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Difficulty: MediumScientific Notation and Unit Conversions

During a laboratory study on cellular respiration, a researcher measures the oxygen consumption rate of a single isolated mitochondrion. The mitochondrion consumes 3.5×10−15 moles3.5 \times 10^{-15}\text{ moles} of oxygen gas (O2\text{O}_2) per second. To compare this with macro-scale metabolic rates, the researcher needs to express this value in picomoles (pmol\text{pmol}) per hour. Which of the following is closest to the oxygen consumption rate of the mitochondrion in pmol/hour\text{pmol/hour}?

  1. A
    9.72×10−7 pmol/hour9.72 \times 10^{-7}\text{ pmol/hour}
  2. B
    1.26×10−2 pmol/hour1.26 \times 10^{-2}\text{ pmol/hour}
  3. 1.26×101 pmol/hour1.26 \times 10^1\text{ pmol/hour}Answer
  4. D
    1.26×104 pmol/hour1.26 \times 10^4\text{ pmol/hour}

Answer

1.26×101 pmol/hour1.26 \times 10^1\text{ pmol/hour}
The correct option is obtained by performing a two-step dimensional analysis. First, convert moles to picomoles using the relationship 1 mole=1012 pmol1\text{ mole} = 10^{12}\text{ pmol}. This gives 3.5×10−15×1012=3.5×10−3 pmol/second3.5 \times 10^{-15} \times 10^{12} = 3.5 \times 10^{-3}\text{ pmol/second}. Second, convert seconds to hours by multiplying by the conversion factor of 3,600 seconds per hour3,600\text{ seconds per hour}. This calculation yields 3.5×10−3×3,600=12.6 pmol/hour3.5 \times 10^{-3} \times 3,600 = 12.6\text{ pmol/hour}. Expressing this in scientific notation gives 1.26×101 pmol/hour1.26 \times 10^1\text{ pmol/hour}.

Step-by-Step Solution

1
Convert the oxygen consumption rate from moles per second to picomoles per second.
3.5×10−15 moles/second×1012 pmol/mole=3.5×10−3 pmol/second3.5 \times 10^{-15}\text{ moles/second} \times 10^{12}\text{ pmol/mole} = 3.5 \times 10^{-3}\text{ pmol/second}
Since 1 picomole (pmol)=10−12 moles1\text{ picomole (pmol)} = 10^{-12}\text{ moles}, there are 1012 picomoles10^{12}\text{ picomoles} in 1 mole1\text{ mole}. Multiplying by this factor converts the unit of quantity.
2
Convert the rate from per second to per hour.
3.5×10−3 pmol/second×3,600 seconds/hour=1.26×101 pmol/hour3.5 \times 10^{-3}\text{ pmol/second} \times 3,600\text{ seconds/hour} = 1.26 \times 10^1\text{ pmol/hour}
There are 3,600 seconds3,600\text{ seconds} in one hour. Multiplying the per-second rate by 3,6003,600 gives the total consumption over the duration of an hour.

Key Concept

Scientific Notation and Unit Conversions
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Scientific Notation and Unit Conversions

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