Question

What will be the final concentration of a solution of \(50 \mathrm{ml}\) of \(.5 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) added to \(75 \mathrm{ml}\) of \(25 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) (the final volume is \(125 \mathrm{ml}\) )?

Short answer

The final concentration of the mixed solution of \(\mathrm{H}_{2}\mathrm{SO}_{4}\) is \(15\,\mathrm{M}\).

Step-by-step solution

Calculate the moles of \(\mathrm{H}_{2}\mathrm{SO}_{4}\) in each solution

First, we need to determine the number of moles of \(\mathrm{H}_{2}\mathrm{SO}_{4}\) in each solution. We can use the formula: moles = concentration × volume. For the first solution: moles of \(\mathrm{H}_{2}\mathrm{SO}_{4} = 0.5\,\mathrm{M} \times 50\,\mathrm{ml}\) For the second solution: moles of \(\mathrm{H}_{2}\mathrm{SO}_{4} = 25\,\mathrm{M} \times 75\,\mathrm{ml}\)

Determine the total moles of \(\mathrm{H}_{2}\mathrm{SO}_{4}\)

Now that we have the moles of \(\mathrm{H}_{2}\mathrm{SO}_{4}\) in each solution, we need to add them together to get the total moles of \(\mathrm{H}_{2}\mathrm{SO}_{4}\) in the final mixture. Total moles of \(\mathrm{H}_{2}\mathrm{SO}_{4} = 0.5\,\mathrm{M} \times 50\,\mathrm{ml} + 25\,\mathrm{M} \times 75\,\mathrm{ml}\)

Calculate the final concentration of \(\mathrm{H}_{2}\mathrm{SO}_{4}\)

Finally, to find the final concentration of \(\mathrm{H}_{2}\mathrm{SO}_{4}\) in the mixture, we will divide the total moles of \(\mathrm{H}_{2}\mathrm{SO}_{4}\) by the total volume of the mixture (given as \(125\,\mathrm{ml}\)). Final concentration of \(\mathrm{H}_{2}\mathrm{SO}_{4} = \frac{0.5\,\mathrm{M} \times 50\,\mathrm{ml} + 25\,\mathrm{M} \times 75\,\mathrm{ml}}{125\,\mathrm{ml}}\) Now, calculate the final concentration: Final concentration of \(\mathrm{H}_{2}\mathrm{SO}_{4} = \frac{(0.5\,\mathrm{M} \times 50\,\mathrm{ml}) + (25\,\mathrm{M} \times 75\,\mathrm{ml})}{125\,\mathrm{ml}}\) Simplifying, Final concentration of \(\mathrm{H}_{2}\mathrm{SO}_{4} = \frac{25\,\mathrm{M} \times 75\,\mathrm{ml}}{125\,\mathrm{ml}} = \frac{1875\,\mathrm{M} \,\mathrm{ml}}{125\,\mathrm{ml}} = 15\,\mathrm{M}\) So, the final concentration of the mixed solution will be \(15\,\mathrm{M}\) of \(\mathrm{H}_{2}\mathrm{SO}_{4}\).

Key concepts

Molarity

Molarity, denoted by the symbol 'M', is a unit of concentration used in chemistry to describe the amount of a substance in a given volume of liquid. Specifically, molarity refers to the number of moles of a substance per liter of solution. A mole is simply a standard number of particles, about 6.022 × 10²³ particles, which is Avogadro's number.

Molarity is calculated using the formula:
\[ \text{Molarity} (M) = \frac{\text{moles of solute}}{\text{liters of solution}} \].
When students need to determine the molarity of a diluted or mixed solution, they need to compute how the concentration changes when volumes are combined. If you have a certain volume of one molarity solution and mix it with another volume of a different molarity, the final molarity can be found by ensuring the total moles of solute are accounted for in the total volume of the new solution.

Solution Concentration

Understanding solution concentration is crucial when working with chemical solutions, as it tells us how much solute is present in a given volume of solvent. Concentration can be expressed in many ways, such as molarity, mass percent, or parts per million (ppm). The concept of concentration is essential in predicting how substances will interact in a solution, including reaction rates and equilibrium positions.

To avoid any confusion, always remember to check units when performing concentration calculations. It's also important to distinguish between the solute (the substance being dissolved) and the solvent (the liquid it's being dissolved in). In our exercise, the solute is sulfuric acid (\(\mathrm{H}_{2}\mathrm{SO}_{4}\)), and the solvent is water, which together make up our acidic solution.

Moles and Volume

The relationship between moles and volume is central to understanding how to calculate concentrations. Moles provide a way to measure the amount of a substance, while volume provides information about the space it takes up. To calculate the number of moles from a solution's molarity and volume, you use the formula: \[ \text{moles} = \text{molarity} \times \text{volume} \].
When the volume is given in milliliters (ml), it needs to be converted to liters (L) by dividing by 1000, because molarity is defined as moles per liter. This conversion is a simple but crucial step in ensuring the accuracy of your calculations.

Remember, the volume of a solution may not be the sum of the volumes of the individual components due to volume contraction or expansion during mixing, a concept to keep in mind while working through dilution problems.

Dilution of Solutions

Dilution is the process of reducing the concentration of a solute in a solution, usually by adding more solvent. In chemistry, this is a common practice to achieve the desired concentration for a particular reaction or analysis.

There's a key principle in dilution: the amount of solute remains constant before and after the dilution, since you're not adding or removing the solute, only changing the amount of solvent. Mathematically, this principle is captured by the dilution formula: \[ M_1 V_1 = M_2 V_2 \],
where \(M_1\) and \(V_1\) represent the molarity and volume of the initial concentrated solution, respectively, and \(M_2\) and \(V_2\) are the molarity and volume of the final diluted solution. This equation allows us to calculate the final concentration after dilution, as we illustrated in the textbook exercise with sulfuric acid.