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Give the empirical formula of each of the following compounds if a sample contains (a) \(0.0130 \mathrm{~mol} \mathrm{C}, 0.0390 \mathrm{~mol} \mathrm{H},\) and \(0.0065 \mathrm{~mol} \mathrm{O} ;\) (b) \(11.66 \mathrm{~g}\) iron and \(5.01 \mathrm{~g}\) oxygen; (c) \(40.0 \% \mathrm{C}, 6.7 \% \mathrm{H},\) and \(53.3 \% \mathrm{O}\) by mass.

Short Answer

Expert verified
The empirical formulas for the given compounds are: (a) C鈧侶鈧哋, (b) Fe鈧侽鈧, and (c) CH鈧侽.

Step by step solution

01

(a) Given moles of elements

The given amount of each element is: C: 0.0130 mol H: 0.0390 mol O: 0.0065 mol Next, we need to find the simplest whole number ratio between these moles.
02

(a) Determining the ratio

Divide the moles of each element by the smallest moles value: C: \(\frac{0.0130}{0.0065}\) = 2 H: \(\frac{0.0390}{0.0065}\) = 6 O: \(\frac{0.0065}{0.0065}\) = 1 The empirical formula is C鈧侶鈧哋鈧, which is simplified to C鈧侶鈧哋.
03

(b) Finding moles of elements

We are given the mass of each element in the sample: Fe: 11.66 g O: 5.01 g Now convert mass to moles using their respective molar masses: Fe: \(\frac{11.66\,\text{g}}{55.85\,\text{g/mol}}\) = 0.2086 mol O: \(\frac{5.01\,\text{g}}{16.00\,\text{g/mol}}\) = 0.3131 mol
04

(b) Determining the ratio

Divide the moles of each element by the smaller moles value: Fe: \(\frac{0.2086}{0.2086}\) = 1 O: \(\frac{0.3131}{0.2086}\) 鈮 1.5 Since we need whole numbers, multiply the ratio by 2 to get integers: Fe: 1 脳 2 = 2 O: 1.5 脳 2 = 3 The empirical formula is Fe鈧侽鈧.
05

(c) Finding mass of elements

We are given the mass percentages of each element. Consider a 100 g sample, so the mass of each element in the sample would be: C: 40.0 g H: 6.7 g O: 53.3 g Next, convert mass to moles using their respective molar masses: C: \(\frac{40.0\,\text{g}}{12.01\,\text{g/mol}}\) = 3.330 mol H: \(\frac{6.7\,\text{g}}{1.008\,\text{g/mol}}\) = 6.646 mol O: \(\frac{53.3\,\text{g}}{16.00\,\text{g/mol}}\) = 3.331 mol
06

(c) Determining the ratio

Divide the moles of each element by the smallest moles value: C: \(\frac{3.330}{3.330}\) = 1 H: \(\frac{6.646}{3.330}\) 鈮 2 O: \(\frac{3.331}{3.330}\) = 1 The empirical formula is CH鈧侽.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mole Ratio
When working with chemical formulas, understanding the mole ratio is essential. Mole ratio helps us identify the simplest integer ratio of different types of atoms in a compound. In general, this concept allows chemists to determine the empirical formula from a given set of chemical data.

For example, let's consider a compound containing 0.0130 moles of carbon, 0.0390 moles of hydrogen, and 0.0065 moles of oxygen. To find the mole ratio, divide the moles of each element by the smallest value among them.
  • Carbon: \( \frac{0.0130}{0.0065} = 2 \)
  • Hydrogen: \( \frac{0.0390}{0.0065} = 6 \)
  • Oxygen: \( \frac{0.0065}{0.0065} = 1 \)
Once the values are simplified to a whole number ratio, which indicates the empirical formula, we get C鈧侶鈧哋. It is crucial to ensure that these numbers are exact whole numbers, which sometimes involves multiplying by a common factor to achieve this.

Mastering the concept of mole ratios will improve your ability to analyze and understand the composition of compounds.
Molar Mass
Molar mass is a comprehensive measure of the mass of one mole of a substance, often expressed in grams per mole (g/mol). It is a critical concept in converting between the mass and the mole of a component in chemical reactions and formulas.

To calculate the molar mass, you must sum up the atomic masses of all elements present in that molecule. For instance, when determining the empirical formula for the compound containing iron and oxygen, we start by converting grams to moles using their respective molar masses:
  • Iron (Fe): Molar mass is 55.85 g/mol, calculated as \( \frac{11.66 \, \text{g}}{55.85 \, \text{g/mol}} = 0.2086 \, \text{mol} \)
  • Oxygen (O): Molar mass is 16.00 g/mol, calculated as \( \frac{5.01 \, \text{g}}{16.00 \, \text{g/mol}} = 0.3131 \, \text{mol} \)
From these calculations, the mole ratio is established to deduce the empirical formula Fe鈧侽鈧.

