Calculating the Volume of 12.0 M HCl Needed for a Specific Amount of HCl

Understanding how to calculate the volume of a solution needed to contain a specific number of moles is crucial for any chemistry experiment or laboratory work. Whether you're a student, a researcher, or a practicing chemist, knowing the correct formula and steps to determine the required volume can significantly enhance the accuracy and efficiency of your procedures.

Definition of Molar Concentration

The molar concentration (also known as molarity) of a solution is defined as the number of moles of solute per liter of solution. This is denoted by the formula:

[text{Molar concentration (M)} frac{text{Moles of solute}}{text{Volume of solution (L)}}]

In simpler terms, the product of the volume of the solution and the molar concentration will give us the moles of solute:

[text{Volume of solution} times text{molar concentration} text{Moles of solute}]

Calculation for 12.0 M HCl and 3.00 Moles of HCl

For the specific example, we need to find the volume of a 12.0 M hydrochloric acid (HCl) solution that contains 3.00 moles of HCl. We can use the formula for molar concentration:

[text{Volume (L)} frac{text{Moles}}{text{Concentration (M)}}]

Plugging in the values:

[text{Volume (L)} frac{3.00 text{ moles}}{12.0 text{ M}} 0.25 text{ L}]

To convert this volume from liters to milliliters, we use the conversion factor 1 L 1000 mL:

[text{Volume (mL)} 0.25 text{ L} times 1000 text{ mL/L} 250 text{ mL}]

Additional Calculations and Context

It is worth noting that the question was not set by a chemist but rather for educational purposes. In a laboratory setting, concentrated HCl is often available with a molarity of 10.6 M. However, higher concentrations are not typically available. The process to find the required volume remains the same, but you may need to work with available concentrations.

For example, if you need to determine how much 15.0 M HCl is needed to contain 3.0 moles of HCl, the calculation is as follows:

[text{Volume (L)} frac{3.0 text{ moles}}{15.0 text{ M}} 0.200 text{ L} 200 text{ mL}]

Similarly, if 1000 mL of 1 M HCl contains 1 mole, and you need 3 moles of HCl, the required volume can be calculated as:

[1000 text{ mL} times frac{3}{12} 250 text{ mL}]

Using the definition of molarity and the unitary method, you can determine that 250 mL of 12 M HCl contains 3 moles of HCl.

Molarity - The molarity of a solution is simply the number of moles of solute per liter of solution. Thus, 12 M HCl means that there are 12 moles of HCl in 1 liter of solution. Using the unitary method, you can calculate the volume needed to obtain a specific amount of moles.

[text{Volume needed} frac{3 text{ moles}}{12 text{ moles/L}} times 1000 text{ mL/L} 250 text{ mL}]

If you still have any doubts or questions, feel free to comment below. Keep learning and stay curious!