Animated Solution for Chemistry - Basic Concepts in Chemistry: The molarity of a solution obtained by mixing $750\text{ mL}$ of $0.5\text{ M}$ HCl with $250\text{ mL}$ of $2\text{ M}$ HCl will be

Finding the Final Molarity

Imagine you are in a chemistry lab, and you have two beakers containing the exact same acid, but at different concentrations. One is a large beaker filled with a dilute solution, and the other is a smaller beaker with a highly concentrated solution. What happens when you pour them both into a single, larger container?

This is a classic scenario in stoichiometry, and solving it relies on one of the most fundamental principles in chemistry: The Conservation of Moles.

When you mix two solutions of the same substance, the total amount of the solute (the acid, in this case) doesn't magically disappear or multiply. The total number of moles in the final mixture is simply the sum of the moles from the first beaker and the moles from the second beaker.

Mathematically, we can express this as:

We also know that the number of moles ($n$) is the product of Molarity ($M$) and Volume ($V$). Therefore, $n=M\times V$. If we substitute this into our conservation equation, we get the master equation for mixing solutions.

By substituting $M\times V$ for the moles, we arrive at the formula for the final molarity ($M_f$):

Here, $M_1{V}_1$ represents the millimoles of HCl from the first beaker, and $M_2{V}_2$ represents the millimoles from the second beaker. The denominator, $V_1+V_2$, is the total volume of the new mixture.

Let's bring back the values from our specific problem. We have: - Beaker 1: $V_1=750\text{ mL}$ and $M_1=0.5\text{ M}$ - Beaker 2: $V_2=250\text{ mL}$ and $M_2=2\text{ M}$

Now, we carefully substitute these values into our master equation:

Let's calculate the numerator first. Don't rush through this; silly mistakes often happen here. $0.5\times 750=375$ millimoles $2\times 250=500$ millimoles

The total volume in the denominator is simply $750+250=1000\text{ mL}$.

Putting it all together:

And there we have it! The final molarity of the mixed solution is $0.875\text{ M}$.

This method works perfectly when mixing two solutions of the same nature (like two acids or two bases). But what if you mixed an acid and a base? In that case, they would neutralize each other. Instead of adding the moles, you would subtract them to find the remaining unreacted moles: $M_f=\frac{|M_1{V}_1-M_2{V}_2|}{V_1+V_2}$. Keep this in mind, as it's a favorite twist in competitive exams!