Question

A \(1.88 \mathrm{M}\) solution of \(\mathrm{NaCl}\) has an initial volume of \(34.5 \mathrm{~mL}\). What is the final concentration of the solution if it is diluted to \(134 \mathrm{~mL} ?\)

Short answer

The final concentration is approximately 0.484 M.

Step-by-step solution

Identify Given Information

We are given that the initial concentration of the solution is \(1.88 \text{ M}\) (molarity), the initial volume is \(34.5 \text{ mL}\), and the final volume after dilution is \(134 \text{ mL}\).

Apply the Dilution Formula

Use the dilution formula \(C_1V_1 = C_2V_2\), where \(C_1\) and \(V_1\) are the initial concentration and volume, and \(C_2\) and \(V_2\) are the final concentration and volume, respectively.

Substitute Known Values

Substitute \(C_1 = 1.88 \text{ M}\), \(V_1 = 34.5 \text{ mL}\), and \(V_2 = 134 \text{ mL}\) into the dilution formula: \[1.88 \times 34.5 = C_2 \times 134\]

Solve the Equation

Solve the equation for \(C_2\): Divide both sides of the equation by \(134\) to isolate \(C_2\): \[ C_2 = \frac{1.88 \times 34.5}{134} \] Calculate the value: \[ C_2 \approx 0.484 \text{ M}\]

Key concepts

Dilution formula

The dilution formula is a powerful tool you use when working with solutions. It helps you find out the new concentration of a solution after it has been diluted. Dilution simply means adding more solvent (usually water) to a solution, which lowers its concentration. This doesn't remove any of the solute (the substance dissolved in the solvent), but spreads it out over a larger volume.

Here's how it works: the formula is written as \( C_1V_1 = C_2V_2 \). What this means is that the product of the initial concentration \( C_1 \) and the initial volume \( V_1 \) is equal to the product of the final concentration \( C_2 \) and the final volume \( V_2 \). You'll notice that concentration and volume are inversely related—if one goes up, the other goes down.

To use the formula, you just need to know three of the values, and you can solve for the fourth. For instance, if you know your initial concentration, initial volume, and final volume, you can find out what the final concentration will be after dilution. Just plug those numbers into the equation, and solve any basic algebra to find your answer.

Solution concentration

Solution concentration tells you how much solute is present in a given amount of solution. In most chemistry problems, this is expressed using molarity, also denoted by "M". Molarity is one way to express concentration in terms of moles of solute per liter of solvent.

Let's break this down:

• Solute: The substance being dissolved. In our exercise, this is NaCl (table salt).
• Solvent: The substance that does the dissolving. Water is the most common solvent for chemistry solutions.
• Molarity (M): The number of moles of solute per liter of solution.

When you dilute a solution, the number of moles of solute stays the same, but the total volume of the solution increases. This naturally decreases the concentration. For example, in the given problem, we began with a solution that had a molarity of 1.88 M and increased the volume, which resulted in a new concentration of approximately 0.484 M after dilution. Always remember, that while the concentration changes, the total amount of solute (in moles) remains unchanged.

Chemical solution

A chemical solution is a homogenous mixture of two or more substances. It consists of a solute and a solvent. In our example, we have a solution where NaCl (salt) is the solute and water is the solvent.

A key trait of solutions is that they are uniform. This means that parts of the solution are the same throughout. If you take a bit of the solution from the top or the bottom, it will have the same concentration of solute.

Understanding chemical solutions involves knowing the roles of solutes and solvents:

• Solute: This is the part that gets dissolved. In a saltwater solution, salt is the solute.
• Solvent: This is what the solute dissolves in. In our example, water acts as the solvent.

Chemical solutions are everywhere in daily life—from the air we breathe to the beverages we drink. Recognizing this helps us understand the importance of concepts like dilution and concentration, especially when studying chemistry.