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Chapter 3: Problem 127

Lysine, an essential amino acid in the human body, contains \(\mathrm{C}, \mathrm{H}, \mathrm{O},\) and \(\mathrm{N} .\) In one experiment, the complete combustion of \(2.175 \mathrm{~g}\) of lysine gave \(3.94 \mathrm{~g}\) \(\mathrm{CO}_{2}\) and \(1.89 \mathrm{~g} \mathrm{H}_{2} \mathrm{O} .\) In a separate experiment, \(1.873 \mathrm{~g}\) of lysine gave \(0.436 \mathrm{~g} \mathrm{NH}_{3}\). (a) Calculate the empirical formula of lysine. (b) The approximate molar mass of lysine is \(150 \mathrm{~g}\). What is the molecular formula of the compound?

Short Answer

Expert verified
The empirical formula of Lysine is \( \mathrm{C}_3\mathrm{H}_7\mathrm{N}_1\mathrm{O}_1 \). With the given molar mass, the molecular formula of Lysine is \( \mathrm{C}_6\mathrm{H}_{14}\mathrm{N}_2\mathrm{O}_2 \).

Step by step solution

01

Calculate the Moles of Carbon and Hydrogen

From the given data, we know that 2.175 g of Lysine yields 3.94 g of \( \mathrm{CO}_2 \) and 1.89 g of \( \mathrm{H}_2\mathrm{O} \). We know that one mole of \( \mathrm{CO}_2 \) contains 1 mole of Carbon and one mole of \( \mathrm{H}_2\mathrm{O} \) contains 2 moles of Hydrogen. By using the molar masses of \( \mathrm{CO}_2 \) (44.01 g/mol) and \( \mathrm{H}_2\mathrm{O} \) (18.02 g/mol), we can find the moles of Carbon and Hydrogen.
02

Calculate the Moles of Nitrogen

From the second experiment data, we know that 1.873 g Lysine yields 0.436 g of \(\mathrm{NH}_3\). 1 mole of \(\mathrm{NH}_3\) contains 1 mole of Nitrogen. By using the molar mass of \(\mathrm{NH}_3\) (17.03 g/mol), we can find the moles of Nitrogen.
03

Calculate the Moles of Oxygen

To calculate the moles of Oxygen, subtract the mass of Carbon, Hydrogen, and Nitrogen from the total mass of Lysine. Convert the obtained mass of Oxygen to moles by using the molar mass of Oxygen (16.00 g/mol).
04

Calculate the Ratios

For finding the empirical formula, we should express these moles in a simple ratio to each other. We divide each mole value by the smallest mole value found.
05

Calculate the Molecular Formula

Divide the molar mass of Lysine (150 g) by the molar mass of the empirical formula to find the ratio. Multiply the subscripts of the empirical formula by this ratio to obtain the molecular formula of lysine.

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Most popular questions from this chapter

In the formation of carbon monoxide, CO, it is found that \(2.445 \mathrm{~g}\) of carbon combine with \(3.257 \mathrm{~g}\) of oxygen. What is the atomic mass of oxygen if the atomic mass of carbon is 12.01 amu?

Nitroglycerin \(\left(\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{~N}_{3} \mathrm{O}_{9}\right)\) is a powerful explosive. Its decomposition may be represented by$$4 \mathrm{C}_{3} \mathrm{H}_{5} \mathrm{~N}_{3} \mathrm{O}_{9} \longrightarrow 6 \mathrm{~N}_{2}+12 \mathrm{CO}_{2}+10 \mathrm{H}_{2} \mathrm{O}+\mathrm{O}_{2} $$This reaction generates a large amount of heat and many gaseous products. It is the sudden formation of these gases, together with their rapid expansion, that produces the explosion. (a) What is the maximum amount of \(\mathrm{O}_{2}\) in grams that can be obtained from \(2.00 \times 10^{2} \mathrm{~g}\) of nitroglycerin? (b) Calculate the percent yield in this reaction if the amount of \(\mathrm{O}_{2}\) generated is found to be \(6.55 \mathrm{~g}\).

The following reaction is stoichiometric as written$$\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{Cl}+\mathrm{NaOC}_{2}\mathrm{H}_{5} \longrightarrow \mathrm{C}_{4}\mathrm{H}_{8}+\mathrm{C}_{2} \mathrm{H}_{5}\mathrm{OH}+\mathrm{NaCl}$$ but it is often carried out with an excess of \(\mathrm{NaOC}_{2} \mathrm{H}_{5}\) to react with any water present in the reaction mixture that might reduce the yield. If the reaction shown was carried out with \(6.83 \mathrm{~g}\) of \(\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{Cl}\), how many grams of \(\mathrm{NaOC}_{2} \mathrm{H}_{5}\) would be needed to have a 50 percent molar excess of that reactant?

A sample of a compound of \(\mathrm{Cl}\) and \(\mathrm{O}\) reacts with an excess of \(\mathrm{H}_{2}\) to give \(0.233 \mathrm{~g}\) of \(\mathrm{HCl}\) and \(0.403 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O} .\) Determine the empirical formula of the \(\mathrm{com}-\) pound.

The aluminum sulfate hydrate \(\left[\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3} \cdot x \mathrm{H}_{2} \mathrm{O}\right]\)contains 8.10 percent \(\mathrm{Al}\) by mass. Calculate \(x-\) that is, the number of water molecules associated with each \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) unit.
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