Question

One mole of a chemical element contains approximately 6.02 × 1023 atoms. How many atoms are present in 4.6 × 104 moles of oxygen? Represent the answer in scientific notation. Round so the first factor goes to the hundredths place.

A.
2.77 × 10^27 atoms
B.
2.77 × 10^28 atoms
C.
27.7 × 10^27 atoms
D.
27.7 × 10^28 atoms

Answer 1

Answer: B.
`2.77*10^{28\text{ atoms}}`

Explanation:

Given : One mole of a chemical element contains approximately
`6.02*10^(23)\text{ atoms}`

Then , the number of atoms present in
`4.6*10^(4)\text{ moles}` is given by :-

`6.02*10^(23)*4.6*10^(4)\\\\=6.02*4.6*10^(23)*10^(4)`

Using exponents property:

`a^m* a^n=a^(m+n)`

`=27.692*10^(23+4)\\\\\approx2.77*10^(23+4+1)=2.77*10^{28\text{ atoms}}`

Answer 2

B. 2.77 · 10^28

Explanation:

The total number of atoms is ...

(6.02·10^23 atoms/mol)·(4.6·10^4 mol) = (6.02·4.6)·10^(23+4) atoms

≈ 27.7·10^27 atoms

≈ 2.77·10^28 atoms . . . . . . put in scientific notation form

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Scientific notation has one non-zero digit to the left of the decimal point and the exponent adjusted accordingly.

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Your calculator can help you figure this out. If necessary, put the display into scientific notation mode. (For numbers this size, it is usually not necessary.)