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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 \(1.01 \mathrm{~g} / \mathrm{mL}\)

Short Answer

Expert verified
There are approximately 17.19 grams of sodium chloride in 0.5 gallons of saline solution.

Step by step solution

01

Convert gallons to milliliters

First, we need to convert 0.5 gallons to milliliters using the conversion factor: \(1 \mathrm{~gal} = 3785.41 \mathrm{~mL}\). To do so, multiply 0.5 gallons by the conversion factor: \[0.5 \mathrm{~gal} \times 3785.41 \mathrm{~mL/gal} = 1892.705 \mathrm{~mL}\]
02

Find the mass of the solution

Now, we can use the given density to find the mass of the saline solution. The formula to find mass is: \[mass = volume \times density\] So, the mass of the solution is: \[1892.705 \mathrm{~mL} \times 1.01 \mathrm{~g/mL} = 1910.53205 \mathrm{~g}\]
03

Calculate the mass of sodium chloride

The saline solution is 0.9% sodium chloride by mass. To find the mass of sodium chloride, simply multiply the mass of the solution by 0.9%. \[mass_{NaCl} = mass_{solution} \times 0.9 \% \] \[mass_{NaCl} = 1910.53205 \mathrm{~g} \times 0.009 \] \[mass_{NaCl} = 17.19478845 \mathrm{~g}\]
04

Round to appropriate decimal places

Since we are working with grams, it is appropriate to round our answer to two decimal places. In this case, we have: \[mass_{NaCl} \approx 17.19 \mathrm{~g}\] So, there are approximately 17.19 grams of sodium chloride in 0.5 gallons of saline solution.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Percentage Composition
When dealing with solutions like saline, understanding percentage composition is essential. Percentage composition tells us how much of a particular component is present in a solution, expressed as a percentage of the total mass. In our exercise, the saline solution contains 0.9% sodium chloride by mass.

This means that for every 100 grams of the solution, 0.9 grams are sodium chloride. To find the actual mass of sodium chloride in a specific amount of solution, you multiply the total mass of the solution by the percentage (expressed as a decimal).
  • Percentage as a decimal is 0.9% = 0.009.
  • By calculating: mass of solution 脳 0.009, you obtain the mass of sodium chloride.
Understanding percentage composition is vital in chemistry to analyze how solutions are mixed and to prepare them correctly.
Unit Conversion
Converting units is often the first step in solving many chemistry problems. It's crucial because measurements in chemistry must be consistent. In our problem, we started with gallons and needed to determine the volume in milliliters.

Here鈥檚 how unit conversion works:
  • Know the conversion factor: 1 gallon = 3785.41 mL.
  • Multiply the given volume by the conversion factor to change gallons to milliliters.
  • For this problem: 0.5 gallons 脳 3785.41 mL/gal = 1892.705 mL.
Mastering unit conversion ensures you can work with the appropriate units, crucial when dealing with formulas involving mass, volume, or density.
Mass Calculation
Calculating mass using volume and density is a common task in chemistry. Once you know the volume and the density of a solution, you can find its mass easily with a simple formula:
  • Mass = Volume 脳 Density.
In our exercise, the density of the saline solution was 1.01 g/mL, and the volume was converted to 1892.705 mL.

Using the formula:
  • Mass = 1892.705 mL 脳 1.01 g/mL = 1910.53205 g.
This formula is vital for determining how much material is present when dealing with solutions, especially in laboratory settings where precise measurements are needed. Once you have the mass, you can do further calculations, like finding out how much of a specific component is in your solution using percentage composition.

