Question

Monosodium glutamate (MSG), a food-flavor enhancer, has been blamed for "Chinese restaurant syndrome," the symptoms of which are headaches and chest pains. MSG has the following composition by mass: 35.51 percent C \(, 4.77\) percent \(\mathrm{H}, 37.85\) percent \(\mathrm{O}, 8.29\) percent \(\mathrm{N},\) and 13.60 percent Na. What is its molecular formula if its molar mass is about \(169 \mathrm{~g}\) ?

Short answer

The molecular formula for MSG is C_5H_8NNaO_4.

Step-by-step solution

Find Moles of Each Element

To find the moles of each element, we divide the percentage composition by the element's atomic mass. For carbon (C), moles = \( \frac{35.51}{12.01} \). For hydrogen (H), moles = \( \frac{4.77}{1.008} \). For oxygen (O), moles = \( \frac{37.85}{16.00} \). For nitrogen (N), moles = \( \frac{8.29}{14.01} \). For sodium (Na), moles = \( \frac{13.60}{22.99} \).

Determine Ratios

Using the moles calculated from Step 1, divide each value by the smallest number of moles to determine the ratio of each element. Round to the nearest whole number if possible.

Determine Empirical Formula

From the ratios obtained, the empirical formula of MSG can be deduced. This is represented by C, H, O, N, Na in the corresponding ratio determined in Step 2.

Find Empirical Formula Mass

Calculate the mass of the empirical formula by multiplying the atomic mass of each element by the number of atoms in the empirical formula and summing them up.

Calculate Molecular Formula

Divide the molar mass of MSG (169 g/mol) by the empirical formula mass determined in Step 4 to find a multiplication factor. Multiply the subscripts in the empirical formula by this factor to find the molecular formula.

Key concepts

Atomic Mass

Atomic mass is a fundamental concept in understanding stoichiometry. It represents the average mass of atoms of an element, measured in atomic mass units (amu). Different isotopes of the same element contribute to this average. Knowing the atomic mass allows you to compare the mass of different types of atoms. It is crucial when converting between grams and moles. To find the number of moles of an element, you divide the mass by the atomic mass.

• Atomic mass of Carbon (C): 12.01 amu
• Atomic mass of Hydrogen (H): 1.008 amu
• Atomic mass of Oxygen (O): 16.00 amu
• Atomic mass of Nitrogen (N): 14.01 amu
• Atomic mass of Sodium (Na): 22.99 amu

These values are essential in the calculation of the moles of each element in a compound.

Percentage Composition

The percentage composition of a compound indicates the relative amounts of each element present, expressed as a percentage. It is calculated by dividing the mass of each element by the total mass of the compound and multiplying by 100. This concept helps identify the simplest ratio of elements in a compound, leading to the empirical formula.

• For example, MSG has 35.51% Carbon, 4.77% Hydrogen, 37.85% Oxygen, 8.29% Nitrogen, and 13.60% Sodium.

Percentage composition is used to calculate the empirical formula by finding the number of moles of each element and then comparing these relative numbers.

Empirical Formula

The empirical formula is the simplest representation of a compound showing the simplest whole-number ratio of the elements present. Unlike the molecular formula, it doesn’t convey the actual number of atoms but just their ratio.

• To find it, first calculate the moles of each element by using the percentage composition and their respective atomic mass.
• Then, divide each mole value by the smallest number of moles calculated to get a ratio.

The empirical formula is derived from these ratios by rounding to whole numbers, giving you a basic insight into the compound’s structure without specifying the exact number of atoms.

Molar Mass Calculations

Molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). It is obtained by adding the atomic masses of each atom in the formula. Calculating the molar mass is critical when determining the molecular formula from the empirical formula.

• First, determine the empirical formula mass by summing the atomic masses of its constituent elements.
• Then, divide the compound's actual molar mass by the empirical formula mass. This gives a factor, often a whole number, indicating how many times the empirical formula must be multiplied to obtain the molecular formula.
• For MSG, with an empirical formula mass calculated and a given molar mass of 169 g/mol, you find the ratio to adjust the empirical formula accordingly.

This step ensures the molecular formula accurately reflects the total composition of the compound.