Question

Calculate the volume occupied by the $5.0g$ of acetylene gas at ${50^ \circ }C$ and $740mm$ of pressure.
A. $5.237L$
B. $5.5L$
C. $4.5L$
D. None of the above

Answer 1

As we all know that an ideal gas obeys the gas law and using the ideal gas equation we can find out about the nature and behaviour of many gases. It depends mainly on pressure, volume and moles.

Complete answer:
As we all know that all gases follow the ideal gas law or ideal gas equation which is
$PV = nRT$ where P is the pressure of the gas, V is volume of the gas, n is the number of moles or amount of substance of gas, R is the gas constant and T is the temperature. From this equation we can find out any parameter which is not given. Like in the question we are given with $P = 740mm$, $mass = 5.0g$ and $T = {50^ \circ }C$ and we need to find the volume of the gas. So to calculate it we will first convert these quantities into standard forms for we know that:
$760mmHg = 1atm \\\ P = \dfrac{{740}}{{760}}atm \\\$
$T = 273 + 50 \\\ T = 323K \\\$
$moles = \dfrac{{mass}}{{molecular\;mass}} \\\ moles = \dfrac{5}{{26}} \\\$
As the molecular mass of acetylene is $26g$. Now by applying the ideal gas equation, we can get the volume of the gas:
$PV = nRT \\\ \Rightarrow V = \dfrac{{nRT}}{P} \\\ \Rightarrow V = \dfrac{{5 \times 323 \times 760 \times 0.0821}}{{740 \times 26}} \\\ \Rightarrow V = 5.23L \\\$

**Therefore the correct answer is (A).

Additional information: **
Some important points:
1. Gases exert equal pressure in all directions.
2. Mass of a gas can be calculated by taking the difference of mass of gas filled vessel and mass of empty vessel.
3. Gases do not have their own volume, thus the volume of the container is taken as the volume of gas.
4. Gases which obey the gas law at all ranges of temperature and pressure are called ideal gases and which obey gas law at high temperature and low pressure are called real gases.
5. At a particular temperature a real gas behaves as an ideal gas and that temperature is called Boyle’s temperature.

Note:
If we heat a gas or say increase the temperature the gas molecules will start moving faster and thus the kinetic energy will increase and when the volume is decreased the temperature will decrease. Also if we are given the density and molecular mass of a gas we can calculate the other parameters by simply replacing n and V quantities in the ideal gas equation.