2 }{ V }_{ 1 } }{ { P }_{ 1 } } $, we will get the answer by substituting the values into it.

Complete answer:
We have been provided with the initial volume of the gas which is equal to 750 mL.
We need to find the final volume of the gas when its pressure changes from 840.00 mmHg to 360.00 mmHg.
Consider, 1 as the initial condition and 2 as the final condition,
Therefore,${ P }_{ 1 }$ = 840 mmHg
${ P }_{ 2 }$= 360 mmHg
${ V }_{ 1 }$ = 750 mL
${ V }_{ 2 }$ = ?
We need to find the value of ${ V }_{ 2 }$,
Let us assume the temperature remains constant during the process, then we can apply Boyle’s law over here.
According to Boyle’s law, at constant temperature, volume of a gas is inversely proportional to the pressure of that gas.
So, we can write as $\dfrac { { P }_{ 1 } }{ { V }_{ 1 } } =\frac { { P }_{ 2 } }{ { V }_{ 2 } } $
Rearrange the equation in order to find ${ V }_{ 2 }$,
${ V }_{ 2 }=\dfrac { { P }_{ 2 }{ V }_{ 1 } }{ { P }_{ 1 } } $ -----(i)
Substitute the values in equation (i),
${ V }_{ 2 }=\dfrac { 360\times 750 }{ 840 } $ mL = 1750 mL = 1.750 L.
So, the correct answer is “Option C”.

Additional Information: We can now look at some real life application of Boyle’s Law,
(i)While filling the bike tires with air. When we pump air into a tire, the gas molecules inside the tire get compressed and packed closer together. This causes an increase in the pressure of the gas, and it starts to push against the walls of the tire. We can feel how the tire becomes pressurized and tighter.
(ii) Another example we can easily observe is carbonated drinks. To get carbon dioxide gas into the liquid, the whole bottle is usually pressurized with carbon dioxide gas. As long as the bottle is closed, it is very hard to squeeze, as the gas is confined to a small space and pushes against the bottle walls. When we remove the cap, however, the available volume increases and some of the gas escapes. At the same time the pressure decreases.
One of the most important applications of Boyle’s law one can find is in our breathing. Inhaling and exhaling basically means increasing and decreasing the volume of our chest cavity (thorax region) . This creates low pressure and high pressure in our lungs, resulting in air getting sucked into our lungs and leaving our lungs which is the inhalation and exhalation.

Note: Boyle’s Law is only valid under constant temperature conditions. Also, one should take care of the unit conversions. Over here, the answer is given in the SI unit of volume i.e,Litre. 1 L=1000mL.