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Concept explainers
(a)
Interpretation:
The volume of a bacterial cell in cubic millimeters (mm3) is to be calculated.
Concept introduction:
Volume is a physical quantity and its SI unit is cubic meter (m3). The volume of an object is equal to the product of the height, length, and breadth of the object. Length, breadth, and height of an object is measured in the units of length. Therefore, volume has the unit of length to the cubic power. The other unit of the volume are liter, milliliter, cubic decimeter, microliter.
The conversion of one unit into another can be done using a proper conversion factor. Conversion factors are the ratios that relate the two different units of a quantity. It is also known as dimensional analysis or factor label method.
In the unit conversion problems, the given information is multiplied by the conversion factors to obtain the desired information. The unit conversion can be done as follows:
(beginning unit)(Final unitbeginning unit)=Final unit
(a)
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Answer to Problem 1.36P
The volume of a bacterial cell in cubic millimeters (mm3) is 2.56×10−9 mm3/cell.
Explanation of Solution
The volume of a bacterial cell in cubic micrometer (μm3) is 2.56 μm3.
The road map to calculate the volume of a bacterial cell in cubic millimeters (mm3) is as follows:
The conversion factor to convert volume from cubic micrometer (μm3) to cubic meter (m3) is,
(1 μm)3=(1×10−6 m)3
The conversion factor to convert volume from cubic meter (m3) to cubic millimeters (mm3) is,
(1×10−3 m)3=(1 mm)3
Convert the volume from cubic micrometer (μm3) to cubic millimeters (mm3) as:
Volume(mm3)=2.56 μm3((1×10−6 m)3(1 μm)3)((1 mm)3(1×10−3 m)3)=2.56×10−9 mm3/cell
The volume of a bacterial cell in cubic millimeters (mm3) is 2.56×10−9 mm3/cell.
(b)
Interpretation:
The volume of 105 bacterial cell in liter (L) is to be calculated.
Concept introduction:
Volume is a physical quantity and its SI unit is cubic meter (m3). The volume of an object is equal to the product of the height, length, and breadth of the object. Length, breadth, and height of an object is measured in the units of length. Therefore, volume has the unit of length to the cubic power. The other unit of the volume are liter, milliliter, cubic decimeter, microliter.
The conversion of one unit into another can be done using a proper conversion factor. Conversion factors are the ratios that relate the two different units of a quantity. It is also known as dimensional analysis or factor label method.
In the unit conversion problems, the given information is multiplied by the conversion factors to obtain the desired information. The unit conversion can be done as follows:
(beginning unit)(Final unitbeginning unit)=Final unit
(b)
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Answer to Problem 1.36P
The volume of 105 bacterial cell in liter (L) is 10−10 L.
Explanation of Solution
The volume of a bacterial cell in cubic micrometer (μm3) is 2.56 μm3.
The road map to calculate the volume of 105 bacterial cell in liter (L) is as follows:
The conversion factor to convert volume from cubic micrometer (μm3) to cubic meter (m3) is,
(1 μm)3=(1×10−6 m)3
The conversion factor to convert volume from cubic meter (m3) to cubic centimeters (cm3) is,
(1×10−2 m)3=(1 cm)3
The conversion factor to convert volume from cubic centimeters (cm3) to milliliters (mL) is,
(1 cm)3=1 mL
The conversion factor to convert volume from milliliters (mL) to liter (L) is,
1 mL=10−3 L
Convert the volume from cubic micrometer (μm3) to liter (L) as:
Volume(L)=2.56 μm3((1×10−6 m)3(1 μm)3)((1 cm)3(1×10−2 m)3)(1 mL(1 cm)3)(10−3 L1 mL)=2.56×10−15 L/cell
Calculate the volume of 105 bacterial cell in liter (L) as:
Volume(L)=(105 cell)(2.56×10−15 L/cell)=2.56×10−10 L=10−10 L
The volume of 105 bacterial cell in liter (L) is 10−10 L.
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Chapter 1 Solutions
Chemistry: The Molecular Nature of Matter and Change
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