Question

$6.022\ \text{x 1}{{\text{0}}^{20}}$ molecules of urea are present in $100 mL$ of its solution at STP. The concentration of solution is:
(A) 0.02 M
(B) 0.01 M
(C) 0.001 M
(D) 0.1 M

Answer 1

The type of concentration we have to calculate is molarity as the options are in terms of molar concentration. First, find the number of moles of solute i.e. urea. After that substitute the values in the formula for molarity given below.
$\text{M = }\dfrac{\text{n}}{\text{V}}$
Where,
M is molarity of the solution
n is the number of moles of solute
V is the volume of the solution in liters

Complete step by step solution:
We will try to define what STP is to gain a clear understanding of the conditions present.
STP stands for Standard Temperature and Pressure.
-Standard Temperature is ${{0}^{0}}C$ or $273.15 K$.
-Standard Pressure is $1 atm$ or $76$ $cm$ $of$ $Hg$ or $101.325 kPa$
To avoid the interference of Temperature and pressure in calculation reactions are performed at STP.
We will find the number of moles of urea dissolved in the solvent.
$n=\dfrac{total\ molecules}{{{N}_{A}}}$
$n=\dfrac{6.02\ \text{x 1}{{\text{0}}^{20}}}{6.02\text{ x 1}{{\text{0}}^{23}}}$
$n={{10}^{-3}}$
Substituting the values in the question given in hint,
$\text{M = }\dfrac{{{10}^{-3}}}{0.1}$ $= 0.01 M$

Therefore, the correct answer is option (B).

Note: NTP stands for normal temperature and pressure. NTP is used as an alternative to STP for calculation. At NTP,
- Temperature is taken as ${{20}^{0}}C$ or $293.15 K$,
- Pressure is taken as $1atm$ or $101.325 kPa$.
Always remember to convert the volume of the solution into litres before substituting into the formula for molarity. This will help avoid confusion as well as errors.