Animated Solution for Chemistry - Basic Concepts in Chemistry: Two solutions of a substance (non-electrolyte) are mixed in the following manner. $480\text{ mL}$ of $1.5\text{ M}$ first solution + $520\text{ mL}$ of $1.2\text{ M}$ second solution. What is the molarity of the final mixture ?

Imagine you are a chemist standing in a laboratory. In front of you are two beakers containing solutions of the exact same non-electrolyte substance. The first beaker holds $480\text{ mL}$ of a $1.5\text{ M}$ solution, and the second beaker holds $520\text{ mL}$ of a $1.2\text{ M}$ solution. Your task is to pour both of these solutions into a single, larger container.

What happens to the concentration? It won't just be the sum of the two molarities, nor will it be a simple average. Because the volumes are different, the final concentration will be a weighted average of the two initial concentrations.

To find the exact molarity of the final mixture, we rely on a fundamental principle of chemistry: the conservation of mass (or moles). When you mix two solutions, the total number of moles of the solute in the final mixture is simply the sum of the moles from each individual solution.

Mathematically, since moles ($n$) equal molarity ($M$) multiplied by volume ($V$), we can express the total moles as $n_{\text{total}}=M_1{V}_1+M_2{V}_2$.

The final molarity ($M_f$) is then the total moles divided by the total volume:

Now, let's substitute our known values into this master equation.

For the first solution, we have $M_1=1.5\text{ M}$ and $V_1=480\text{ mL}$. For the second solution, $M_2=1.2\text{ M}$ and $V_2=520\text{ mL}$.

You might be wondering, "Shouldn't we convert milliliters to liters?" In this specific formula, you don't have to! Because we have volume in both the numerator and the denominator, the conversion factor of $10^{-3}$ will perfectly cancel out. We are essentially calculating total millimoles divided by total milliliters, which still gives us moles per liter (Molarity).

Let's perform the arithmetic.

First, calculate the millimoles from each beaker: $1.5\times 480=720\text{ mmol}$ $1.2\times 520=624\text{ mmol}$

Next, add them together to find the total millimoles in the numerator: $720+624=1344\text{ mmol}$

Now, add the volumes to find the total volume in the denominator: $480+520=1000\text{ mL}$

Finally, divide the total millimoles by the total volume:

Rounding to two decimal places, we get $1.34\text{ M}$. This perfectly matches option (b). It's a beautifully straightforward application of the mole concept, but it forms the bedrock for much more complex titration and equilibrium problems you'll face in the future!