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Most popular questions from this chapter

Gold is alloyed (mixed) with other metals to increase its hardness in making jewelry. (a) Consider a piece of gold jewelry that weighs \(9.85 \mathrm{~g}\) and has a volume of \(0.675 \mathrm{~cm}^{3}\). The jewelry contains only gold and silver, which have densities of 19.3 and \(10.5 \mathrm{~g} / \mathrm{cm}^{3}\), respectively. If the total volume of the jewelry is the sum of the volumes of the gold and silver that it contains, calculate the percentage of gold (by mass) in the jewelry. (b) The relative amount of gold in an alloy is commonly expressed in units of carats. Pure gold is 24 carat, and the percentage of gold in an alloy is given as a percentage of this value. For example, an alloy that is \(50 \%\) gold is 12 carat. State the purity of the gold jewelry in carats.

(a) A baseball weighs \(145.4 \mathrm{~g}\). What is the kinetic energy, in joules, of this baseball when it is thrown by a major league pitcher at \(150 \mathrm{~km} / \mathrm{h} ?\) (b) By what factor will the kinetic energy change if the speed of the baseball is decreased to \(90 \mathrm{~km} / \mathrm{h} ?\) (c) What happens to the kinetic energy when the baseball is caught by the catcher? Is it converted mostly to heat or to some form of potential energy?

(a) After the label fell off a bottle containing a clear liquid believed to be benzene, a chemist measured the density of the liquid to verify its identity. A \(25.0-\mathrm{mL}\) portion of the liquid had a mass of 21.95 g. A chemistry handbook lists the density of benzene at \(15^{\circ} \mathrm{C}\) as \(0.8787 \mathrm{~g} / \mathrm{mL}\). Is the calculated density in agreement with the tabulated value? (b) An experiment requires \(15.0 \mathrm{~g}\) of cyclohexane, whose density at \(25^{\circ} \mathrm{C}\) is \(0.7781 \mathrm{~g} / \mathrm{mL}\). What volume of cyclohexane should be used? (c) A spherical ball of lead has a diameter of \(5.0 \mathrm{~cm}\). What is the mass of the sphere if lead has a density of \(11.34 \mathrm{~g} / \mathrm{cm}^{3} ?\) (The volume of a sphere is \((4 / 3) \pi r^{3},\) where \(r\) is the radius.)

(a) The speed of light in a vacuum is \(2.998 \times 10^{8} \mathrm{~m} / \mathrm{s}\). Calculate its speed in miles per hour. (b) The Sears Tower in Chicago is \(1454 \mathrm{ft}\) tall. Calculate its height in meters. \((\mathbf{c})\) The Vehicle Assembly Building at the Kennedy Space Center in Florida has a volume of \(3,666,500 \mathrm{~m}^{3}\). Convert this volume to liters and express the result in standard exponential notation. (d) An individual suffering from a high cholesterol level in her blood has \(242 \mathrm{mg}\) of cholesterol per \(100 \mathrm{~mL}\) of blood. If the total blood volume of the individual is \(5.2 \mathrm{~L}\), how many grams of total blood cholesterol does the individual's body contain?

(a) To identify a liquid substance, a student determined its density, Using a graduated cylinder, she measured out a \(45-\mathrm{mL}\). sample of the substance. She then measured the mass of the sample, finding that it weighed \(38.5 \mathrm{~g}\). She knew that the substance had to be either isopropyl alcohol (density \(0.785 \mathrm{~g} / \mathrm{mL}\) ) or toluene (density \(0.866 \mathrm{~g} / \mathrm{mL}\) ). What are the calculated density and the probable identity of the substance? (b) An experiment requires \(45.0 \mathrm{~g}\) of ethylene glycol, a liquid whose density is \(1.114 \mathrm{~g} / \mathrm{mL}\). Rather than weigh the sample on a balance, a chemist chooses to dispense the liquid using a graduated cylinder. What volume of the liquid should he use? (c) Is a graduated cylinder such as that shown in Figure 1.21 likely to afford the (d) A cubic piece of metal accuracy of measurement needed? measures \(5.00 \mathrm{~cm}\) on each edge. If the metal is nickel, whose density is \(8.90 \mathrm{~g} / \mathrm{cm}^{3}\), what is the mass of the cube?
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