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Chapter 5: Problem 140

A binary compound between an unknown element \(\mathrm{E}\) and hydrogen contains \(91.27 \%\) E and \(8.73 \%\) H by mass. If the formula of the compound is \(\mathrm{E}_{3} \mathrm{H}_{8},\) calculate the atomic mass of E.

Short Answer

Expert verified
The atomic mass of the unknown element E in the binary compound E3H8, containing \(91.27\%\) E and \(8.73\%\) H by mass, is approximately \(27.84 \, g/mol\).

Step by step solution

01

Calculate the mass of hydrogen in the compound

Since we know that the mass percentage of hydrogen in the compound is \(8.73 \%\), let's assume we have \(100 \, g\) of the compound, so there will be \(8.73 \, g\) of hydrogen.
02

Calculate the mass of the unknown element E in the compound

Similarly, we know that the mass percentage of E in the compound is \(91.27 \%\), we can calculate the mass of E in \(100 \, g\) of the compound as \(91.27 \, g\).
03

Calculate the moles of hydrogen in the compound

To find the moles of hydrogen in the compound, we can use the formula: Moles = mass of the element / atomic mass of the element For hydrogen, the atomic mass is approximately \(1 \, g/mol\). Therefore, the moles of hydrogen in the compound are: Moles = \( \frac{8.73 \, g}{1 \, g/mol} = 8.73 \, mol \)
04

Calculate the moles of E in the compound

Since we know the formula of the compound is E3H8, the mole ratio of E to H is 3:8. We can use this ratio to find the moles of E in the compound. Moles of E = \( \frac{3}{8} \: \times \: 8.73 \, mol \) Moles of E = \( 3.27375 \, mol \)
05

Calculate the atomic mass of E

Now that we have the moles of E and its mass in the compound, we can calculate the atomic mass of E using the formula: Atomic mass of E = mass of the element / moles of the element Atomic mass of E = \( \frac{91.27 \, g}{3.27375 \, mol} = 27.84 \, g/mol \) Thus, the atomic mass of the unknown element E is approximately \( 27.84 \, g/mol \).

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