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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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Most popular questions from this chapter

(a) The diameter of Earth at the equator is \(12756.27 \mathrm{~km}\). Round this number to three significant figures and express it in standard exponential notation. (b) The circumference of Earth through the poles is \(40,008 \mathrm{~km}\). Round this number to four significant figures and express it in standard exponential notation.

Round each of the following numbers to three significant figures and express the result in standard exponential notation: $(\mathbf{a}) 2048732.23(\mathbf{b}) 0.000292945(\mathbf{c})-82454.09$ (d) \(942.057024(\mathbf{e})-0.00000324683 .\)

Which of the following would you characterize as pure or nearly pure substance? (a) stomach acid; (b) dry ice; (c) ice-cream; (d) stainless steel; (e) petroleum; (f) distilled water; \((\mathbf{g})\) carbon monoxide gas; \((\mathbf{h})\) compressed air in balloon.

Indicate which of the following are exact numbers: (a) the mass of a 7.5 - by \(12.5-\mathrm{cm}\) index card, \((\mathbf{b})\) the number of grams in a kilogram, \((\mathbf{c})\) the volume of a cup of Seattle's Best coffee, (d) the number of centimeters in a kilometer, \((\mathbf{e})\) the number of microseconds in a week, \((\mathbf{f})\) the number of pages in this book.

Use appropriate metric prefixes to write the following measurements without use of exponents: (a) \(7.29 \times 10^{6} \mathrm{~g}\) (b) \(6.1 \times 10^{-10} \mathrm{~m}\) (c) \(1.828 \times 10^{-3} \mathrm{~s}\) (d) \(3.523 \times 10^{9} \mathrm{~m}^{3}\) (g) \(3.552 \times 10^{12} \mathrm{~L}\) (e) $9.62 \times 10^{2} \mathrm{~m} / \mathrm{s}(\mathbf{f}) 8.923 \times 10^{-12} \mathrm{~kg}$
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