Question

If ${{10}^{-4}}d{{m}^{3}}$ of water is introduced into a $1.0d{{m}^{3}}$ flask at 300K, then how many moles of water are in the vapour phase when equilibrium is established?
(given vapour pressure of ${{H}_{2}}O$ at 300 K is 3170 Pa; $R = 8.314J{{K}^{-1}}mo{{l}^{-1}}$)
A. $5.56\times {{10}^{-3}}mol$
B. $1.53\times {{10}^{-2}}mol$
C. $4.46\times {{10}^{-2}}mol$
D. $1.27\times {{10}^{-3}}mol$

Answer 1

Hint: To solve this question we have to use the Ideal gas equation that is PV = nRT. In the question vapour pressure of water is given so, the relation between the vapour pressure and ideal gas of water is ${{P}_{vap}}V = {{n}_{vap}}RT$. Convert the values of volume in the S.I unit from the C.G.S unit. 1dm = 0.1 m

Complete Solution :
As you have learned about the Ideal gas law in your chemistry lessons, Ideal gas is also known as perfect gas. This law establishes a relationship between pressure, volume, temperature and amount of gas(n) and they are four variables of gases.
Ideal gas equation is written as,
PV = nRT
Where P = Pressure of the gas
V = Volume of the gas
n = moles or amount of gas
R = universal gas constant
T = temperature.
If we have to write this equation in term of vapour pressure of then we write it as,
${{P}_{vap}}V = {{n}_{{{H}_{2}}O}}RT$ ……..(1)
Where, ${{P}_{vap}}$ = vapor pressure of water
${{n}_{{{H}_{2}}O}}$ = moles of water

- In the question it is told that we have to find the moles of water in vapour phase, and the values that are given in the question are,
${{P}_{vap}}$ = 3170 Pa
V =${{10}^{-4}}d{{m}^{3}}={{10}^{-3}}{{m}^{3}}$
T = 300 K
$R = 8.314J{{K}^{-1}}mo{{l}^{-1}}$
Now put all the values in formula 1, you will get,
$3170\times {{10}^{-3}}={{n}_{{{H}_{2}}O}}\times 8.314\times 300$
\[\Rightarrow {{n}_{{{H}_{2}}O}}=\dfrac{3170\times {{10}^{^{-3}}}}{8.314\times 300}=1.27\times {{10}^{-3}}mol\]
So, the correct answer is “Option D”.

Note: Change the units wherever needed and change according to the requirement. Vapour pressure is known as pressure of a vapour when it comes in contact with its solid or liquid form. The value of universal gas constant also changes according to the units.