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Chapter 5: Problem 39

The element rhenium (Re) has two naturally occurring isotopes, \(^{185} \mathrm{Re}\) and \(^{187} \mathrm{Re},\) with an average atomic mass of 186.207 u. Rhenium is \(62.60 \%\) is \(^{187} \mathrm{Re},\), and the atomic mass of \(^{187}\)Re is 186.956 u. Calculate the mass of \(^{185} \mathrm{Re}\).

Short Answer

Expert verified
The mass of the isotope \(^{185}\mathrm{Re}\) is 185.458 u.

Step by step solution

01

Since the total percentages of both isotopes must add up to 100%, the percentage of \(^{185}\mathrm{Re}\) is the difference between 100% and the percentage of \(^{187}\mathrm{Re}\). Percentage of \(^{185}\mathrm{Re} = 100\% - \%of\, ^{187}\mathrm{Re} = 100\% - 62.60\% = 37.40\%\) #Step 2: Convert the percentages to decimal form#

We need to convert the percentage values to their decimal equivalents for further calculations. Decimal of \(^{185}\mathrm{Re} = \frac{37.40}{100} = 0.374\) Decimal of \(^{187}\mathrm{Re} = \frac{62.60}{100} = 0.626\) #Step 3: Plug in the known values into the weighted average formula#
02

Now we need to rewrite the weighted average formula with all the available information. \[186.207 = 0.374 \times mass\, of\,{^{185}\mathrm{Re}} + 0.626 \times 186.956\] #Step 4: Solve for the mass of \(^{185}\mathrm{Re}\)#

To solve for the mass of \(^{185}\mathrm{Re}\), we first need to isolate it on one side of the equation. \[mass\, of\,{^{185}\mathrm{Re}} = \frac{186.207 - 0.626 \times 186.956}{0.374}\] Now, calculate the value: \[mass\, of\,{^{185}\mathrm{Re}} = \frac{186.207 - 117.277}{0.374} = \frac{68.93}{0.374} =185.458\,u\] #Conclusion# The mass of the isotope \(^{185}\mathrm{Re}\) is 185.458 u.

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Most popular questions from this chapter

One of relatively few reactions that takes place directly between two solids at room temperature is $$\begin{aligned}\mathrm{Ba}(\mathrm{OH})_{2} \cdot 8 \mathrm{H}_{2} \mathrm{O}(s)+\mathrm{NH}_{4} \mathrm{SCN}(s) & \longrightarrow \\\\\mathrm{Ba}(\mathrm{SCN})_{2}(s) &+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{NH}_{3}(g)\end{aligned}$$ In this equation, the \(\cdot 8 \mathrm{H}_{2} \mathrm{O}\) in \(\mathrm{Ba}(\mathrm{OH})_{2} \cdot 8 \mathrm{H}_{2} \mathrm{O}\) indicates the presence of eight water molecules. This compound is called barium hydroxide octahydrate. a. Balance the equation. b. What mass of ammonium thiocyanate \(\left(\mathrm{NH}_{4} \mathrm{SCN}\right)\) must be used if it is to react completely with 6.5 g barium hydroxide octahydrate?

Acrylonitrile \(\left(\mathrm{C}_{3} \mathrm{H}_{3} \mathrm{N}\right)\) is the starting material for many synthetic carpets and fabrics. It is produced by the following reaction. $$2 \mathrm{C}_{3} \mathrm{H}_{6}(g)+2 \mathrm{NH}_{3}(g)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{C}_{3} \mathrm{H}_{3} \mathrm{N}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$$ If \(15.0 \mathrm{g}\) \(\mathrm{C}_{3} \mathrm{H}_{6}, 10.0 \mathrm{g} \mathrm{O}_{2},\) and \(5.00 \mathrm{g}\) \(\mathrm{NH}_{3}\) are reacted, what mass of acrylonitrile can be produced, assuming \(100 \%\) yield?

Methane \(\left(\mathrm{CH}_{4}\right)\) is the main component of marsh gas. Heating methane in the presence of sulfur produces carbon disulfide and hydrogen sulfide as the only products. a. Write the balanced chemical equation for the reaction of methane and sulfur. b. Calculate the theoretical yield of carbon disulfide when 120. g of methane is reacted with an equal mass of sulfur.

Ammonia is produced from the reaction of nitrogen and hydrogen according to the following balanced equation: $$\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)$$ a. What is the maximum mass of ammonia that can be produced from a mixture of \(1.00 \times 10^{3} \mathrm{g} \mathrm{N}_{2}\) and \(5.00 \times 10^{2} \mathrm{g} \mathrm{H}_{2} ?\) b. What mass of which starting material would remain unreacted?

A 0.4230-g sample of impure sodium nitrate was heated, converting all the sodium nitrate to 0.2864 g of sodium nitrite and oxygen gas. Determine the percent of sodium nitrate in the original sample.
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