Question

The two bulbs of volume 5 liter and 10 liter containing an ideal gas at 9atm and 6atm respectively are connected. What is the final pressure in the two bulbs if the temperature remains constant?
(A) 15 atm
(B) 7 atm
(C) 12 atm
(D) 21 atm

Answer 1

Hint The two bulbs are connected together so the final product of pressure and volume will be equal to the individual products of pressure and volume. As given according to Boyle's law the product of pressure and volume remains constant provided the temperature remains constant. The final volume will be equal to the sum of individual volumes and thus we will find the final pressure.
Formula Used: ${{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}}=P({{V}_{1}}+{{V}_{2}})$
where ${{P}_{1}}$ is pressure of first gas
${{P} {2}}$ is pressure of second gas
${{V} {1}}$is volume of first gas
${{V} {2}}$ is volume of second gas
P is final pressure

Complete Step By Step Solution:
Given are two ideal gases with their pressure equal to 9atm and 6atm respectively and their volumes being equal to 5 liter and 10 liter. The final volume will be simply the addition of these two volumes i.e. $9atm+6atm\, =\, 15atm$
To find the final pressure we have the relation, ${{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}}=P({{V}_{1}}+{{V}_{2}})$
So, substituting the values we get,
\begin {align} & 9\times \,5\,+\,6\times 10\, =\, P (15) \\\ & 45+60=P\times 15 \\\ & 105=P\times 15 \\\ & \ \,P\,=\frac{105}{15}=7 \\\ \end{aligned}

Therefore, the final pressure is 7atm. So, the correct choice is (B).

Additional Information:
Ideal gas law is given by $PV=n R T$. An ideal gas is a hypothetical gas in which intermolecular forces do not exist to complicate the simple Ideal Gas Law. The term $\frac{PV}{n R T}$ is called the compression factor and it is a measure of the ideality of the gas. An ideal gas will always equal 1 when plugged into this equation. The greater it deviates from the number 1, the more it will behave like a real gas rather than an ideal. . An ideal gas law is formed by combining Boyle’s law, Avogadro law and Charles’s law.
Boyle’s Law was given by Robert Boyle in 1662. According to this law, the pressure of a gas varies inversely with its volume at constant temperature. If the pressure is decreased the volume increases and vice versa. This law has many practical applications. The simplest real life example of Boyle’s law is breathing air in and out of the lungs.
According to Charles’s Law volume and temperature are in direct proportion with each other provided pressure is kept constant.
Avogadro Law states that at given conditions of temperature and pressure there is equal no. of molecules in equal volumes of different gases.

Note: The S.I unit of pressure is Pascal which is basically equal to the force of 1 N applied on 1 square meter of area. The other units of pressure are ‘atm’ and ‘torr’, 1 atm= 101325 Pa = 760 torr. The concept of ideal gas is a theoretical concept in which the atoms or molecules are considered completely elastic without any intermolecular forces between them.