Question

Drinking water is routinely disinfected by adding chlorine to a concentration of about \(2 \mathrm{ppm}\). How many milligrams is this per liter of water?

Short answer

2 mg per liter.

Step-by-step solution

Understanding Parts per Million (ppm)

The unit ppm stands for parts per million and is a way to express very dilute concentrations of substances. When talking about a concentration of \(2\) ppm, it means there are \(2\) parts of the substance (chlorine, in this case) for every million parts of the solution (water).

Conversion to Milligrams per Liter

To calculate how many milligrams 2 ppm is per liter of water, we can use the conversion: 1 ppm is equivalent to 1 mg/L. This is because the density of water is approximately \(1 ext{ g/mL}\), so \(1 ext{ L}\) of water approximately weighs \(1000\) grams or \(1,000,000\) milligrams. Thus, 2 ppm of chlorine corresponds to \(2 ext{ mg/L}\).

Key concepts

Understanding Parts per Million (ppm)

Parts per million (ppm) is a measurement used to describe the concentration of a substance in a solution. It is akin to finding a needle in a haystack—the measurement is used for substances present in very small amounts. Simply put, ppm means "parts per million." That means if you're talking about 2 ppm of chlorine, for instance, you're dealing with 2 parts of chlorine to every million parts of the entire solution. This unit is especially useful when measuring pollutants or chemicals in water and is a favorite in scenarios where precision needs to be communicated simply.

• 1 ppm = 1 part substance per 1,000,000 parts solution
• 2 ppm chlorine in water = 2 parts chlorine per million parts water

Using ppm helps us understand and communicate chemical concentrations in a straightforward way, making it easier for scientists and engineers to ensure safety and effectiveness.

Chlorine Disinfection in Water Treatment

Chlorine disinfection is a key process in making water safe to drink. Chlorine is added to water in very small quantities but with massive impact. Why is this important? Because chlorine acts to kill bacteria, viruses, and other pathogens that can be harmful or even deadly.

• Chlorine's job is to clean water by eradicating undesirable microorganisms.
• It is a commonly used disinfectant due to its effectiveness and cost efficiency.

The addition of chlorine is carefully calculated, often guided by standards such as 2 ppm, to ensure there is enough chlorine to disinfect the water effectively without posing harm to human health. In the case previously discussed, 2 ppm means there is 2 mg of chlorine in each liter of water—a tiny but powerful amount.

Concentration Conversion: From ppm to mg/L

Often in chemistry, especially when dealing with substances in solutions like water, you'll need to convert one unit to another. Thankfully, converting ppm to milligrams per liter (mg/L) is pretty straightforward. In fact, when dealing with water where we assume the density is 1 g/mL, ppm and mg/L are essentially the same thing.

• 1 ppm equals 1 mg/L for water since 1 liter of water weighs 1,000,000 mg.
• Therefore, for 2 ppm chlorine, it directly becomes 2 mg/L.

This equivalence allows chemists to seamlessly switch between guidance on concentrations in ppm and their implementation in mg/L when handling water solutions in practice.

Density of Water and Its Role in Calculations

The density of water is an essential factor in many calculations involving solutions. Water's density is approximately 1 g/mL at standard temperature and pressure, which is equivalent to 1,000 kg/m³ or 1,000,000 mg/L. This knowledge simplifies calculations in chemistry, especially those involving concentration.

• Knowing that 1 L of water weighs 1 kg helps in direct unit conversions when dealing with chemical concentrations.
• It's this density which enables ppm to be equivalent to mg/L.

Whenever you need to calculate the concentration of a substance in water, remembering that the density is 1 will make your life much easier. This uniformity is handy when dealing with chemical problems and helps simplify complex calculations into more manageable numbers.