Question

A solid mixture with density 3.25x10^-7 megagrams per cubic centimeter (Mg/cm³) is 2.00% silver by mass. How many ounces (oz) of silver are contained in a cube of the mixture that measures 30 nanometers (nm) on each side? Please use correct sig figs and show the steps clearly.

Answer 1

The solution calls for using consistent units for weight and volume

The folowing conversions are applicable in this case-

1 Mg = 1.0 x 10⁶ gms. , 3.25 x 10^-7 Mg = 0.325 gms.

So given density of the solid mixture = 0.325 gms / cm³

1 nm = 10^-7 cm ,    30nm = 30 x 10^-7 cm.

volume of the cube = { 30 x 10^-7 }³

hence , weight of the cube = volume x density

......................................... = { ( 30 x 10^-7 )³ x 0.325 }

weight of silver is 2.00%.... = { (30 x 10^-7 )³ x 0.325 x 0.02 } gms.

weight of silver in oz............ = { (30 x 10^-7 )³  x 0.325 x 0.02 } / 28.3495

...............................................= 6.1906 x 10^-21 oz.

Note ;

28.3495 gms. = 1 oz.

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