Q66E - Chemistry (OpenStax)

Question

The distance between the centers of the two oxygen atoms in an oxygen molecule is 1.21 × 10⁻⁸ cm. What is this distance in inches?

Step-by-Step Solution

Answer

The distance between the centers of the two oxygen atoms in the oxygen molecule in inches is 4.76x10^-9 inches.

Step 1: Describing the inch and centimeters terms

An inch is used in imperial and US customary unit systems, while a centimeter is used in an international unit system. They both are a measure of length and height.

Here we define that

\(1\,\,{\rm{inch}}\,\, = \,\,2.54\,\,{\rm{centimeters}}\)

\(1\,\,{\rm{centimeter}} = 0.393701\,\,{\rm{inch}}\,\,\)

One foot is twelve times an inch which is used in regular life.

Step 2: Calculating the distance between the centers of the two oxygen atoms in the oxygen molecule in inches

The given distance between the centers of the two oxygen atoms of the oxygen molecule is 1.21   10^-8 cm.

For the conversion,

\(1\,\,{\rm{inch}}\,\, = \,\,2.54\,\,{\rm{centimeters}}\)

Hence,

\(\begin{array}{c}1.21\, \times \,{10^{ - 8}}\,{\rm{centimeters}}\,\,\\ = \,\,1.21\, \times \,{10^{ - 8}}\left( {\,{\rm{centimeters}}\, \times \,\frac{{{\rm{inch}}}}{{2.54\,\,{\rm{centimeters}}}}} \right)\,\,\\ = \,\,\frac{{1.21\, \times \,{{10}^{ - 8}}}}{{2.54}}\,\,{\rm{inch}}\,\,\\ = \,\,0.4764\, \times \,{10^{ - 8}}\,{\rm{inch}}\,\,\\ \approx \,\,4.764\, \times \,{10^{ - 9}}\,{\rm{inch}}\end{array}\)

Therefore, the distance between the centers of the two oxygen atoms in the oxygen molecule in inches is 4.76   10^-9 inches (rounding off to 3 significant figures).