Question

A \(150 \mathrm{~mL}\) sample of \(0.450 \mathrm{M} \mathrm{HNO}_{3}\) is diluted to \(450 \mathrm{~mL}\). What is the molarity of the resulting solution?

Short answer

The molarity of the resulting solution after dilution is \(0.150 \mathrm{M}\).

Step-by-step solution

Understand the Concept of Dilution

Dilution refers to the process of adding more solvent to a solution to decrease its concentration. The amount of solute remains the same. In this case, the solute is nitric acid, HNO3. The dilution formula can be used: \( M_1V_1 = M_2V_2 \), where \( M_1 \) and \( V_1 \) are the molarity and volume of the initial solution, and \( M_2 \) and \( V_2 \) are the molarity and volume of the final solution.

Set Up the Equation

Using the dilution formula, we can plug in the known values: \( M_1 = 0.450 \mathrm{M} \), \( V_1 = 150 \mathrm{mL} \), and \( V_2 = 450 \mathrm{mL} \). The only unknown is \( M_2 \), the molarity of the diluted solution, which we are trying to find.

Plug Values into the Dilution Formula

Substitute the known values into the dilution equation: \( (0.450 \mathrm{M})(150 \mathrm{mL}) = M_2(450 \mathrm{mL}) \).

Solve for the Final Molarity \(M_2\)

Rearrange the equation to solve for \( M_2 \): \( M_2 = \frac{(0.450 \mathrm{M})(150 \mathrm{mL})}{450 \mathrm{mL}} \).

Perform the Calculation

Carry out the calculation to find out \( M_2 \): \( M_2 = \frac{(0.450)(150)}{450} = 0.150 \mathrm{M} \).

Key concepts

Solution Concentration

When the topic of 'solution concentration' comes up, picture a cup of coffee. Just as you might add more water to make your coffee less strong, adding solvent to a solution reduces the concentration of what's dissolved in it — the solute. Solution concentration is a measure of how much solute is dissolved in a specific amount of solvent.

Concentration can be expressed in various units, but one common unit is molarity, which measures solute concentration as moles of solute per liter of solution. Understanding this is key to many fields, including chemistry, biology, and environmental science, where precise solution preparations are essential. In the problem at hand, we are dealing with changing concentrations by diluting a nitric acid solution.

Solute and Solvent

Let's break down 'solute and solvent' with a simple analogy: if you're making lemonade, the sugar you dissolve is the solute, and the water you mix it into is the solvent. In chemistry, a solute is a substance dissolved in another substance, known as the solvent. Together, they form a solution.

The solvent is typically the component in greater quantity, and its state (solid, liquid, or gas) often determines the state of the resulting solution. Understanding the roles of solute and solvent is fundamental when manipulating solution concentrations, as dilution involves adding more solvent without increasing the amount of solute.

Dilution Equation

The 'dilution equation' is a chemist’s trusty tool, symbolizing the relationship between the concentrations and volumes before and after dilution. It's conveniently expressed as \( M_1V_1 = M_2V_2 \). Here, \( M_1 \) and \( V_1 \) correspond to the initial molarity and volume, while \( M_2 \) and \( V_2 \) refer to the final molarity and volume after dilution.

Remember, the amount of solute stays constant in dilution – you're just spreading it out more evenly in a greater volume of solvent, which lowers the solution’s concentration. The dilution equation lets us quantify this change without directly measuring the amount of solute.

Molarity

Molarity might sound mysterious at first, but it’s simply a measurement of 'how concentrated' a solution is. The molarity (\( M \)) is defined as the number of moles of a solute per liter of solution. It's given the unit moles per liter (\( mol/L \) or \( M \) when shorthand notation is used).

Molarity is invaluable in science for preparing solutions with precise properties. For our exercise, the molarity changed as we added more water. By performing a molarity calculation, we determined the strength of the nitric acid solution after dilution, which is critical in applications like titrations, where reagent strength governs the reaction.