Question

How many milliliters of water must be added to \(150.0 \mathrm{~mL}\) of \(2.50 \mathrm{M} \mathrm{KOH}\) to give a \(1.00 \mathrm{M}\) solution? (Assume the volumes are additive.)

Short answer

225.0 milliliters of water must be added to the solution.

Step-by-step solution

Identify the Dilution Formula

The dilution formula that relates the concentration and volume before and after dilution is given by: \[\begin{equation}M_1V_1 = M_2V_2\text{,}\end{equation}\]where - \(M_1\) is the initial molarity of the solution (before dilution),- \(V_1\) is the initial volume of the solution,- \(M_2\) is the final molarity of the solution (after dilution),- \(V_2\) is the final volume of the solution after dilution.

Input the Known Values

In this exercise, the initial molarity \(M_1\) is \(2.50 \mathrm{M}\), the final molarity \(M_2\) is \(1.00 \mathrm{M}\), and the initial volume \(V_1\) is \(150.0 \mathrm{mL}\). We want to find the final volume \(V_2\), which is the sum of the initial volume and the volume of water added.

Rearrange the Formula to Solve for \(V_2\)

Rearrange the dilution formula to solve for \(V_2\):\[\begin{equation}V_2 = \frac{M_1V_1}{M_2}\text{.}\end{equation}\]

Calculate the Final Volume \(V_2\)

Plug the known values into the rearranged formula to calculate \(V_2\):\[\begin{equation}V_2 = \frac{(2.50 \mathrm{M})(150.0 \mathrm{mL})}{1.00 \mathrm{M}} = 375.0 \mathrm{mL}\end{equation}\]

Calculate the Volume of Water to be Added

To find the amount of water needed to be added, subtract the initial volume \(V_1\) from the final volume \(V_2\):\[\begin{equation} \text{Volume of water} = V_2 - V_1\end{equation}\]\[\begin{equation} \text{Volume of water} = 375.0 \mathrm{mL} - 150.0 \mathrm{mL} = 225.0 \mathrm{mL}\end{equation}\]

Key concepts

Molarity

Molarity is a term used to describe the concentration of a solution, representing the number of moles of solute per liter of solution. In simpler terms, it tells us how much of a substance is dissolved in a specific volume of liquid. The unit for molarity is moles per liter (M). To calculate molarity, you use the formula:

\[\begin{equation}M = \frac{moles \, of \, solute}{liters \, of \, solution}\text{.}\end{equation}\]
For example, if you dissolve 1 mole of a substance in 1 liter of water, the solution has a molarity of 1 M; if you dissolve 1 mole in 2 liters of water, its molarity is 0.5 M. In terms of homework exercises, understanding molarity helps students accurately measure and mix chemicals for laboratory experiments.

Solution Concentration

Solution concentration is all about how much solute is packed into a given volume of solvent. It's a measure of the intensity or strength of the solution. There are several ways to express this, including molarity (M), described above, but also mass percent, mole fraction, and parts per million (ppm). Since molarity is one of the primary units of concentration in chemistry, it's often the focal point for calculation problems in this area.

When working with solution concentration problems, it's useful to visualize the process. Imagine adding sugar to your tea—the more sugar you add, the sweeter the tea becomes. Similarly, the more solute present in a solution, the higher its concentration. This basic concept directly ties into various applications in scientific fields, from preparing buffer solutions in biology to mixing reactants in chemical synthesis.

Dilution Formula

The dilution formula is an essential tool in chemistry for adjusting the concentration of a solution by adding solvent. It is based on the principle that the amount of solute in the solution remains constant during the dilution process; only the volume changes. The formula is represented as:

\[\begin{equation}M1V1 = M2V2\text{,}\end{equation}\]
where:

• is the initial molarity,
• is the initial volume,
• is the final molarity,
• is the final volume after dilution.

Using this formula, you can calculate any one of the variables as long as the other three are known. It's widely used in chemistry labs when you need to prepare solutions of more manageable concentrations from highly concentrated stock solutions.

Chemical Solution Preparation

Chemical solution preparation involves creating a solution with a specific concentration by dissolving a measured amount of solute (like a solid, liquid, or gas) into a solvent. The process is a fundamental skill in chemistry, whether you're a student in a lab class or a professional in research. Some useful tips for preparing accurate solutions include:

• Measure the solute and solvent precisely, using appropriate lab equipment like graduated cylinders, pipettes, or balance scales.
• Calculate the correct volume of solvent needed for dilution based on the desired concentration, using the dilution formula to find the right proportions.
• Thoroughly mix the solution to ensure that the solute is completely dissolved and evenly distributed.

Mindful preparation prevents mishandling of chemicals and inaccurate results in experiments. As with our textbook exercise, the careful addition of water to a stronger KOH solution lowers its concentration to the desired molarity, which is a crucial practice in both educational and professional laboratories.