Question

Glycine, an amino acid used by organisms to make proteins, is represented by the molecular model below. (a) Write its molecular formula. (b) Determine its molar mass. (c) Calculate the mass of 3 moles of glycine. (d) Calculate the percent nitrogen by mass in glycine. [Sections \(3.3\) and \(3.5]\)

Short answer

(a) \(C_2H_5NO_2\) (b) 75.08 g/mol (c) 225.24 g (d) 18.65%

Step-by-step solution

Identify the elements in the molecule

In glycine, the molecular model contains carbon (C), hydrogen (H), nitrogen (N), and oxygen (O).

Calculate the molecular formula

The molecular formula of glycine is \(C_2H_5NO_2\), which means it has 2 atoms of carbon (C), 5 atoms of hydrogen (H), 1 atom of nitrogen (N), and 2 atoms of oxygen (O).

Determine the molar mass of glycine

We'll need to use the atomic masses of the elements: \(C=12.01 g/mol\), \(H=1.01 g/mol\), \(N=14.01 g/mol\), and \(O=16.00 g/mol\). Multiply the atomic mass of each element by the number of atoms in the molecular formula and add them up: Molar mass of glycine = (2 × 12.01) + (5 × 1.01) + (1 × 14.01) + (2 × 16.00) = 24.02 + 5.05 + 14.01 + 32.00 = 75.08 g/mol

Calculate the mass of 3 mol of glycine

To find the mass of 3 mol of glycine, multiply the number of moles by the molar mass of glycine: Mass of 3 mol of glycine = 3 mol × 75.08 g/mol = 225.24 g

Calculate the percent nitrogen by mass in glycine

To find the percent nitrogen by mass in glycine, divide the mass contribution of nitrogen in the molecular mass by the total molecular mass, and then multiply by 100%: Percent nitrogen by mass = \(\frac{(1 \times 14.01)}{75.08}\) × 100% = 0.1865 × 100% = 18.65% In summary: (a) The molecular formula of glycine is \(C_2H_5NO_2\). (b) The molar mass of glycine is 75.08 g/mol. (c) The mass of 3 mol of glycine is 225.24 g. (d) The percent nitrogen by mass in glycine is 18.65%.

Key concepts

Molecular Formula

Glycine is a simple molecule yet important to life due to its role as an amino acid, the building block of proteins. The molecular formula represents the specific number and type of atoms in a molecule. In glycine, the molecular formula is \(C_2H_5NO_2\). This shows that each molecule contains:

• 2 carbon (C) atoms
• 5 hydrogen (H) atoms
• 1 nitrogen (N) atom
• 2 oxygen (O) atoms

The formula gives a clear picture of how these elements are combined in a single glycine molecule.

Molar Mass

The molar mass of a molecule is a critical concept in chemistry that helps us understand the mass of one mole of a substance, usually expressed in grams per mole (g/mol). To find the molar mass of glycine, we sum the atomic masses of all the atoms in its molecular formula \( C_2H_5NO_2 \):- Carbon (C) has an atomic mass of 12.01 g/mol. With 2 carbon atoms, we have \(2 \times 12.01 = 24.02\) g/mol.
- Hydrogen (H) has an atomic mass of 1.01 g/mol. With 5 hydrogen atoms, we have \(5 \times 1.01 = 5.05\) g/mol.
- Nitrogen (N) has an atomic mass of 14.01 g/mol. With 1 nitrogen atom, we have \(1 \times 14.01 = 14.01\) g/mol.
- Oxygen (O) has an atomic mass of 16.00 g/mol. With 2 oxygen atoms, we have \(2 \times 16.00 = 32.00\) g/mol.Adding these up, the molar mass of glycine is \( 24.02 + 5.05 + 14.01 + 32.00 = 75.08 \) g/mol.

Percent Composition

Percent composition is a valuable concept used to understand the makeup of a compound in terms of the mass percentage each element contributes to the total molecular weight. For glycine, we are particularly interested in the percent composition of nitrogen.To calculate this, we divide the total mass from nitrogen in the molecular formula by the molar mass of the entire molecule, then multiply by 100%:\[ \text{Percent nitrogen} = \frac{(1 \times 14.01)}{75.08} \times 100\% = 18.65\% \]
This means 18.65% of the total molar mass of glycine is due to nitrogen, which is significant given nitrogen's vital role in amino acids and proteins.

Atomic Mass

Atomic mass, typically expressed in atomic mass units (amu), is an essential chemistry concept for understanding the weight of individual elements in a molecule relative to carbon-12, which is set at exactly 12 amu. In glycine, knowing the atomic masses of carbon, hydrogen, nitrogen, and oxygen allows us to precisely calculate the molar mass.

• Carbon (C) has an atomic mass of approximately 12.01 amu.
• Hydrogen (H) has an atomic mass of about 1.01 amu.
• Nitrogen (N) has an atomic mass roughly 14.01 amu.
• Oxygen (O) has an atomic mass around 16.00 amu.

The atomic mass values of each element contribute directly to the molecular and molar mass calculations, enabling us to compute things like the mass of multiple moles of the compound and analyze its percent composition.