Question

If $500ml$ of $0.2MNaCl$ solution is mixed with $200ml$ of $0.16MNaCl$ solution and then diluted to one liter with water, what is the molarity of the resulting solution?

• A. $0.2M$
• B. $0.33M$
• C. $0.42M$
• D. $0.54M$

Answer 1

Answer: (C)

$0.42M$

Two solutions are mixed, hence the molarity of the resulting solution is calculated using the formula-

$M_1{V}_1$ $+$ $M_2{V}_2$ $=$ $M$$\ast$($V_1$$+$$V_2$)

where $M_1$ is $0.2M$, $V_1$ is $500ml$, $M_2$ is $.16M$ and $V_2$ is $200ml$ and $M$ is the molarity of the resulting solution which is to be found out. Putting the values in the equation we get,

($0.2$$\ast$$500$) $+$ ($0.16$$\ast$$200$) $=$ $M$$\ast$($500$$+$$200$)

From this, the value of $M$ is obtained as $0.18M$.

The solution was then diluted to one litre. We already had ($500$$+$$200$)ml that is $700ml$. Thus to make it one litre, we added $300ml$ of water. And the new molarity has now become $M^{\prime \prime }$

We will now use the formula $M$$V$$=$$M^{\prime \prime }$$V^{\prime \prime }$

$M$ is $0.18M$, $V$ is $700ml$, $M^{\prime \prime }$ is to be found out and $V^{\prime \prime }$ is $300ml$

Putting these values in the above equation we get,

$0.18$$\ast$$700$$=$$M^{\prime \prime }$$\ast$$300$

Thus, $M^{\prime \prime }$ $=$ $\frac{126}{300}$, which is equal to $0.42M$

Option C is the correct answer.