Ch.3 - Mass Relationships in Chemical Reactions

Problem 33

Chapter 3, Problem 33

What is the percent composition of cysteine, one of the 20 amino acids commonly found in proteins? (Gray = C, red = O, blue = N, yellow = S, ivory = H.)

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Identify the molecular formula of cysteine. Cysteine is composed of carbon (C), hydrogen (H), nitrogen (N), oxygen (O), and sulfur (S). Its molecular formula is typically C3H7NO2S.

Calculate the molar mass of cysteine. Use the atomic masses from the periodic table: C = 12.01 g/mol, H = 1.01 g/mol, N = 14.01 g/mol, O = 16.00 g/mol, S = 32.07 g/mol. Multiply each atomic mass by the number of atoms of that element in the formula and sum them up.

Determine the mass contribution of each element. Multiply the number of atoms of each element by its atomic mass to find the mass contribution of each element in the molecule.

Calculate the percent composition of each element. Divide the mass contribution of each element by the total molar mass of cysteine and multiply by 100 to get the percentage.

Summarize the percent composition. List the percent composition of each element in cysteine: %C, %H, %N, %O, and %S.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Molecular Formula

The molecular formula of a compound indicates the types and numbers of atoms present in a molecule. For cysteine, the formula is C3H7N1O2S1, which shows it contains 3 carbon (C), 7 hydrogen (H), 1 nitrogen (N), 2 oxygen (O), and 1 sulfur (S) atom. Understanding the molecular formula is essential for calculating percent composition.

Percent Composition

Percent composition is a way to express the relative amounts of each element in a compound as a percentage of the total mass. It is calculated by dividing the mass of each element in one mole of the compound by the molar mass of the compound, then multiplying by 100. This concept is crucial for determining the contribution of each element in cysteine.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To find the molar mass of cysteine, one must sum the molar masses of all its constituent atoms based on the molecular formula. This value is necessary for calculating the percent composition of each element in the amino acid.

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