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How to Calculate Atomic Ratio?

Published in Atomic Ratios 3 mins read

To calculate the atomic ratio, you need to determine the mole ratio of elements in a compound. Here’s a step-by-step guide, incorporating the information from the reference:

Steps to Calculate Atomic Ratio

  1. Assume a 100g Sample: If you're given the composition of a compound in percentages, it's convenient to assume you have a 100-gram sample. This allows you to convert the percentages directly into grams. For example, if a compound is 40% carbon, you would assume 40 grams of carbon in your 100g sample.

  2. Convert Grams to Moles: Use the molar mass of each element (found on the periodic table) to convert the mass of each element (in grams) into moles.

    • Formula: Moles = Mass (g) / Molar Mass (g/mol)

  3. Determine the Smallest Number of Moles: After calculating the number of moles for each element, identify the smallest value.

  4. Divide by the Smallest Value: Divide the number of moles of each element by the smallest number of moles you identified in the previous step. This will give you the mole ratio of the elements, and thus the atomic ratio.

Example:

Let's say you have a compound with 40% Carbon (C), 6.7% Hydrogen (H), and 53.3% Oxygen (O).

Element Percentage Mass (g) Molar Mass (g/mol) Moles Moles Ratio
Carbon 40% 40 12.01 3.33 3.33/3.33 = 1
Hydrogen 6.7% 6.7 1.008 6.65 6.65/3.33 ≈ 2
Oxygen 53.3% 53.3 16.00 3.33 3.33/3.33 = 1
  • Step 1: Assume a 100g sample, we then have 40g of C, 6.7g of H, and 53.3g of O.
  • Step 2:
    • Moles of C = 40 g / 12.01 g/mol = 3.33 mol
    • Moles of H = 6.7 g / 1.008 g/mol = 6.65 mol
    • Moles of O = 53.3 g / 16.00 g/mol = 3.33 mol
  • Step 3: The smallest number of moles is 3.33.
  • Step 4:
    • Ratio of C = 3.33 / 3.33 = 1
    • Ratio of H = 6.65 / 3.33 = 2
    • Ratio of O = 3.33 / 3.33 = 1

Therefore, the atomic ratio is approximately C1H2O1 or CH2O.

Key Insights

  • Simplifying Ratios: After dividing by the smallest number, you might not get whole numbers. If the numbers are close to a fraction, multiply all the ratios by a common factor to achieve a whole number ratio. For example, if the ratios were 1:1.5:1, multiplying by 2 results in a 2:3:2 ratio.
  • Molar Mass: Always double check the molar mass of each element. Use the atomic mass from a reliable periodic table source.
  • Experimental Data: This calculation is essential when you’re working with experimental data and trying to determine the empirical formula of a compound.

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