A gold wire has a diameter of 1.00 mm. What length of this wire contains exactly 1.00 mol of gold? (density of Au = 17.0 g/cm3)

The answer to your question is 7160 cm

Explanation:

Data

diameter = 1 mm

length = ?

amount of gold = 1 mol

density = 17 g/cm³

Process

1.- Get the atomic mass of gold

Atomic mass = 197 g

then, 197g 1 mol

2.- Calculate the volume of this wire

density = mass/volume

volume = mass/density

volume = 197/17

volume = 5.7 cm³

3.- Calculate the length of the wire

Volume = πr²h

solve for h

h = volume /πr²

radius = 0.05 cm

substitution

h = 5.7/(3.14 x 0.05²)

h = 5.7 / 0.0025

h = 7159.2 cm ≈ 7160 cm

The length of this wire is 1477 cm

Explanation:

Step 1: Data given

diameter = 1.00 mm

Number of moles of gold = 1.00 mol

Density of gold = 17.0 g/cm³

Molar mass of gold = 196.97 g/mol

Step 2: Calculate volume

Volume = mass / density

Volume = 196.97 grams /17.0 g/cm³

Volume = 11.6 cm³

Step 3: Calculate length

Volume =  π*r²*length

11.6 =  π *(0.05)²  *length

length = 1477 cm

The length of this wire is 1477 cm