# Empirical formula from mass percentage.

• andrewr
In summary, there are several potential issues with the standard technique for computing empirical formulas and there are improved methods available to address these issues, such as least squares fitting and linear programming. It is important to use precise and accurate measurements and to consider the potential sources of error in order to obtain an accurate empirical formula.
andrewr
Hi!

I'm interested in computing empirical formulas with integer subscripts from mass percentages (or measured mass of substance.)

The standard technique is to compute a possible mass for each element (either measured, or mass percentage times a constant like 100g); and then convert this value to moles of substance for each element.

Once the moles of each element are known, all values are divided by the number of moles found in the element with least moles.

The result is the ratio of the number of atoms of one element to the minimal element; and still may contain decimal fractions. The remainder of the task is simply to find the best "fit" of an integer multiplication that will remove the decimal fractions from all elements.

But... There are the problems that I see by using the outlined method indiscriminately, and perhaps there are even others problems that I don't see; and I wonder what is available that overcomes these pitfalls.

• A measurement has an error of granularity and of scale; Smaller masses have high error.
• Often elements with least moles have nearly the largest random error.
• Sometimes parts of equations are not strictly related to other parts of equations (eg:Water of crystallization may vary).

Since the knee jerk method merely divides out the element with minimum mass or moles; it's clear that statistically, close to the largest possible error is being made.

Does anyone know of papers addressing any of the issues I am mentioning? or can anyone outline an improved method for determining empirical formulas from raw mass measurements?

Thanks!

Hello!

Thank you for your interest in computing empirical formulas from mass percentages or measured mass of substances. There are indeed some potential problems with the standard technique you mentioned, and it is important to address these issues to accurately determine empirical formulas.

One potential issue is the error of granularity and scale in measurements. As you mentioned, smaller masses may have a higher error, which can affect the accuracy of the calculated empirical formula. To address this, it is important to use precise and accurate measurement techniques, such as using a balance with a high precision and accuracy.

Additionally, the element with the least moles may not always be the most accurate representation of the compound's composition. This can occur if the element with the least moles has a high random error, as you mentioned. To improve accuracy, it may be helpful to use multiple measurements and calculate an average value for each element.

Another issue to consider is the presence of water of crystallization, as this can vary in different samples and affect the calculated empirical formula. To account for this, it may be helpful to determine the water of crystallization separately and adjust the calculated empirical formula accordingly.

In terms of improved methods for determining empirical formulas, there are several techniques that have been developed to address these potential issues. One approach is to use a method called "least squares fitting," which takes into account all the measurements and their errors to find the best fit for an integer ratio of elements. Another method is called "linear programming," which uses a mathematical optimization approach to find the most accurate empirical formula that fits the given measurements.

I would recommend looking into these methods and considering which may be most suitable for your specific research needs. It may also be helpful to consult with a statistician or chemist who specializes in empirical formula calculations for guidance and further insight.

I hope this information helps and good luck with your research!

## 1. What is an empirical formula?

An empirical formula is the simplest ratio of elements in a compound, based on the relative number of atoms of each element present. It does not necessarily represent the actual number of atoms in a molecule.

## 2. How is an empirical formula determined?

An empirical formula can be determined from the mass percentage of each element in a compound. This information is used to calculate the relative number of atoms of each element and the simplest ratio between them.

## 3. Can an empirical formula be the same as a molecular formula?

Yes, if a compound has the simplest ratio of elements in its molecular formula, then the empirical formula and the molecular formula will be the same.

## 4. What is the difference between an empirical formula and a molecular formula?

An empirical formula represents the simplest ratio of elements in a compound, while a molecular formula represents the actual number of atoms of each element in a molecule.

## 5. How is the mass percentage of each element used to calculate the empirical formula?

The mass percentage of each element is used to determine the relative number of atoms of each element in a compound. These numbers are then simplified to the simplest ratio, which gives the empirical formula.

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