An ether contains 60% carbon and 13.3% hydrogen. What is the formula of the ether?

C₃H₈O

The correct answer is option 2. \(C_3H_8O\).

To determine the molecular formula of the ether from the given percentages of carbon and hydrogen, we can follow these steps:

Let us assume we have 100 grams of the ether. This simplifies the calculation because the percentages directly translate to grams.

Carbon: 60% of 100 grams = 60 grams

Hydrogen: 13.3% of 100 grams = 13.3 grams

Oxygen: Since the ether contains only carbon, hydrogen, and oxygen, the remaining percentage must be oxygen. So, oxygen percentage = 100% - 60% - 13.3% = 26.7% or 26.7 grams.

Molar mass of carbon (C) is 12.01 g/mol

\(\text{Moles of C} = \frac{60 \text{ g}}{12.01 \text{ g/mol}} \approx 4.996 \text{ moles}\)

Molar mass of hydrogen (H) is 1.008 g/mol

\(\text{Moles of H} = \frac{13.3 \text{ g}}{1.008 \text{ g/mol}} \approx 13.198 \text{ moles}\)

Molar mass of oxygen (O) is 16.00 g/mol

\(\text{Moles of O} = \frac{26.7 \text{ g}}{16.00 \text{ g/mol}} \approx 1.669 \text{ moles}\)

Divide the number of moles of each element by the smallest number of moles calculated:

\(\text{C: } \frac{4.996}{1.669} \approx 3\)

\(\text{H: } \frac{13.198}{1.669} \approx 7.9 \approx 8\)

\(\text{O: } \frac{1.669}{1.669} = 1\)

The simplest whole number ratio gives us approximately C₃H₈O.

So, the formula of the ether is: C₃H₈O