Question

What volume will a gas occupy at 740mm pressure which at 1480 mm occupies 500 cc? [Temperature being constant].

Answer 1

Hint: Boyle in the mid 1600’s observed that the product of the pressure and volume of a gas are observed to be nearly constant provided that the temperature is kept constant. This is always true in the case of an ideal gas.
 $ P \times V = {\text{constant}} $
This relationship between pressure and volume of an ideal gas is known as the Boyle's Law.

Complete answer:
Since it is given in the question that temperature can be assumed as constant, we can apply Boyle’s Law.
According to Boyle's Law we know that:
 $ \Rightarrow P \times V = {\text{constant}} $
We can rewrite this as
 $ \Rightarrow {P_1} \times {V_1} = {P_2} \times {V_2} $
Where $ {P_1} $ is the pressure at the volume $ {V_1} $
 $ {P_2} $ is the pressure at the volume $ {V_2} $
Thus from the given question we can say that:
 $ {P_1} $ = 1480 mm
 $ {V_1} $ = 500 cc
 $ {P_2} $ = 740 mm
 $ {V_2} $ = x
Thus we can rewrite the equation and substitute the above values and obtain the equation given below:
 $ \Rightarrow {V_2} = \dfrac{{{P_1} \times {V_1}}}{{{P_2}}} $
 $ \Rightarrow {V_2} = \dfrac{{1480 \times 500}}{{740}} $
 $ \Rightarrow {V_2} = 1000cc $
Thus the volume of gas occupied at a pressure of 740 mm is 1000 cc.

Note:
Another method of getting the given equation is by assuming the ideal gas equation. According to the ideal gas equation which is derived by using Boyle’s Law, Charles law and Avogadro’s law,
 $ \Rightarrow P \times V = n \times R \times T $
Thus we can say that at constant temperature the entire right hand side of the equation becomes constant. Thus we can equate
 $ \Rightarrow {P_1} \times {V_1} = {P_2} \times {V_2} $
This will again give us the relation that we want to use in a given question.