Problem 84 - Chemistry The Central Science In Si Units

Question

Saline solution used in hospital contains \(0.9 \%\) sodium chloride by mass. Calculate the number of grams of sodium chloride in 0.5 gal of saline solution if the solution has a density of \(1.01 \mathrm{~g} / \mathrm{mL}\).

Step-by-Step Solution

Answer

The saline solution contains approximately 17.20 grams of sodium chloride.

Step 1: Convert Gallons to Milliliters

First, we need to convert the volume of the saline solution from gallons to milliliters. We know that 1 gallon is equivalent to 3,785.41 milliliters. Therefore, we calculate the volume in milliliters by multiplying the number of gallons by this conversion factor: \[0.5 \text{ gal} \times 3785.41 \text{ mL/gal} = 1892.705 \text{ mL}\]

Step 2: Calculate Mass of the Saline Solution

Next, we use the density of the saline solution to calculate its mass. Density is given as \(1.01 \text{ g/mL}\), and we already know the volume is 1892.705 mL. Therefore, the mass \(m\) of the solution is calculated by multiplying the volume by the density:\[m = 1892.705 \text{ mL} \times 1.01 \text{ g/mL} = 1911.63155 \text{ g}\]

Step 3: Calculate Mass of Sodium Chloride

The saline solution is \(0.9\%\) sodium chloride by mass. Therefore, we find the mass of sodium chloride by calculating \(0.9\%\) of the total mass of the saline solution:\[\text{Mass of NaCl} = 0.009 \times 1911.63155 \text{ g} = 17.20468395 \text{ g}\]

Key Concepts

Mass-Volume Relationships

Understanding the relationship between mass and volume is a key concept in chemistry. When dealing with solutions, you often need to switch between these two measures. Volume typically tells us how much space a substance occupies, while mass tells us how much matter is present.
To convert from volume to mass or vice versa, you must know the substance's density. The formula connecting these variables is:

• Mass = Volume × Density

In calculations similar to the saline solution exercise, you begin with a volume measurement, such as half a gallon, which is converted into milliliters using known conversion factors (e.g., 1 gallon = 3,785.41 mL).
Once you have the volume in milliliters, you use the density (given as grams per milliliter) to find the mass. This avoids direct weighing and is useful in scenarios where volume is more easily measured, like for liquids in labs.

Density of Solutions

The density of a solution is crucial for understanding its composition and calculating various properties. Density is defined as mass per unit volume:

• Density = Mass ÷ Volume

In most chemistry problems involving solutions, density provides a link between how much of a substance exists in a certain volume. This is extremely helpful when direct measurement of mass is impractical.
For example, the density of the saline solution in the exercise is 1.01 g/mL. This means every milliliter of the solution weighs 1.01 g. By knowing this, you can easily find the total mass of the solution when its volume is known.
Density variations can also tell you about the concentration of solutes in a solution, which can vary depending on the solute amount and the solution's overall makeup.

Chemical Solutions

A chemical solution is a homogeneous mixture composed of two or more substances. In the context of chemistry, the main component is usually a liquid solvent, such as water, and the other components are dissolved substances, known as solutes.
Solutions are characterized by their concentration, which indicates the amount of solute in a given amount of solvent or solution. The percentage by mass concentration provides how much solute is present per 100 units of total solution mass.
In the saline solution problem, you have a 0.9% concentration by mass. This implies that there are 0.9 grams of sodium chloride for every 100 grams of solution. By multiplying this percentage by the total solution's mass, you determine the solute's mass present in any given volume of solution.
Understanding different units of concentration, like mass percentage, is necessary for calculating precise chemical mixtures in practical settings like hospitals or chemistry labs.