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Chapter 1: Problem 79

Percent error is often expressed as the absolute value of the difference between the true value and the experimental value, divided by the true value: percent error \(=\frac{\mid \text { true value }-\text { experimental value } \mid}{\mid \text { true value } \mid} \times 100 \%\) The vertical lines indicate absolute value. Calculate the percent error for the following measurements: (a) The density of alcohol (ethanol) is found to be \(0.802 \mathrm{~g} / \mathrm{mL}\). (True value: \(0.798 \mathrm{~g} / \mathrm{mL}\).) (b) The mass of gold in an earring is analyzed to be \(0.837 \mathrm{~g}\). (True value: \(0.864 \mathrm{~g}\).)

Short Answer

Expert verified
The percent error for the density of alcohol (ethanol) is 0.501%, and the percent error for the mass of gold in the earring is 3.124%.

Step by step solution

01

Understanding the percent error formula

The formula for percent error is expressed as the absolute value of the difference between the true value and the experimental value, divided by the true value and multiplied by 100 to get the percentage. So, Percent Error = \( \frac{| \text{true value} - \text{experimental value} |}{| \text{true value} |} \times 100% \)
02

Calculate percent error for the density of alcohol

In the given problem, for the density of alcohol, the true value is 0.798 g/mL, and the experimental value is 0.802 g/mL. Substituting these values into the formula, we get Percent Error = \( \frac{|0.798 - 0.802|}{|0.798|} \times 100% = \frac{0.004}{0.798} \times 100% = 0.501% \) .
03

Calculate percent error for the mass of gold

In the given problem, for the mass of gold, the true value is 0.864 g, and the experimental value is 0.837 g. Substituting these values into the formula, we get Percent Error = \( \frac{|0.864 - 0.837|}{|0.864|} \times 100% = \frac{0.027}{0.864} \times 100% = 3.124% \) .

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Most popular questions from this chapter

Calculate the mass of each of the following: (a) a sphere of gold with a radius of \(10.0 \mathrm{~cm}\) [ the volume of a sphere with a radius \(r\) is \(V=(4 / 3) \pi r^{3} ;\) the density of gold \(\left.=19.3 \mathrm{~g} / \mathrm{cm}^{3}\right],\) (b) a cube of platinum of edge length \(0.040 \mathrm{~mm}\) (the density of platinum \(=\) \(\left.21.4 \mathrm{~g} / \mathrm{cm}^{3}\right),\) (c) \(50.0 \mathrm{~mL}\) of ethanol (the density of cthanol \(=0.798 \mathrm{~g} / \mathrm{mL}\) ).

Give the names of the elements represented by the chemical symbols \(\mathrm{Li}, \mathrm{F}, \mathrm{P}, \mathrm{Cu}, \mathrm{As}, \mathrm{Zn}, \mathrm{Cl}, \mathrm{Pt}, \mathrm{Mg},\) \(\mathrm{U}, \mathrm{Al}, \mathrm{Si},\) Ne. (See Table 1.1 and the list of The Elements with Their Symbols and Atomic Masses.)

Express the answers to the following calculations in scientific notation: (a) \(145.75+\left(2.3 \times 10^{-1}\right)\) (b) \(79,500 \div\left(2.5 \times 10^{2}\right)\) (c) \(\left(7.0 \times 10^{-3}\right)-\left(8.0 \times 10^{-4}\right)\) (d) \(\left(1.0 \times 10^{4}\right) \times\left(9.9 \times 10^{6}\right)\)

A resting adult requires about \(240 \mathrm{~mL}\) of pure oxygen min and breathes about 12 times every minute. If inhaled air contains 20 percent oxygen by volume and exhaled air 16 percent, what is the volume of air per breath? (Assume that the volume of inhaled air is equal to that of exhaled air.)

What is the mass of one mole of ants? (Useful information: A mole is the unit used for atomic and subatomic particles. It is approximately \(6 \times 10^{23}\). A \(1-\mathrm{cm}\) -long ant weighs about \(3 \mathrm{mg}\).
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