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Chapter 5: Problem 37

An element consists of \(1.40 \%\) of an isotope with mass 203.973 u, \(24.10 \%\) of an isotope with mass 205.9745 u, \(22.10 \%\) of an isotope with mass \(206.9759 \mathrm{u},\) and \(52.40 \%\) of an isotope with mass 207.9766 u. Calculate the average atomic mass, and identify the element.

Short Answer

Expert verified
The average atomic mass of the element is approximately 207.212 u, and the element is Lead (Pb).

Step by step solution

01

Set up the problem

Write down the given percentage and mass of each isotope. - Isotope 1: 1.40% and 203.973 u - Isotope 2: 24.10% and 205.9745 u - Isotope 3: 22.10% and 206.9759 u - Isotope 4: 52.40% and 207.9766 u
02

Convert percentages to decimals

Divide each percentage by 100 to convert them to decimals. - Isotope 1: 0.0140 and 203.973 u - Isotope 2: 0.2410 and 205.9745 u - Isotope 3: 0.2210 and 206.9759 u - Isotope 4: 0.5240 and 207.9766 u
03

Calculate the weighted average

Multiply the fraction of each isotope by its respective atomic mass and then add up these products to find the average atomic mass. The average atomic mass = (Fraction of Isotope 1 × Mass of Isotope 1) + (Fraction of Isotope 2 × Mass of Isotope 2) + (Fraction of Isotope 3 × Mass of Isotope 3) + (Fraction of Isotope 4 × Mass of Isotope 4) The average atomic mass = (0.0140 × 203.973 u) + (0.2410 × 205.9745 u) + (0.2210 × 206.9759 u) + (0.5240 × 207.9766 u)
04

Calculate the result

Plug the values into the equation to calculate the average atomic mass. The average atomic mass = (0.0140 × 203.973 u) + (0.2410 × 205.9745 u) + (0.2210 × 206.9759 u) + (0.5240 × 207.9766 u) = 2.85562 u + 49.639545 u + 45.741709 u + 108.975424 u The average atomic mass = 207.212291 u
05

Identify the element

Consult the periodic table to identify the element with an average atomic mass of approximately 207.212 u. The element is found to be Lead (Pb), which has an atomic mass of approximately 207.2 u. In conclusion, the average atomic mass of the element is approximately 207.212 u, and the element is Lead (Pb).

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Most popular questions from this chapter

A compound with molar mass \(180.1 \mathrm{g} / \mathrm{mol}\) has the following composition by mass: $$\begin{array}{|ll|}\hline C & 40.0 \% \\\H & 6.70 \% \\\O & 53.3 \% \\\\\hline\end{array}$$ Determine the empirical and molecular formulas of the compound.

A \(9.780-\mathrm{g}\) gaseous mixture contains ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)\) and propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right) .\) Complete combustion to form carbon dioxide and water requires 1.120 mole of oxygen gas. Calculate the mass percent of ethane in the original mixture.

Consider samples of phosphine \(\left(\mathrm{PH}_{3}\right),\) water \(\left(\mathrm{H}_{2} \mathrm{O}\right),\) hydrogen sulfide \(\left(\mathrm{H}_{2} \mathrm{S}\right),\) and hydrogen fluoride (HF), each with a mass of \(119 \mathrm{g} .\) Rank the compounds from the least to the greatest number of hydrogen atoms contained in the samples.

Arrange the following substances in order of increasing mass percent of carbon. a. caffeine, \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{N}_{4} \mathrm{O}_{2}\) b. sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) c. ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\)

In the production of printed circuit boards for the electronics industry, a 0.60-mm layer of copper is laminated onto an insulating plastic board. Next, a circuit pattern made of a chemically resistant polymer is printed on the board. The unwanted copper is removed by chemical etching, and the protective polymer is finally removed by solvents. One etching reaction is $$\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}(a q)+4 \mathrm{NH}_{3}(a q)+\mathrm{Cu}(s) \longrightarrow 2 \mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}(a q)$$ A plant needs to manufacture 10,000 printed circuit boards, each \(8.0 \times 16.0 \mathrm{cm}\) in area. An average of \(80 . \%\) of the copper is removed from each board (density of copper \(=8.96 \mathrm{g} / \mathrm{cm}^{3}\)). What masses of \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\) and \(\mathrm{NH}_{3}\) are needed to do this? Assume \(100 \%\) yield.
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