Question

A softened water sample contains \(245 \mathrm{ppm} \mathrm{Na}\). If a person consumes \(1.5 \mathrm{~L}\) of this water per day, how many \(\mathrm{mg}\) of sodium are consumed?

Short answer

367.5 mg of sodium are consumed per day.

Step-by-step solution

Understand the Units

Firstly, it's important to understand that ppm stands for 'parts per million', which can be understood as milligrams per liter (mg/L) for water solutions. This is because 1 liter of water approximately weighs 1 million milligrams.

Calculate Sodium Intake Per Day

Since the concentration of sodium is given as 245 ppm, it means there are 245 mg of sodium in every liter of water. To find out how much sodium is consumed per day, we multiply the daily consumption of water in liters (1.5 L) by the concentration of sodium in mg/L.

Perform the Multiplication

Multiply 1.5 L (the amount of water consumed per day) by 245 mg/L (the concentration of sodium) to calculate the daily sodium intake in milligrams. \[ 1.5 \, \text{L/day} \times 245 \, \text{mg/L} = 367.5 \, \text{mg/day} \]

Key concepts

ppm to mg/L Conversion

When dealing with the analysis of substances in water, such as determining the amount of a mineral or contaminant, the term 'ppm' or parts per million is frequently used. This unit of measure is critical because it helps to quantify extremely dilute concentrations. In the context of water, which has a density close to 1 gram per milliliter, 1 ppm is essentially equivalent to 1 milligram of substance per liter of water (mg/L).

To convert ppm to mg/L, no actual mathematical conversion is necessary because they are essentially the same when referring to water. For example, 245 ppm of Na (sodium) in water translates directly to 245 mg of sodium in each liter of that water. This one-to-one conversion is helpful in quickly determining the amount of a substance when given its concentration in ppm.

Daily Sodium Consumption

Monitoring daily sodium consumption is an important aspect of managing a healthy diet. Too much sodium can lead to health issues, such as hypertension and cardiovascular disease. The Centers for Disease Control and Prevention (CDC) recommend an upper limit of 2,300 milligrams of sodium per day for adults.

Understanding how to calculate daily sodium intake, especially from various sources like drinking water, is key to managing one's diet effectively. By knowing the concentration of sodium in the water (given in ppm or mg/L), and multiplying it by the volume of water consumed, one can determine their daily sodium intake from water. For example, consuming 1.5 liters of water with a sodium concentration of 245 ppm, as given in our exercise, results in an intake of 367.5 mg of sodium, which is a significant portion of the recommended daily amount. Being aware of this intake is crucial for individuals who are on sodium-restricted diets.

Stoichiometry in Chemistry

Stoichiometry is the section of chemistry that focuses on the quantitative relationships between the reactants and products in chemical reactions. It involves using balanced chemical equations to calculate the masses of reactants and products, and it is a foundational tool for chemists in determining how much of a substance is consumed or produced in a reaction.

In the context of understanding sodium intake, stoichiometry is not directly used, but the principles of calculating and balancing units and measurements apply. Knowing the initial concentration of sodium and the volume of water consumed, one applies basic mathematical calculations to determine the total intake. This is comparable to determining how much of a reactant is consumed when a chemical reaction takes place. Beneath these calculations is a fundamental stoichiometric concept: the conservation of mass, which states that mass cannot be created or destroyed. This principle ensures that the quantity of sodium calculated will be the same before and after its dissolution in the water consumed.