Question

1L of a gas is at a pressure of \[{{10}^{-6}}\]of Hg at \[{{25}^{o}}C\]. How many molecules are present?
(A)- \[3.2\times {{10}^{6}}\]
(B)- \[3.2\times {{10}^{13}}\]
(C)- \[3.2\times {{10}^{10}}\]
(D)- \[3\times {{10}^{4}}\]

Answer 1

Hint: We can calculate the number of molecules using the ideal gas equation. In the above question we are given the pressure, volume and temperature of the gas.
\[PV=nRT\](Ideal gas equation)
Number of molecules …

…where Na is Avogadro number


Complete step by step solution:
Let’s look at the answer

The formula for the ideal gas equation is:
\[PV=nRT\]…..Where P is pressure, V is volume, R is gas constant, n is number of moles, and T is absolute temperature.
On transforming the equation for the number of moles, n, we get
\[n=\dfrac{PV}{RT}\]……..eq1
Now, it is given in the question that
\[P={{10}^{-6}}\]of Hg \[=\dfrac{{{10}^{-6}}}{760}atm\]
\[V=1L\]
\[R=0.0821{}^{Latm}/{}_{molK}\]
\[T={{25}^{o}}C=25+273=298K\]
Now, put the values of P, V, T in eq1
We get,
\[n=\dfrac{{{10}^{-6}}\times 1}{760\times 0.0821\times 298}\]……..eq2
Now, using the formula for number of molecules
We get,
Number of molecules ……where Na is Avogadro number
On putting the values of n from eq2 and Na\[=6.02\times {{10}^{23}}\]
We get the number of molecules as:
Number of molecules \[=\dfrac{{{10}^{-6}}\times 6.02\times {{10}^{23}}}{760\times 0.0821\times 298}\]\[=3.2\times {{10}^{13}}\]
So, the number of molecules of the given gas are\[=3.2\times {{10}^{13}}\]

Hence, our final answer is option (B).


Note: The temperature should be converted into kelvin. The pressure should be taken into atmospheres. The value of R should be taken according to the units of P and V. If temperature is not given then take 298K as the standard temperature.