Understanding molar mass helps in making conversions between mass and mole, a common requirement in empirical formula determination.
Mass Percentage
Mass percentage, also known as mass percent, indicates the concentration of an element in a compound relative to the total mass, expressed as a percentage. It is a useful concept in chemistry when determining the empirical formula based on mass data.

To calculate mass percentage, divide the mass of the element by the total mass of the compound, then multiply by 100. Considering a case with a compound that is 40.0% carbon, 6.7% hydrogen, and 53.3% oxygen, we can imagine 100 g of the compound, making the masses 40.0 g of carbon, 6.7 g of hydrogen, and 53.3 g of oxygen.
  • Carbon: 40.0 g
  • Hydrogen: 6.7 g
  • Oxygen: 53.3 g
These masses are then converted to moles using their molar masses:
  • Carbon: \( \frac{40.0 \, \text{g}}{12.01 \, \text{g/mol}} = 3.330 \, \text{mol} \)
  • Hydrogen: \( \frac{6.7 \, \text{g}}{1.008 \, \text{g/mol}} = 6.646 \, \text{mol} \)
  • Oxygen: \( \frac{53.3 \, \text{g}}{16.00 \, \text{g/mol}} = 3.331 \, \text{mol} \)
After deriving the mole ratio and simplifying, we determine the empirical formula CH鈧侽.

Thus, understanding mass percentage aids in converting percentage data into practical amounts to deduce empirical formulas accurately.

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Most popular questions from this chapter

Very small crystals composed of 1000 to 100,000 atoms, called quantum dots, are being investigated for use in electronic devices. (a) A quantum dot was made of solid silicon in the shape of a sphere, with a diameter of \(4 \mathrm{nm} .\) Calculate the mass of the quantum dot, using the density of silicon \(\left(2.3 \mathrm{~g} / \mathrm{cm}^{3}\right)\) (b) How many silicon atoms are in the quantum dot? (c) The density of germanium is \(5.325 \mathrm{~g} / \mathrm{cm}^{3}\). If you made a 4-nm quantum dot of germanium, how many Ge atoms would it contain? Assume the dot is spherical.

Calculate the percentage by mass of oxygen in the following compounds: (a) morphine, \(\quad \mathrm{C}_{17} \mathrm{H}_{19} \mathrm{NO}_{3}\); (b) codeine, \(\mathrm{C}_{18} \mathrm{H}_{21} \mathrm{NO}_{3} \quad\) (c) cocaine, \(\mathrm{C}_{17} \mathrm{H}_{21} \mathrm{NO}_{4}\); (d) tetracycline, \(\mathrm{C}_{22} \mathrm{H}_{24} \mathrm{~N}_{2} \mathrm{O}_{8} ;\) (e) digitoxin, \(\mathrm{C}_{41} \mathrm{H}_{64} \mathrm{O}_{13} ;\) (f) vancomycin, \(\mathrm{C}_{66} \mathrm{H}_{75} \mathrm{Cl}_{2} \mathrm{~N}_{9} \mathrm{O}_{24}\)

Serotonin is a compound that conducts nerve impulses in the brain. It contains 68.2 mass percent C, 6.86 mass percent \(\mathrm{H}\), 15.9 mass percent \(\mathrm{N},\) and 9.08 mass percent \(\mathrm{O}\). Its molar mass is \(176 \mathrm{~g} / \mathrm{mol}\). Determine its molecular formula.

Automotive air bags inflate when sodium azide, \(\mathrm{NaN}_{3}\), rapidly decomposes to its component elements: $$ 2 \mathrm{NaN}_{3}(s) \longrightarrow 2 \mathrm{Na}(s)+3 \mathrm{~N}_{2}(g) $$ (a) How many moles of \(\mathrm{N}_{2}\) are produced by the decomposition of \(1.50 \mathrm{~mol}\) of \(\mathrm{NaN}_{3} ?\) (b) How many grams of \(\mathrm{NaN}_{3}\) are required to form \(10.0 \mathrm{~g}\) of nitrogen gas? (c) How many grams of \(\mathrm{NaN}_{3}\) are required to produce \(10.0 \mathrm{ft}^{3}\) of nitrogen gas, about the size of an automotive air bag, if the gas has a density of \(1.25 \mathrm{~g} / \mathrm{L}\) ?

The molecular formula of aspartame, the artificial sweetener marketed as NutraSweet \(^{\oplus}\), is \(\mathrm{C}_{14} \mathrm{H}_{18} \mathrm{~N}_{2} \mathrm{O}_{5} .\) (a) What is the molar mass of aspartame? (b) How many moles of aspartame are present in \(1.00 \mathrm{mg}\) of aspartame? (c) How many molecules of aspartame are present in \(1.00 \mathrm{mg}\) of aspartame? (d) How many hydrogen atoms are present in \(1.00 \mathrm{mg}\) of aspartame?

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