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Chapter 3: Problem 140

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

Short Answer

Expert verified
The atomic mass of the unknown element E is approximately 28.099 g/mol.

Step by step solution

01

Calculate the mass of hydrogen in the compound

Since we know that hydrogen makes up 8.73% of the compound's mass, and we also know the formula is E3H8, we can calculate the total mass of hydrogen in the compound. From the periodic table, the atomic mass of hydrogen is 1.008 g/mol. We have 8 hydrogen atoms in one molecule of the compound, so the total mass of hydrogen in the compound is: 8 * 1.008 g/mol = 8.064 g/mol
02

Calculate the mass of E in the compound

We know that element E makes up 91.27% of the compound's mass. Also, we know that the total mass of hydrogen in the compound is 8.064 g/mol. Therefore, we can find the mass of the unknown element E in the compound by subtracting the mass of hydrogen from the total mass of the compound: Total mass of the compound = mass of E + mass of hydrogen let x be the mass of the compound and y be the mass of E, then we get \(y = x - 8.064\) Since we know the compound is 91.27% E and 8.73% hydrogen, this means that \(\frac{y}{x} = 0.9127\), or \(y = 0.9127x\).
03

Solve for E's mass in the compound

Now we have two equations with two variables (x and y). We can solve these equations to find the mass of E in the compound: \(y = 0.9127x\) \(y = x - 8.064\) Substituting the first equation into the second equation, we get: \(0.9127x = x - 8.064\) Rearrange the equation to isolate x: \(x - 0.9127x = 8.064\) \(0.0873x = 8.064\) Now, solve for x: \(x = \frac{8.064}{0.0873} \approx 92.36 \ g/mol\).
04

Calculate atomic mass of E

Now that we have found the mass of the compound, we can find the mass of E by substituting x back into one of the equations (using the first one): \(y = 0.9127x\) \(y = 0.9127 (92.36)\) \(y \approx 84.296\ g/mol\). However, there are 3 atoms of element E in the formula (E3H8), so we need to divide the mass of E in the compound by 3 to find the atomic mass of the element E: Atomic mass of E \(= \frac{84.296}{3}\) Atomic mass of E \(\approx 28.099\ g/mol\). So the atomic mass of the element E is approximately 28.099 g/mol.

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Most popular questions from this chapter

A compound contains only carbon, hydrogen, and oxygen. Combustion of \(10.68 \mathrm{mg}\) of the compound yields \(16.01 \mathrm{mg}\) \(\mathrm{CO}_{2}\) and \(4.37 \mathrm{mg} \mathrm{H}_{2} \mathrm{O}\). The molar mass of the compound is \(176.1 \mathrm{~g} / \mathrm{mol}\). What are the empirical and molecular formulas of the compound?

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