Question

Calculate the volume occupied by $5g$ of acetylene gas at ${{50}^{0}}C$ and 740mm of pressure.

Answer 1

Hint: The equation of ideal gas is only followed by the ideal gases. A gas that would obey Charles and Boyle’s Law under all the conditions of pressure and temperature is called an ideal gas. The behaviour of gases is described by certain laws as Boyle's Law Avogadro's Law, , Charles'Law.

Complete step by step solution:
According to Avogadro's Law: volume is proportional to number of moles (P and T constant)
According to Boyle's Law: Volume is proportional to Pressure (T and n constant)
According to Charles' Law ; Volume is proportional to Temperature (P and n constant)
 Combining the three laws ; we get:
\[V=\dfrac{RnT}{P}\]
'R' is the proportionality constant.
On rearranging the above equation we get:
\[PV=nRT\]
This is the ideal gas equation as it is obeyed by the gases, being hypothetical called ideal gases under all conditions of pressure and temperature.
However no gas exists in nature that is perfectly ideal. But the gases may show nearly ideal behaviour under the conditions of high temperature and low pressure and these gases are called real gases. Equation of state : As the equation of ideal gas expresses the relation between the four variables that describe the condition of a gas, therefore it is called the equation of state for gases.
Considering 1 mole of gas, then
$PV = RT$ (:n =1 mol)
Now, we have R (Proportionality constant). The properties of R are:
(i) It is Gas constant
(ii) It is same for all the gases
Therefore it is also called universal gas constant. The value of 'R' is very much dependent on which pressure and volume are taken. So, the value of 'R' when pressure and volume are expressed in different units.
Now acetylene is ${{C}_{2}}{{H}_{2}}$
So it's molar mass is 26 gram
So no of moles of ${{C}_{2}}{{H}_{2}}$ is $\dfrac{26}{5}=5.2$
Now using the equation $PV=nRT$
$V=\dfrac{nRT}{P}$
$V=\dfrac{5.2\times 8.314\times (273+50)\times 760}{740\times 26}=5.24L$
So the volume occupied is 5.24 litre.

Note: i. Gases have a tendency to occupy all available space. So the volume of gas can be considered as the volume of a container.
ii. Temperature is the degree of hotness and coldness.
iii. Pressure is the force exerted by gas per unit area.