Question

A chemist wants to dilute \(50 \mathrm{ml}\) of \(3.50 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) to \(2.00 \mathrm{M}\) \(\mathrm{H}_{2} \mathrm{SO}_{4}\). To what volume must it be diluted?

Short answer

The chemist must dilute the 50 mL of 3.50 M H₂SO₄ solution to \(87.5 \mathrm{mL}\) to achieve a concentration of 2.00 M.

Step-by-step solution

Write down the given information

We are given the following information: Initial concentration, c₁ = 3.50 M Initial volume, V₁ = 50 mL Desired final concentration, c₂ = 2.00 M

Write down the dilution formula

We can use the dilution formula to find the final volume: c₁V₁ = c₂V₂

Plug in the given values to the formula

Now, plug in the given values into the formula: (3.50 M)(50 mL) = (2.00 M)V₂

Solve for the final volume V₂

Rearrange and solve for V₂: V₂ = (3.50 M * 50 mL) / (2.00 M)

Calculate the final volume V₂

Now, divide the product of the initial concentration and volume by the final concentration to get the final volume: V₂ = (3.50 * 50) / (2.00) V₂ = 175 / 2 V₂ = 87.5 mL The chemist must dilute the 50 mL of 3.50 M H₂SO₄ solution to \(87.5 \mathrm{mL}\) to achieve a concentration of 2.00 M.

Key concepts

Understanding Solution Concentration

In chemistry, the concentration of a solution is a critical concept, defining how much solute is present in a given volume of solution. This concentration can be represented in several ways, but molarity is one of the most common. Molarity, denoted by the symbol M, measures the number of moles of solute per liter of solution.
For example, a 3.50 M solution of sulfuric acid ( H₂SO₄ ) means there are 3.50 moles of H₂SO₄ molecules in every liter of the solution. The concentration is essential to know how reactants will interact in a chemical reaction and determines the dosage needed in applications. Concentration is adjustable; you can change it by altering the amount of solute or solvent.

Molarity Calculations Simplified

Molarity calculations are essential for working with solutions and involve finding or working with the concentration of solutes in a solution. The basic formula for molarity is:\[ M = \frac{n}{V} \]where M is the molarity, n is the number of moles of solute, and V is the volume of the solution in liters.
In practical terms, molarity helps us understand how concentrated a solution is. For instance, when given a solution of 50 mL with a concentration of 3.50 M, we know it equates to 3.50 moles of solute per liter of that H₂SO₄ solution. Sometimes, you may need to use molarity calculations to determine the amount of solute needed to make up a solution of desired volume and concentration. Additionally, these calculations are critical for understanding the mix between reactants in a solution.

What is the Dilution Formula?

Dilution involves lowering the concentration of a solute in a solution, usually by adding more solvent. This process is critical when the concentration needs to be adjusted for specific reactions or uses. The dilution formula provides a simple way to determine how to achieve the desired concentration:\[ c₁V₁ = c₂V₂ \]Where c₁ and V₁ are the initial concentration and volume, respectively, and c₂ and V₂ are the final concentration and volume after dilution.
In the given exercise, the chemist needed to dilute 50 mL of a 3.50 M H₂SO₄ solution to reach a concentration of 2.00 M. By using the dilution formula, they calculated the final volume, V₂, required to achieve the desired concentration was 87.5 mL. This calculation shows how you can alter a solution's concentration without changing the quantity of solute, simply by increasing the solution's volume.