Question

What is the concentration in ppm of sodium fluoride in tap water that has been fluoridated by the addition of \(32 \mathrm{mg}\) of NaF for every \(20 \mathrm{~kg}\) of solution?

Short answer

The concentration of sodium fluoride in the water is 1.6 ppm.

Step-by-step solution

Understand the Concept of PPM

PPM stands for 'parts per million' and is often used to measure concentrations in solutions. It quantifies how many parts of a substance are found in a million parts of another substance or mixture.

Set Up the Calculation

To find the concentration in ppm, you need to divide the mass of the solute (sodium fluoride, NaF) by the mass of the solution and then multiply by one million. Mathematically, it is expressed as \( \text{ppm} = \left( \frac{\text{mass of solute}}{\text{mass of solution}} \right) \times 10^6 \).

Insert the Given Values

Substitute the given values into the equation. Here, the mass of the solute (NaF) is \(32 \text{ mg}\) and the mass of the solution is \(20 \text{ kg}\). Note that \(20 \text{ kg} = 20,000 \text{ g}\) since 1 kg = 1000 g. The formula becomes \( \text{ppm} = \left( \frac{32 \text{ mg}}{20,000 \text{ g}} \right) \times 10^6 \).

Convert Units

Convert the mass of NaF from mg to g to ensure that both masses are in the same units. Knowing that \(1 \text{ mg} = 0.001 \text{ g}\), we have \(32 \text{ mg} = 0.032 \text{ g}\).

Perform the Calculation

Now substitute the converted values into the equation: \( \text{ppm} = \left( \frac{0.032 \text{ g}}{20,000 \text{ g}} \right) \times 10^6\). Simplifying the fraction gives \(1.6 \times 10^{-6}\). Then multiply by \(10^6\) to get the concentration in ppm: \(1.6\).

Key concepts

Concentration of Solutions

Understanding the concentration in a solution is crucial when working with mixtures of substances. Concentration measures how much of a solute is present in a given amount of solvent or solution. It essentially tells you how strong or weak a solution is. Different units exist to measure concentration, such as molarity, molality, and parts per million (ppm).

PPM, or parts per million, is particularly helpful for measuring small amounts of solute. It is commonly used for substances found at low concentrations, like trace elements in water. The formula for calculating ppm is \( ext{ppm} = rac{ ext{mass of solute}}{ ext{mass of solution}} \times 10^6 \). This formula allows us to express the concentration as parts of solute per million parts of the entire solution.

This approach simplifies understanding concentrations because it scales them to millionths, making it easier to handle very small numbers. When you're working with ppm, it's crucial to ensure that both the solute and the solution masses are in the same units, which typically requires converting units, as we'll discuss later.

Sodium Fluoride

Sodium fluoride, represented chemically as NaF, is a compound frequently used in the fluoridation of drinking water. It consists of sodium (Na) and fluoride (F) ions. Its primary purpose is to help prevent tooth decay by strengthening tooth enamel.

In the context of calculating concentration in water, sodium fluoride acts as the solute. Its addition to water must be carefully controlled to ensure safety and effectiveness. The concentration of sodium fluoride in drinking water is typically very low, making ppm a suitable unit to measure it.

Understanding how to calculate the exact concentration of sodium fluoride helps ensure it is within the recommended safety levels. For instance, knowing the initial mass of NaF added compared to the volume of water helps in assessing whether the concentration falls within the desired range.

Unit Conversion

Unit conversion is a crucial aspect when calculating concentrations in solutions like our sodium fluoride example. Often, the different components of a solution are measured in different units, such as milligrams and kilograms. To accurately assess concentration, these units need to be consistent.

For example, converting the mass of sodium fluoride from milligrams (mg) to grams (g) is necessary when the mass of the solution is given in kilograms (kg). Knowing that 1 mg equals 0.001 grams, we can easily convert 32 mg to 0.032 g. Similarly, converting kilograms to grams helps align units since 1 kg equals 1000 grams. Hence, 20 kg of solution equates to 20,000 g.

By ensuring both the solute and solvent are expressed in the same units, accurate calculations can be made, maintaining correctness and reliability in scientific assessments. Proper conversion of units is fundamental in achieving an accurate ppm value for the solution.