Question:
$1 \,L$ of a gas is at a pressure of $10^{-6} \, mm$ of Hg at $25^{\circ} C$. How many molecules are present in the vessel?
$1 \,L$ of a gas is at a pressure of $10^{-6} \, mm$ of Hg at $25^{\circ} C$. How many molecules are present in the vessel?
Updated On: Jan 30, 2025
- $3.2 \times 10^6$
- $3.2 \times 10^{13}$
- $3.2 \times 10^{10}$
- $3 \times 10^4$
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The Correct Option is B
Solution and Explanation
$\frac{\rho_{1} V _{1}}{ T _{1}}=\frac{\rho_{2} V _{2}}{ T _{2}}$
$\Rightarrow \frac{10^{-6} \times 1000}{298}=\frac{760 \times V _{2}}{273}$
$V _{2}=1.2 \times 10^{-6} cc ($ at $\quad STP )$
No. of molecules $=\frac{6.02 \times 10^{23}}{22400} \times 1.2 \times 10^{-6}$
$=3.2 \times 10^{13}$
$\Rightarrow \frac{10^{-6} \times 1000}{298}=\frac{760 \times V _{2}}{273}$
$V _{2}=1.2 \times 10^{-6} cc ($ at $\quad STP )$
No. of molecules $=\frac{6.02 \times 10^{23}}{22400} \times 1.2 \times 10^{-6}$
$=3.2 \times 10^{13}$
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Concepts Used:
Gas Laws
The gas laws were developed at the end of the 18th century, when scientists began to realize that relationships between pressure, volume and temperature of a sample of gas could be obtained which would hold to approximation for all gases.
The five gas laws are:
- Boyle’s Law, which provides a relationship between the pressure and the volume of a gas.
- Charles’s Law, which provides a relationship between the volume occupied by a gas and the absolute temperature.
- Gay-Lussac’s Law, which provides a relationship between the pressure exerted by a gas on the walls of its container and the absolute temperature associated with the gas.
- Avogadro’s Law, which provides a relationship between the volume occupied by a gas and the amount of gaseous substance.
- The Combined Gas Law (or the Ideal Gas Law), which can be obtained by combining the four laws listed above.