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Chapter 3: Problem 105

An oxoacid with the formula \(\mathrm{H}_{x} \mathrm{E}_{y} \mathrm{O}_{z}\) has a formula mass of 178 u, has 13 atoms in its formula unit, contains \(34.80 \%\) by mass, and \(15.38 \%\) by number of atoms, of the element E. What is the element \(\mathrm{E}\), and what is the formula of this oxoacid?

Short Answer

Expert verified
The Element E is Phosphorus and the formula of the oxoacid is \( \mathrm{H}_{3} \mathrm{P}_{2} \mathrm{O}_{8} \).

Step by step solution

01

Find the Mass of the Element E

Since it's given that the element \(\mathrm{E}\) constitutes \(34.80 \%\) by mass of the oxoacid, the mass of \(\mathrm{E}\) in the oxoacid can be determined by multiplying the total mass of the oxoacid with the percentage of mass of \(\mathrm{E}\) in the molecule. So,\(E_{mass} = \frac{34.80}{100} \times 178u = 61.944u\)
02

Determine the Atomic Mass of the Element E

The given oxoacid has a 15.38% of its atoms as element E. Since the total number of atoms in the molecule is 13, the number of atoms of element E is 15.38% of 13 which is 2. From the previous step we know that the total mass of element E in the molecule is 61.944u. Hence, the atomic mass of element E is the total mass of E divided by the number of E atoms which is \( \frac{61.944u}{2} = 30.972u \).
03

Compare with Elements in Periodic Table

The approximate atomic mass of element E is 30.972u. Looking at the periodic table, element E is Phosphorus (P) which has an atomic mass of approximately 30.974u.
04

Determine the Formula of the Oxoacid

Now that we know that the element E is Phosphorus (P) and there are 2 P atoms, there are remaining 11 atoms left for hydrogen (H) and oxygen (O) given that the total atoms in the oxoacid is 13. Since this is an oxoacid, there must be more oxygen atoms than hydrogen. The most reasonable scenario is having 8 oxygen and 3 hydrogen atoms. Thereby, the formula of the oxoacid is \( \mathrm{H}_{3} \mathrm{P}_{2} \mathrm{O}_{8} \).

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Most popular questions from this chapter

Name the following compounds and specify which ones are best described as ionic: (a) \(\mathrm{KNO}_{2} ;\) (b) \(\mathrm{Br} \mathrm{F}_{3}\) (c) \(\mathrm{S}_{2} \mathrm{Cl}_{2} ;\) (d) \(\mathrm{Mg}(\mathrm{ClO})_{2} ;\) (e) \(\mathrm{Cl}_{2} \mathrm{O}\)

A thoroughly dried 1.271 g sample of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) is exposed to the atmosphere and found to gain \(0.387 \mathrm{g}\) in mass. What is the percent, by mass, of \(\mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O}\) in the resulting mixture of anhydrous \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) and the decahydrate?

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Write a formula for (a) an oxide of nitrogen with \(\mathrm{N}\) in the O.S. \(+5 ;\) (b) an oxoacid of nitrogen with \(\mathrm{N}\) in the O.S. \(+3 ;\) (c) an oxide of carbon in which the apparent O.S. of \(C\) is \(+4 / 3 ;\) (d) a sulfur- containing oxoanion in which the apparent O.S. of \(S\) is +2.5 and the ionic charge is \(2-\).
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