Question

7.0 mL of 6.0 M NaOH are diluted with water to a volume of 400 mL. We are asked to find the molarity of the resulting solution. a. First find out how many moles of NaOH there are in $7.0\mathrm{mL}$ of $6.0\mathrm{M}$ NaOH. Use Equation $1.$ Note that the volume must be in liters. _______ moles b. since the total number of moles of NaOH is not changed on dilution, the molarity after dilution can also be found by Equation 1, using the final volume of the solution. Calculate that molarity. ________ M

Short answer

a. First, we find the number of moles of NaOH in the 7.0 mL of 6.0 M NaOH solution: $$0.007\mathrm{L}\times 6.0\mathrm{M}=0.042\mathrm{mol}$$ b. After diluting the solution, the molarity of the resulting solution can be found by dividing the moles of NaOH by the new volume: $${\displaystyle \frac{0.042\mathrm{mol}}{0.4\mathrm{L}}}=0.105\mathrm{M}$$

Step-by-step solution

Convert volume to liters

First, we need to convert the initial volume from milliliters (mL) to liters (L). To do this, divide the volume in mL by 1000. $7.0\mathrm{mL}={\displaystyle \frac{7.0}{1000}}\mathrm{L}=0.007\mathrm{L}$

Calculate the initial number of moles of NaOH

Now, using Equation 1, calculate the number of moles of NaOH by multiplying the initial volume (in liters) by the initial molarity of the solution. Here's the formula: Moles $=$Volume (in liters) $\times$ Molarity Moles $=0.007\mathrm{L}\times 6.0\mathrm{M}$ Moles $=0.042\mathrm{mol}$

Calculate the final volume of the solution

Now, we need to convert the final volume of the diluted solution from 400 mL to liters. $400\mathrm{mL}={\displaystyle \frac{400}{1000}}\mathrm{L}=0.4\mathrm{L}$

Calculate the molarity of the diluted solution

Since the number of moles of NaOH doesn't change upon dilution, we can use Equation 1 to find the molarity of the diluted solution by dividing the number of moles of NaOH by the new volume (in liters). Diluted Molarity $={\displaystyle \frac{\text{Moles of NaOH}}{\text{Final Volume (in liters)}}}$ Diluted Molarity $={\displaystyle \frac{0.042\mathrm{mol}}{0.4\mathrm{L}}}$ Diluted Molarity $=0.105\mathrm{M}$ The molarity of the resulting solution after dilution is $0.105\mathrm{M}$.

Key concepts

Solution Dilution

Solution dilution is a fundamental concept in chemistry where a solution's concentration is decreased by adding more solvent, typically water. When diluting a solution, the amount of solute (the substance being dissolved) remains constant, while the total volume of the solution increases. An example of this process is taking a concentrated acid and adding water to reduce its molarity to a desired level.

To calculate the new concentration after dilution, you can use the formula: $$C_1{V}_1=C_2{V}_2$$ where $C_1$ is the initial concentration, $V_1$ is the initial volume, $C_2$ is the final concentration, and $V_2$ is the final volume. This equation is a manifestation of the conservation of mass, given that the number of moles of solute remains unchanged during the dilution process.

In the educational exercise provided, to dilute the sodium hydroxide (NaOH) solution, we started with a known volume and concentration and added water to reach a new volume, thereby decreasing the concentration.

Concentration of Solutions

Concentration of solutions refers to the measure of how much solute is present in a given quantity of solvent. It is expressed in various ways, such as molarity, molality, mass percent, and others. Molarity, denoted as 'M', is perhaps the most commonly used unit in chemistry and represents moles of solute per liter of solution.

To find the concentration of a solution, the formula is as follows: $$\text{Molarity (M)}=\frac{\text{moles of solute}}{\text{liters of solution}}$$ When working with concentration, it is crucial to remember that solute quantities are always expressed in moles, while volumes are in liters. This ensures that the molarity calculation gives an accurate picture of the solution's concentration.

This concept was illustrated in the step-by-step solution when we determined the molarity of the diluted NaOH by taking into account the moles of NaOH present and the final volume of the solution.

Stoichiometry

Stoichiometry is a section of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It is based on the conservation of mass and the concept that elements and compounds react in definite proportions. Stoichiometry is often used to predict the amounts of products that will form in a reaction or the amounts of reactants needed to form a certain amount of product.

Key to stoichiometry is the mole concept, which allows chemists to count atoms and molecules by weighing them. Understanding the molar ratios between the substances involved in a reaction, as described by the balanced chemical equation, is crucial.

In relation to solution concentration and dilution, stoichiometry helps us maintain the desired proportions between reactants in a solution. If we know the stoichiometry of a reaction, we can adjust concentrations by dilution or concentration methods to achieve the precise conditions necessary for a reaction to proceed correctly.