Question

For convenience, one form of sodium hydroxide that is sold commercially is the saturated solution. This solution is $19.4\mathrm{M},$ which is approximately $50\mathrm{\%}$ by mass sodium hydroxide. What volume of this solution would be needed to prepare 3.50 L of $3.00M$ NaOH solution?

Short answer

$V1=\frac{(3.00M)(3.50L)}{19.4M}$ $V1\approx 0.54L$ To prepare 3.50 L of 3.00 M NaOH solution, approximately 0.54 L of the saturated $19.4M$ NaOH solution is needed.

Step-by-step solution

Identify the variables given

In this problem, we are given the following information: - Concentration of the concentrated NaOH solution (C1) = 19.4 M - Concentration of the diluted NaOH solution (C2) = 3.00 M - Volume of the diluted NaOH solution (V2) = 3.50 L We need to find the volume of the concentrated NaOH solution (V1).

Use the dilution formula

We can use the dilution formula relating the concentrations and volumes of the concentrated and diluted solutions: C1 * V1 = C2 * V2 This formula implies that the amount of NaOH (in moles) in both solutions is the same.

Solve for the unknown volume (V1)

We can rearrange the formula from Step 2 to solve for the volume of the concentrated solution (V1): V1 = (C2 * V2) / C1 Plugging in the given values: V1 = (3.00 M * 3.50 L) / 19.4 M

Key concepts

Dilution Formula

Preparing a particular concentration from a more concentrated solution requires a fundamental technique known as dilution. The dilution formula is crucial in achieving the desired concentration and is given by the equation $$C1\cdot V1=C2\cdot V2$$. This formula establishes a relationship between the concentration (C) and volume (V) of two solutions - the original concentrated solution (subscript 1) and the diluted solution (subscript 2). The principle behind this is the conservation of solute quantity, meaning the number of moles of solute before dilution ($C1\cdot V1$) must equal the number of moles after dilution ($C2\cdot V2$). ewline This is why, when faced with an exercise such as calculating the required volume of a 19.4 M Sodium Hydroxide (NaOH) solution to prepare 3.50 L of a 3.00 M NaOH solution, the dilution formula is your go-to equation. By rearranging this formula, you can easily solve for the unknown volume of the concentrated solution needed for dilution.

Concentration of Solutions

The concentration of a solution is a measure of how much solute is dissolved in a given volume of solvent. It can express the strength of the solution and is typically expressed in units such as moles per liter (mol/L or M), which is also known as molarity. This expression is vital in various fields such as chemistry, biology, and environmental science. ewline Understanding the concentration allows us to control reactions, formulate products, and make precise scientific calculations. In scenarios like preparing a diluted NaOH solution from a concentrated stock, knowing the initial concentration (19.4 M) and the desired final concentration (3.00 M) is critical. This knowledge helps guide how much of the concentrated solution should be added to achieve the target concentration after dilution.

Molarity

Molarity is a term that frequently comes up when discussing solutions and their concentration. It is defined as the number of moles of solute per liter of solution, and its unit is M (molar). This unit allows chemists and students alike to perform stoichiometric calculations easily. ewline For instance, in the textbook problem mentioned, the molarity is a vital piece of information. If you start with a saturated solution of sodium hydroxide with a molarity of 19.4 M and want to prepare 3.50 L of a 3.00 M NaOH solution, knowing the molarity of both the initial concentrated solution and the final diluted solution allows you to determine how much you should dilute. It's a constant reference to understand how concentrated your solution is and plays a pivotal role in ensuring chemical reactions occur under controlled conditions.