# Empirical calculator

# Empirical calculator

An empirical calculator is a tool used to calculate the empirical formula of a compound given the mass of each element in the compound.

The steps to calculate the empirical formula are as follows:

- Convert the mass of each element to moles by dividing by the molar mass.
- Find the mole ratio of each element by dividing the number of moles of each element by the smallest number of moles calculated in step 1.
- Write the empirical formula using the mole ratios as subscripts.

**For example, let’s say we have a compound with 24.0 g of carbon and 4.0 g of hydrogen.**

**Calculate the number of moles of each element:**

- Moles of carbon = 24.0 g / 12.01 g/mol = 1.999 moles
- Moles of hydrogen = 4.0 g / 1.01 g/mol = 3.96 moles

- Find the mole ratio:

- Carbon: 1.999 / 1.999 = 1
- Hydrogen: 3.96 / 1.999 = 1.98 (rounded to 2)

- Write the empirical formula using the mole ratios as subscripts: The empirical formula for this compound is CH2.

## Empirical step by step

The empirical rule, also known as the 68-95-99.7 rule or the three-sigma rule, is a statistical principle that applies to normal distributions. It states that:

- Approximately 68% of data falls within one standard deviation of the mean.
- Approximately 95% of data falls within two standard deviations of the mean.
- Approximately 99.7% of data falls within three standard deviations of the mean.

**To use the empirical rule:**

- Calculate the mean and standard deviation of the data set.
- Use the empirical rule to estimate the percentage of data that falls within one, two, or three standard deviations of the mean.

**For example, let’s say we have a data set of exam scores with a mean of 75 and a standard deviation of 10. Using the empirical rule, we can estimate that:**

- Approximately 68% of scores are between 65 and 85 (one standard deviation from the mean).
- Approximately 95% of scores are between 55 and 95 (two standard deviations from the mean).
- Approximately 99.7% of scores are between 45 and 105 (three standard deviations from the mean).