# 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:

1. Convert the mass of each element to moles by dividing by the molar mass.
2. 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.
3. 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.

1. 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
1. Find the mole ratio:
• Carbon: 1.999 / 1.999 = 1
• Hydrogen: 3.96 / 1.999 = 1.98 (rounded to 2)
1. 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:

1. Calculate the mean and standard deviation of the data set.
2. 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).