Question

The respective volumes (in ml) of $0.2M\text{ HCl}$and $0.6M\text{ HCl}$ to be mixed together for preparing $1000\text{ }ml\text{ }of 0.3M\text{ }HCl$ are :
(a) $300\text{ and 700 }$
(b)$750\text{ and 250 }$
(c) $250\text{ and 750 }$
(d) $500\text{ and 500 }$

Answer 1

Hint: We have been given the molarities of the solutions of $HCl$ which combines together to form the $1000\text{ }ml\text{ }of0.3M\text{ }HCl$. So, thus we can easily find the volume of the solutions by assuming them as $x$ and $1000-x$ as total volume of solution is $1000ml$ and applying the formula as: ${{M}_{1}}{{V}_{1}}+{{M}_{2}}{{V}_{2}}={{M}_{3}}{{V}_{3}}$. Now you can easily solve it.

Complete Solution :
First of let’s discuss what is molarity. By the term molarity we mean, the no. of moles of the solute to the volume of the solution in litres or milliliters. It denoted as M. So,
$molarity(M)=\dfrac{no.\text{ }of\text{ }moles\text{ }of\text{ }the\text{ }solute}{volume\text{ }of\text{ }the\text{ }solution\text{ }in\text{ }liters}$

- Now considering the statement:
We can find the volume of the solutions having the molarities as $0.2M$ and $0.6M$ which are mixed together to prepare $1000\text{ }ml\text{ } of 0.3M\text{ }HCl$ as;
${{M}_{1}}{{V}_{1}}+{{M}_{2}}{{V}_{2}}={{M}_{3}}{{V}_{3}}$ ----------------(1)
As we know that:
 molarity, ${{M}_{1}}=0.2M$(given)
molarity, ${{M}_{2}}=0.6M$(given)
molarity, ${{M}_{3}}=0.3M$(given)
${{V}_{3}}=1000\text{ ml}$

So. let’s suppose that:
$\begin{align}
 & {{V}_{1}}=x\text{ and} \\
 & {{V}_{2}}=1000-x \\
\end{align}$

Now, put these all values in equation (1), we get:
$\begin{align}
 & 0.2\times x+0.6\times (1000-x)=0.3\times 1000 \\
 & 0.2x+600-0.6x=300 \\
 & 0.4x=600-300 \\
 & x=\dfrac{300}{0.4} \\
 & \text{ =750} \\
\end{align}$

So, the value of :
$\begin{align}
 & {{V}_{1}}=750\text{ }ml\text{ and} \\
 & {{V}_{2}}=1000-750\text{ }ml \\
 & \text{ = 250 }ml \\
\end{align}$
Hence, the volumes of the solutions having the molarities as $0.2M$ and $0.6M$ which are mixed together to prepare $1000\text{ }ml\text{ }of0.3M\text{ }HCl$ are $750\text{ ml and 250 ml}$.
So, the correct answer is “Option B”.

Note: Molarity of the solution changes with change in the temperature of the solution because with the increase in the temperature , the volume of the solution changes and hence the molarity changes. If temperature is increased, volume is increased and hence molarity decreases. On the contrary, if temperature is decreased , volume is decreased but the molarity increases. So, this means that the molarity and the volume are inversely proportional to each other.