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Molarity is a measure of the concentration of a solution. It is calculated as the number of moles of solute (the substance being dissolved) per liter of solution. Molarity is expressed in mol/L and often denoted by the symbol "M." Here's how you can understand it in simple steps:

• Number of Moles: This refers to the amount of solute present in a solution. It's calculated using the formula:
  \[ ext{Number of Moles} = rac{ ext{Mass of Solute (g)}}{ ext{Molar Mass (g/mol)}} \]
• Volume of Solution: This is the total volume in which the solute is dissolved, measured in liters.
• Molarity Formula: Molarity can be calculated using the following formula:
  \[ ext{Molarity (M)} = rac{ ext{Number of Moles}}{ ext{Volume (L)}} \]

To apply this in our problem, we have a concentrated nitric acid solution with a molarity of 16 M and we aim to prepare a solution of 0.10 M. Understanding molarity helps us know how much of the concentrated solution we need to achieve the desired dilution.

Calculating volumes accurately is crucial when working with solutions. Volume calculation involves determining the amount of liquid necessary for a particular application, often in the context of dilution. In the context of dilution:

• Initial Volume: This is the volume of the more concentrated solution you start with.
• Final Volume: This is the volume of the final diluted solution.

To determine how much concentrated nitric acid is needed and ensure the resulting solution has the correct concentration, the dilution formula (which we'll discuss next) is pivotal. Once calculated, the answer might also be converted into milliliters for practical use in laboratory settings. For example, from our problem: calculating 0.03125 liters of nitric acid and then converting it to 31.25 mL demonstrates converting volumes to a more actionable measure.

The dilution formula is a mathematical relationship that helps us calculate how to dilute a solution to a desired concentration. The basic form of this equation is:\[ C_1 \times V_1 = C_2 \times V_2 \]where:

• \(C_1\): Initial concentration of the solution (before dilution).
• \(V_1\): Volume of the initial (concentrated) solution required.
• \(C_2\): Final concentration of the solution (after dilution).
• \(V_2\): Volume of the final solution.

To solve for the unknown, \(V_1\), the equation can be rearranged as:\[ V_1 = \frac{C_2 \times V_2}{C_1} \]In our exercise, substituting the values into the formula helps us determine how much of the concentrated 16 M nitric acid is needed to produce 5 liters of a 0.10 M solution. This understanding of the dilution formula assists in accurately conducting various chemical preparations and laboratory experiments.