Question

A gas has a volume of $580\,c{m^3}$ at a certain pressure. If its pressure is increased by $0.96\,atm$, its volume becomes $100\,c{m^3}$ . The new pressure of the gas is:
A. 1.16 atm
B. 1.60 atm
C. 1.75 atm
D. 1.25 atm

Answer 1

Hint:The behavior of gases is described by some laws based on some experiments. The pressure of a given amount of gas is directly proportional to its absolute temperature, provided that the volume does not change similarly the volume of given gas is inversely proportional to its pressure when the temperature is constant.

Complete answer:
First we have Boyle’s law, which says volume of given gas is inversely proportional to the pressure when temperature remains constant. Mathematically, $V \propto \dfrac{1}{P}$ at constant n and t
Second is Charles’s law, volume of given gas is directly proportional to the temperature at constant pressure. Mathematically, $V \propto T$ at constant P
Third law is Avogadro’s law, under the same temperature and pressure, equal volume of all gases contain the same number of molecules. Mathematically, $V \propto n$ at constant T and P
By combining these three equations or laws, we have ideal gas equation: $V \propto \dfrac{{nT}}{P}$
By removing the proportionality constant, we have, $ PV = nRT $
Now in the given question, we are using Boyle’s law ${P_1}{V_1} = {P_2}{V_2}$
Given, $V_1= 580\,c{m^3}$
$V_2= 100\,c{m^3}$
Let the original pressure be X, then $P_1$ = X
Pressure increases by 0.96 so $P_2$ = X+0.96
By putting all the value at the equation, we have
$
\Rightarrow X \times 580 = (X + 0.96) \times 100 \\
\Rightarrow \dfrac{{X \times 580}}{{100}} = (X + 0.96)
 $
Solving this equation further ,$5.8X = X + 0.96$
On further calculation, we get the value as
$
\Rightarrow (5.8 - 1)X = 0.96 \\
\Rightarrow 4.8X = 0.96
 $
 $\Rightarrow X = 0.2$
The new pressure will be $X + 0.96\,atm = 0.2 + 0.96 = 1.16\,atm$.

Hence the correct option is A. 1.16 atm

Note:
The combination of various laws is also known as ideal gas law. An ideal gas is a hypothetical gas whose behavior is independent of the attractive and repulsive forces that actually are present in the real gases. In reality there is no such gas. But yes, ideal gas law works well at low temperature and high pressure.