Ch.1 - Introduction: Matter, Energy, and Measurement

Problem 84

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Chapter 1, Problem 84

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 g/mL.

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Convert the volume of the saline solution from gallons to milliliters. Recall that 1 gallon is approximately 3.785 liters, and 1 liter is 1000 milliliters.

Calculate the total mass of the saline solution using its density. Multiply the volume in milliliters by the density in g/mL to find the mass in grams.

Determine the mass of sodium chloride in the solution by using the percentage concentration. Since the solution contains 0.9% sodium chloride by mass, multiply the total mass of the solution by 0.9%.

Convert the percentage to a decimal by dividing by 100 before multiplying to find the mass of sodium chloride.

The result from the previous step gives you the mass of sodium chloride in grams contained in 0.5 gallons of the saline solution.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Concentration by Mass

Concentration by mass refers to the amount of solute present in a given mass of solution, expressed as a percentage. In this case, a 0.9% sodium chloride solution means that there are 0.9 grams of sodium chloride in every 100 grams of the solution. Understanding this concept is crucial for calculating the mass of sodium chloride in a specific volume of saline solution.

Density

Density is defined as mass per unit volume and is a critical property for converting between volume and mass. The density of the saline solution is given as 1.01 g/mL, which means that each milliliter of the solution weighs 1.01 grams. This information allows us to determine the total mass of the saline solution when we know its volume, which is essential for calculating the mass of sodium chloride.

Volume to Mass Conversion

To find the mass of sodium chloride in a given volume of solution, we first convert the volume to mass using the solution's density. For example, 0.5 gallons must be converted to milliliters (1 gallon = 3785.41 mL), and then multiplied by the density to find the total mass of the solution. This mass can then be used with the concentration percentage to find the mass of sodium chloride present.

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