Question

The food flavor enhancer monosodium glutamate (MSG) has the composition \(13.6 \%\) Na, \(35.5 \%\) C. \(4.8 \% \mathrm{H}, 8.3 \% \mathrm{N}, 37.8 \% \mathrm{O},\) by mass. What is the empirical formula of MSG?

Short answer

The empirical formula of Monosodium Glutamate (MSG) is \( NaC_5H_8N_1O_4 \).

Step-by-step solution

Convert Percentages to Moles

First, treat the percentages as grams (since percentages are parts per hundred) and convert these to moles. Here's how you convert for each element: For \( Na \), given is 13.6 %. So the moles of \( Na \) will be: \( \frac{13.6}{23.0} = 0.59 \). Similarly, Calculate the moles for all the other elements: \( C = \frac{35.5}{12.01} = 2.96 \), \( H = \frac{4.8}{1.01} = 4.75 \), \( N = \frac{8.3}{14.01} = 0.59 \), and \( O = \frac{37.8}{16.0} = 2.36 \).

Finding the Simplest Ratio

Now you have to find the simplest whole number ratio of these moles. Divide each value by the smallest number of moles calculated in the previous step. So the smallest number of moles in this calculation is 0.59. We divide all the values by 0.59. The result is: \( Na = 1 \), \( C = 5 \), \( H = 8 \), \( N = 1 \), \( O = 4 \). These are the simplest ratios in integers for each element in MSG.

Writing the Empirical Formula

The empirical formula is written by arranging the elements together with their simplest ratios. As per the ratios arrived at in the last step, the empirical formula of Monosodium Glutamate (MSG) is: \( NaC_5H_8N_1O_4 \).

Key concepts

Monosodium Glutamate

Monosodium Glutamate, often referred to as MSG, is a popular flavor enhancer used in various cuisines worldwide. It gives a savory umami flavor that elevates the taste profile of dishes. Chemically, MSG is a sodium salt of the naturally occurring amino acid glutamic acid. It's common in Asian foods, processed meats, canned vegetables, and soups. Understanding its chemical makeup is essential when discussing concepts like empirical formula and chemical composition. Knowing MSG's basic composition can help you connect it to larger scientific concepts. Its empirical formula, obtained from analyzing its elemental components, breaks down MSG into its simplest form:

• It contains Sodium (Na), which is prevalent in salts and critical for its flavor-enhancing properties.
• Carbon (C) forms the backbone structure necessary for many biochemical compounds, including glutamic acid.
• Hydrogen (H) and Nitrogen (N) are part of the amino group, contributing to the acidic nature of glutamic acid.
• Oxygen (O) is involved in the glutamic acid molecule, which is part of the central structure of MSG.

Knowing the role of each element guides us toward understanding how MSG functions at a molecular level, and provides insights into its broader application in food sciences.

Moles Calculation

Moles are a fundamental concept in chemistry, allowing us to express amounts of a substance in terms of quantity, rather than mass. When seeking the empirical formula of a compound like MSG, converting percentages into moles is a crucial step. Here's how you can calculate moles from mass percentages:

• Treat the percentage of each element as if it were in grams when considering a sample of 100 grams. This simplifies conversion since percentage directly translates to mass.
• Calculate the moles of each element by dividing its mass (grams) by its atomic mass (given in atomic mass units on the periodic table). For example, Sodium (Na) has an atomic mass of approximately 23.0.
• Repeat this step for all elements in MSG: Carbon (C), Hydrogen (H), Nitrogen (N), and Oxygen (O).
• As calculated, the moles for each element are: Na = 0.59, C = 2.96, H = 4.75, N = 0.59, O = 2.36.

Understanding this conversion process is vital in analyzing any chemical composition and serves as a stepping stone towards empirical formula calculation.

Chemical Composition Analysis

Chemical composition analysis involves determining the relative percent by mass of each element in a compound. By doing this analysis for MSG, we parse its structure down to a manageable and understandable empirical formula.Follow these steps to find the simplest form of a compound:

• Start by converting mass percentages of elements into moles, as covered in the moles calculation section.
• Next, find the simplest whole number ratio of the elements by dividing each mole value by the smallest number of moles from your calculations. For MSG, this smallest value is 0.59, which sets the baseline for simplifying other mole quantities.
• By dividing, the ratios become: Na=1, C=5, H=8, N=1, O=4.
• This ratio gives a straightforward empirical formula, which is the simplest representation of the compound's molecular structure: \(NaC_5H_8NO_4\).

This process of determining empirical formulas is crucial in chemistry, allowing scientists to infer a compound's basic structure from its composition, thereby extending the understanding of how a molecule behaves in chemical reactions.