A sample of [tex]C_xH_y[/tex] underwent combustion analysis and yielded 36.6 g of carbon dioxide and 18.0 g of water. What is the empirical formula?

Question

02-04-2024
Chemistry

High School

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A sample of [tex]C_xH_y[/tex] underwent combustion analysis and yielded 36.6 g of carbon dioxide and 18.0 g of water. What is the empirical formula?

Answer :

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siddharth8299jai siddharth8299jai · Answer 1 · 2024-08-09T07:45:42-04:00

Final answer:

To determine the empirical formula of cxhy from its combustion products, calculate the moles of carbon and hydrogen, then find their simplest whole number ratio. Based on calculations from the given masses of CO2 and H2O, the empirical formula is approximately CH2.

Explanation:

A sample of cxhy underwent combustion analysis and yielded 36.6 g of carbon dioxide and 18.0 g of water. To find the empirical formula, we first calculate the moles of carbon and hydrogen in the products. The molar mass of carbon dioxide (CO2) is 44.01 g/mol, and each molecule contains one carbon atom. Therefore, from 36.6 g of CO2, the moles of carbon are calculated as follows:

moles of C = mass of CO2 / molar mass of CO2 = 36.6 g / 44.01 g/mol = 0.832 moles of C

The molar mass of water (H2O) is 18.015 g/mol, and each molecule contains two hydrogen atoms. Thus, from 18.0 g of H2O, the moles of hydrogen are:

moles of H = (mass of H2O / molar mass of H2O) * 2 = (18.0 g / 18.015 g/mol) * 2 = 1.998 moles of H

To find the simplest whole number ratio, we divide the moles of each element by the smallest number of moles calculated:

moles of C: 0.832 / 0.832 = 1
moles of H: 1.998 / 0.832 = ~2.4

Therefore, the empirical formula of the compound is approximated as CH2.4. However, since the empirical formula needs to have whole numbers, we need to approximate this ratio to the nearest whole number, which usually involves multiplying all ratios by a common factor to get close to whole numbers. But, considering the precision limit of this calculation and the fact that empirical formulas are simplest ratios, a slight deviation from whole numbers can result from rounding during calculations. The empirical formula, in practice, is typically written as CH2 assuming minimal experimental error.