Question

How many milliliters of \(0.126 \mathrm{M} \mathrm{HClO}_{4}\) (perchloric acid) are required to give \(0.150 \mathrm{~mol} \mathrm{HClO}_{4} ?\)

Short answer

You need 1190.5 mL of 0.126 M HClO₄.

Step-by-step solution

Identify Given Values

We are given the molarity of perchloric acid, which is \(0.126 \text{ M}\), and we need \(0.150 \text{ mol}\) of \(\text{HClO}_{4}\).

Understand the Formula

To find the volume needed, we use the formula relating molarity (\(M\)), moles (\(n\)), and volume (\(V\)). This formula is: \(M = \frac{n}{V}\). Rearranging for volume gives \(V = \frac{n}{M}\).

Substitute the Values

Substitute the given values into the formula to find the volume: \(V = \frac{0.150 \text{ mol}}{0.126 \text{ M}}\).

Calculate the Volume

Perform the calculation: \(V = \frac{0.150}{0.126} \approx 1.1905 \text{ L}\). Convert this to milliliters by multiplying by 1000: \(1.1905 \text{ L} \times 1000 = 1190.5 \text{ mL}\).

Final Answer

The required volume of \(0.126 \text{ M} \text{HClO}_{4}\) is \(1190.5 \text{ mL}\).

Key concepts

Understanding Molarity

Molarity is a way of expressing the concentration of a solution. It tells us the number of moles of solute present in a liter of solution. The formula for molarity is:

• \( M = \frac{n}{V} \)

where:

• \( M \) is the molarity in moles per liter (\( ext{mol/L} \) or \( ext{M} \))
• \( n \) is the number of moles of the solute
• \( V \) is the volume of the solution in liters

In this exercise, knowing the molarity of perchloric acid allows us to calculate the volume required to reach a specific number of moles. By having the molarity \(0.126 \text{ M}\) and the desired moles \(0.150 \text{ mol}\), we can determine how much of the solution you need to get the right amount of solute. This brings in the importance of understanding that molarity is a direct link between the chemical quantity and the solution's total volume. Understanding molarity helps in practical scenarios like mixing the right concentration of solutions in labs or industrial settings.

Calculating Volume Using Molarity

Finding the volume of a solution when the molarity and number of moles are given is a straightforward task. Given the relationship \( M = \frac{n}{V} \), you can rearrange this to solve for volume:

• \( V = \frac{n}{M} \)

Here, the volume \( V \) is what we are seeking. It is expressed in liters. By substituting in the number of moles and molarity, you get:

• \( V = \frac{0.150 \text{ mol}}{0.126 \text{ M}} \)
• \( \approx 1.1905 \text{ L} \)

This means you need about 1.1905 liters of \(0.126 \text{ M} \) perchloric acid to get \(0.150\) moles of \(\mathrm{HClO}_{4}\). Volume calculation in solution stoichiometry enables chemists to prepare solutions of exact concentrations and quantities necessary for experiments and reactions.

The Importance of Unit Conversion

In chemical calculations, correct unit conversion is crucial. Sometimes, volume needs to be presented in different units than initially calculated. Chemists often need volumes in milliliters (mL) for practical use, especially in lab settings where smaller quantities are handled. To convert from liters to milliliters, you use the simple conversion:

• 1 liter = 1000 milliliters

After calculating the volume in liters, \(1.1905 \text{ L}\), the conversion to milliliters is straightforward:

• \(1.1905 \text{ L} \times 1000 = 1190.5 \text{ mL}\)

This gives the volume needed in a more practical unit for handling during experimentation or solution preparation. Mastering unit conversion allows for precise preparation and communication of chemical data, ensuring accuracy in experiments.