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Chapter 3: Problem 44

Peroxyacylnitrate (PAN) is one of the components of smog. It is a compound of \(\mathrm{C}, \mathrm{H}, \mathrm{N},\) and \(\mathrm{O}\). Determine the percent composition of oxygen and the empirical formula from the following percent composition by mass: 19.8 percent \(\mathrm{C}, 2.50\) percent \(\mathrm{H},\) 11.6 percent \(\mathrm{N}\). What is its molecular formula given that its molar mass is about 120 g?

Short Answer

Expert verified
The Oxygen composition is 66.1%. The empirical formula is \(C_{2}H_{5}N_{1}O_{6}\). With a molecular weight of 120 g/mol, the molecular formula is the same as the empirical formula because the empirical formula weight is equal to the molar mass.

Step by step solution

01

Calculate Oxygen Composition

Starting with 100 percent (as the total composition of a compound is always 100 percent), subtract the given percentages of other elements (which are: Carbon - 19.8, Hydrogen - 2.50 and Nitrogen - 11.6). The resulting value should be the percentage of Oxygen in the compound. Consequently: Oxygen percent = 100% - 19.8% - 2.50% - 11.6%.
02

Determine Empirical Formula

Assume that we have 100 grams of the compound. Therefore, the percentages of elements can be considered as their masses in grams. Compute the moles of each element by dividing the mass (in grams) by atomic weight: \(\text{moles of Carbon} = \frac{19.8g}{12.01g/mol}\)\(\text{moles of Hydrogen} = \frac{2.50g}{1.01g/mol}\)\(\text{moles of Nitrogen} = \frac{11.6g}{14.01g/mol}\)\(\text{moles of Oxygen} = \frac{[Oxygen Mass]}{16g/mol}\)Find the smallest mole ratio; this will represent the subscripts for each element in the empirical formula.
03

Find Molecular Formula

To find the molecular formula, we first need to compute the empirical formula weight. Once we have that, we divide the given molar mass by the empirical formula weight. The result usually approximates to a whole number, which is then used as the multiple to determine the molecular formula.

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Most popular questions from this chapter

Tin (Sn) exists in Earth's crust as \(\mathrm{SnO}_{2}\). Calculate the percent composition by mass of \(\mathrm{Sn}\) and \(\mathrm{O}\) in \(\mathrm{SnO}_{2}\).

What is the mass in grams of a single atom of each of the following elements? (a) As, (b) Ni.

Describe how the knowledge of the percent composition by mass of an unknown compound can help us identify the compound.

Tin(II) fluoride \(\left(\mathrm{SnF}_{2}\right)\) is often added to toothpaste as an ingredient to prevent tooth decay. What is the mass of \(\mathrm{F}\) in grams in \(24.6 \mathrm{~g}\) of the compound?

Urea \(\left[\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO}\right]\) is used for fertilizer and many other things. Calculate the number of \(\mathrm{N}, \mathrm{C}, \mathrm{O},\) and \(\mathrm{H}\) atoms in \(1.68 \times 10^{4} \mathrm{~g}\) of urea.
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