Question

A chemist wants to prepare \(0.75 M \mathrm{HCl}\). Commercial hydrochloric acid is \(12.4 \mathrm{M}\). How many milliliters of the commercial acid does the chemist require to make up \(1.50 \mathrm{~L}\) of the dilute acid?

Short answer

The chemist needs approximately 90.7 mL of the commercial acid.

Step-by-step solution

Understand the question

A chemist needs to dilute a concentrated hydrochloric acid solution from 12.4 M to 0.75 M. We need to find out how many milliliters of the concentrated solution are needed to make 1.50 L of the 0.75 M solution.

Use the dilution formula

The dilution formula is: \[ C_1V_1 = C_2V_2 \]Where \(C_1\) is the concentration of the stock solution (12.4 M), \(V_1\) is the volume of the stock solution we need to find, \(C_2\) is the concentration of the dilute solution (0.75 M), and \(V_2\) is the volume of the dilute solution (1.50 L).

Substitute the known values

We substitute the known values into the dilution formula:\[ 12.4 \, \text{M} \times V_1 = 0.75 \, \text{M} \times 1.50 \, \text{L} \]

Solve for \(V_1\)

Rearrange the equation to solve for \(V_1\):\[ V_1 = \frac{0.75 \, \text{M} \times 1.50 \, \text{L}}{12.4 \, \text{M}} \]

Calculate \(V_1\)

Calculate the result:\[ V_1 = \frac{1.125}{12.4} \]\[ V_1 \approx 0.0907 \, \text{L} \]Convert 0.0907 L to milliliters:\[ V_1 \approx 90.7 \, \text{mL} \]

Key concepts

Concentration Calculations

Concentration calculations are a core concept in chemistry that allow you to determine how much of a solute is present in a given volume of solution. In this context, we often refer to the molarity of a solution, which is a common way to express concentration. Molarity is denoted as 'M' and is defined as the number of moles of solute per liter of solution. To calculate concentration, you typically need:

• The volume of the solution.
• The amount of solute (in moles).

To find the concentration, divide the number of moles of solute by the volume of the solution in liters. For example, if you dissolve 1 mole of sodium chloride (NaCl) in 1 liter of water, the concentration is 1 M. This concept is crucial when preparing solutions of a desired concentration.

Molarity

Molarity, often represented by the symbol 'M', plays a pivotal role in solutions chemistry. It measures the concentration of a solute in a mixture, specifically focusing on the number of moles of a solute per liter of solution.
For instance, when a chemist talks about a 0.75 M hydrochloric acid solution, it means there are 0.75 moles of HCl present in every liter of the solution. In practical terms, understanding molarity helps:

• Predict how a solution will react chemically.
• Standardize solutions for experiments.
• Help with scaling up small-scale reactions to larger quantities.

Accurately preparing solutions of known molarity is essential for experiments in labs, as it ensures that reactions proceed as expected.

Dilution Formula

The dilution formula is a straightforward yet powerful tool in chemistry. It provides a way to calculate how to dilute a concentrated solution to achieve a desired lower concentration without altering the amount of solute.
The formula is written as:\[ C_1V_1 = C_2V_2 \]Here, \( C_1 \) is the concentration of the initial concentrated solution and \( V_1 \) is the volume of that solution you'll use. \( C_2 \) is the concentration of the diluted solution you want to make, and \( V_2 \) is its volume.
By rearranging the formula to solve for the unknown variable, you can determine exactly how much of the stock solution you need. This is especially useful in laboratory settings where precise concentrations are necessary. Suppose you have a stock solution of HCl with a concentration of 12.4 M and want to make 1.50 L of a 0.75 M solution. By substituting these values into the formula, you can easily find the required volume of the concentrated solution.