Question

MSG Monosodium glutamate, known as MSG, is sometimes added to food to enhance flavor. Analysis determined this compound to be 35.5% C, 4.77% H, 8.29% N, 13.6% Na, and 37.9% O. What is its empirical formula?

Short answer

The empirical formula of MSG, given its percentage composition, is C₅H₈NO₄Na.

Step-by-step solution

Convert the percent composition to moles

To calculate the moles of each element, we will assume that we have 100 grams of MSG. Then, we can divide the mass of each element in grams by its respective molar mass. $molesofC=\frac{35.5g}{12.01g/mol}=2.956moles$ $molesofH=\frac{4.77g}{1.008g/mol}=4.738moles$ $molesofN=\frac{8.29g}{14.01g/mol}=0.5919moles$ $molesofNa=\frac{13.6g}{22.99g/mol}=0.5916moles$ $molesofO=\frac{37.9g}{16.00g/mol}=2.369moles$

Find the lowest number of moles and divide each element's moles by it.

We will find the smallest number of moles among the elements and divide the number of moles for each element by it to obtain a whole-number ratio. In this case, the smallest number of moles is 0.5916 moles of Na. $ratioofC=\frac{2.956}{0.5916}=4.998\approx 5$ $ratioofH=\frac{4.738}{0.5916}=8.006\approx 8$ $ratioofN=\frac{0.5919}{0.5916}=1.0005\approx 1$ $ratioofNa=\frac{0.5916}{0.5916}=1$ $ratioofO=\frac{2.369}{0.5916}=4.001\approx 4$

Write the empirical formula

Now that we have the whole-number ratios for each element, we can write the empirical formula of MSG: C₅H₈NO₄Na The empirical formula of MSG is C₅H₈NO₄Na.

Key concepts

Percent Composition

Understanding percent composition is crucial when determining a substance's empirical formula. It represents the mass percentage of each element within a compound. To clarify, imagine having a 100-gram sample of a substance; the percent composition tells you how many grams of each element are present in that sample.

For instance, in our example with monosodium glutamate (MSG), the compound consists of 35.5% carbon (C), which means that out of 100 grams of MSG, there would be 35.5 grams of carbon. This step-by-step conversion of percentages into grams is the first and most essential step in finding out the empirical formula.

To emphasize, getting the percent composition right sets the stage for the entire calculation that follows. It also helps compare the same element's abundance across different compounds.

Molar Mass

Moving forward, molar mass is a concept that connects the macroscopic and microscopic worlds. It is the mass of one mole of a substance (usually in grams per mole) and is paramount in converting between grams of a substance and moles. The periodic table provides the molar mass for each element, representing the mass of 6.022 x 10²³ (Avogadro's number) of atoms of that element.

For example, molar mass of carbon is 12.01 g/mol. So when we say we have 2.956 moles of carbon, we mean that there are 2.956 times Avogadro's number of carbon atoms present, which in mass amounts to 35.5 grams in the given sample. This measurement is a fundamental step in our empirical formula calculation, as it bridges the gap between the conceptual moles and practical grams.

Mole-to-Mole Ratio

Upon converting the grams to moles, the next essential step is determining the mole-to-mole ratio. This can be described as the ratio between the moles of different elements in the compound. Establishing this ratio provides the relative number of atoms of each element present in the simplest form of the compound, also known as the empirical formula.

In the case of MSG, after calculating the moles of each element, we searched for the smallest mole figure to use as a divisor. By dividing each element's mole value by this smallest mole value, we achieve a mole-to-mole ratio that most closely represents whole numbers. These ratios are fundamental to expressing the empirical formula, which is a simple integer expression of the compound's composition.

Chemical Analysis

Lastly, chemical analysis refers to the processes and techniques used to determine the composition of a substance. In our MSG example, chemical analysis helps uncover the percent composition, which is the starting point for empirical formula determination. Modern analytical techniques like mass spectrometry, chromatography, and spectroscopy can accurately quantify the elements within a compound.

Chemical analysis not only serves as a foundation for theoretical calculations but is also instrumental in practical applications across various industries such as food science, pharmacology, and materials engineering. Understanding how it works and how to interpret its results brings us closer to unravelling the intricate details of the material world around us.