To calculate the relative atomic mass (also known as the atomic weight) of an element given a ratio, you need to consider the isotopes of the element and their respective abundances. Here's a step-by-step process:
Identify the isotopes: Determine the isotopes of the element for which you have the ratio. Isotopes are variants of an element with different numbers of neutrons in the nucleus. For example, carbon has isotopes such as carbon-12, carbon-13, and carbon-14.
Determine the abundance: Find the abundance or percentage of each isotope in the sample. This information may be given directly or may require research. Abundance refers to the proportion or percentage of each isotope present in a naturally occurring sample of the element.
Convert the abundance to a decimal: Express the abundance of each isotope as a decimal by dividing the percentage value by 100. For example, if an isotope has an abundance of 20%, the decimal representation would be 0.20.
Multiply the abundance by the atomic mass: Multiply the decimal abundance of each isotope by its respective atomic mass. The atomic mass is the mass of an atom of the isotope relative to 1/12th the mass of a carbon-12 atom. The atomic masses of isotopes can be found in the periodic table or other reliable sources.
Sum the products: Add up the products obtained from step 4 to calculate the weighted average atomic mass. Each product represents the contribution of an isotope to the overall atomic mass.
Round the result: Round the weighted average atomic mass to the appropriate number of significant figures or decimal places, depending on the desired precision.
Here's an example calculation using carbon isotopes:
Given the following isotopic ratio and atomic masses for carbon:
Isotope Abundance (%) Atomic Mass Carbon-12 98.93 12.0000 Carbon-13 1.07 13.0034
Calculations:
(0.9893 * 12.0000) + (0.0107 * 13.0034) = 11.8668 + 0.1393 = 12.0061
The relative atomic mass of carbon, given this ratio, is approximately 12.0061.
Remember that the values provided in this example are for demonstration purposes and might not reflect the actual values for carbon. You should consult reliable sources or the latest periodic table for accurate and up-to-date information.