A silver wire has a diameter of 0.500 mm. What length of this wire contains exactly 1.00 mol of silver (density of Ag = 10.5 g/cm³) A) 52.3 m B) 222 m C) 13.1 m D) 2.01 m E) 890 m

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Quizplus · Accepted Answer

To find the length of wire that contains 1.00 mol of silver, we first calculate the mass of 1.00 mol of silver. The molar mass of silver (Ag) is approximately 107.87 g/mol. Therefore, 1.00 mol of silver has a mass of 107.87 g.Next, we calculate the volume of this mass of silver using the density formula: Density = Mass/Volume. Rearranging this formula gives Volume = Mass/Density. Substituting the mass of silver (107.87 g) and its density (10.5 g/cm^3) gives a volume of 10.27 cm^3.The volume of the wire can also be expressed as the product of its cross-sectional area and its length. The diameter of the wire is 0.500 mm, or 0.05 cm. The radius is half of the diameter, which is 0.025 cm. The cross-sectional area of the wire, using the formula for the area of a circle (πr^2), is π(0.025 cm)^2 = 0.0019635 cm^2.To find the length of the wire that has a volume of 10.27 cm^3, we divide the volume by the cross-sectional area: Length = Volume / Cross-sectional area = 10.27 cm^3 / 0.0019635 cm^2 = 5230 cm, or 52.3 m.

A Silver Wire Has a Diameter of 0