Write the empirical formulas for the compound containing carbon to hydrogen in the following ratios:
(a) 1:4
(b) 2:6
(c) 2:2
(d) 6:6
Answer (2)
Find the greatest common divisor (GCD) of the carbon and hydrogen subscripts for each ratio.
Divide both subscripts by the GCD to obtain the simplest whole number ratio.
Write the empirical formula using the simplified ratio.
The empirical formulas are: (a) C H 4 , (b) C H 3 , (c) C H , (d) C H .
Explanation
Understanding the Problem We are given the ratios of carbon to hydrogen in different compounds and asked to find the empirical formulas for each. The empirical formula represents the simplest whole number ratio of atoms in a compound.
Solution Plan For each given ratio, we need to find the greatest common divisor (GCD) of the carbon and hydrogen subscripts. Then, we divide both subscripts by the GCD to obtain the simplest whole number ratio. Finally, we write the empirical formula using the simplified ratio.
Solving (a) (a) The ratio is 1:4. The GCD of 1 and 4 is 1. Dividing both subscripts by 1 gives the ratio 1:4. Therefore, the empirical formula is C H 4 .
Solving (b) (b) The ratio is 2:6. The GCD of 2 and 6 is 2. Dividing both subscripts by 2 gives the ratio 1:3. Therefore, the empirical formula is C H 3 .
Solving (c) (c) The ratio is 2:2. The GCD of 2 and 2 is 2. Dividing both subscripts by 2 gives the ratio 1:1. Therefore, the empirical formula is C H .
Solving (d) (d) The ratio is 6:6. The GCD of 6 and 6 is 6. Dividing both subscripts by 6 gives the ratio 1:1. Therefore, the empirical formula is C H .
Final Answer The empirical formulas for the given carbon to hydrogen ratios are: (a) C H 4 (b) C H 3 (c) C H (d) C H
Examples
Understanding empirical formulas is crucial in various fields. For example, in environmental science, knowing the empirical formula of pollutants helps in assessing their impact and devising strategies for remediation. In materials science, empirical formulas guide the synthesis of new compounds with desired properties. Moreover, in drug discovery, determining the empirical formula of a potential drug candidate is a fundamental step in characterizing its composition and potential efficacy. This knowledge allows scientists and engineers to make informed decisions and develop innovative solutions across diverse scientific and technological domains.
The empirical formulas for the given carbon to hydrogen ratios are: (a) CH₄, (b) CH₃, (c) CH, and (d) CH. Each formula is derived by finding the greatest common divisor of the given ratios and simplifying accordingly. This process helps in understanding the composition of chemical compounds.
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