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

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.