Question

How many milliliters of a \(0.75 M\) HCl solution do you need to obtain \(0.0040 \mathrm{~mol}\) of \(\mathrm{HCl} ?\)

Short answer

You need approximately 5.33 mL of the solution.

Step-by-step solution

Understand the Relationship

To find out how many milliliters of the solution are needed, we'll start by understanding the relationship between moles, concentration, and volume. The formula to relate these is given by:\[ c = \frac{n}{V} \]where \(c\) is the concentration (in mol/L), \(n\) is the number of moles, and \(V\) is the volume (in liters).

Calculate the Volume in Liters

Rearrange the formula to solve for volume \(V\):\[ V = \frac{n}{c} \]Plug in the values: \(n = 0.0040\) mol and \(c = 0.75\) M:\[ V = \frac{0.0040}{0.75} = 0.005333... \text{ L}\]

Convert Volume to Milliliters

Since the result in Step 2 is in liters, convert it to milliliters by multiplying by 1000:\[ V = 0.005333... \times 1000 = 5.3333... \text{ mL}\]Thus, we round the result to two decimal places, as required by context or usual precision:\[ V \approx 5.33 \text{ mL}\]

Key concepts

Molarity calculations

Molarity is a fundamental concept in chemistry that refers to the concentration of a solution. It tells us how many moles of a solute (in this case, HCl) are present in one liter of solution. The unit for molarity is moles per liter (mol/L or M).
To calculate molarity, you would typically use the formula:

• \( c = \frac{n}{V} \)

Here, \( c \) stands for molarity, \( n \) is the number of moles, and \( V \) is the volume in liters.
In the given problem, you were provided with the molarity (0.75 M) and needed to find out how many milliliters of the solution are required to obtain a given amount of HCl (0.0040 mol). When working on such problems, remembering this relationship helps in rearranging the equation to find the missing quantity. This understanding is crucial for solving any molarity-based problems effectively.

Volume conversion

Conversion between different volume units is a typical yet crucial step in chemistry problems. In this context, converting volume from liters to milliliters (and vice versa) is a straightforward process. 1 liter is equivalent to 1000 milliliters.
Our example starts with calculating a volume in liters after solving for \( V \) using the moles and molarity relation, \( V = \frac{n}{c} \). Once you have that volume in liters, you simply convert by multiplying by 1000 to get milliliters.

• For instance, if you have 0.005333 L, multiply it by 1000 to get 5.333 mL.

This method is particularly useful when you need to report your final answer in a more commonly used unit, like milliliters for solution volumes in labs. Always keep in mind the correct usage of these conversions to avoid errors in experiments and calculations.

Dilution calculations

Although the original exercise does not directly include dilution, understanding this process is still important. Dilution is the process of reducing the concentration of a solution by adding more solvent. The key equation for dilution calculations is:

• \( c_i \times V_i = c_f \times V_f \)

Here, \( c_i \) and \( c_f \) are the initial and final concentrations, and \( V_i \) and \( V_f \) are the initial and final volumes, respectively.
Using dilution concepts can help in problems where you need to adjust the concentration of a solution. Bedside this, understanding how volume changes affect concentration aids in grasping more complex chemical processes. This theoretical foundation is beneficial across various scenarios in laboratory work and exam questions.