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UNO
3 months ago
11

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)

Chemistry
2 answers:
KiRa [2.9K]3 months ago
8 0

Answer:

The answer is 7160 cm

Explanation:

Given Data

Diameter = 1 mm

Length =?

Quantity of gold = 1 mol

Density = 17 g/cm³

Steps

1.- Obtain the atomic mass of gold

Atomic mass = 197 g

This means 197g ------------ 1 mol

2.- Find the volume of the wire

Density = mass/volume

Volume = mass/density

Volume = 197/17

Volume = 5.7 cm³

3.- Calculate the wire length

Volume = πr²h

Rearranging for h

h = volume / πr²

Radius = 0.05 cm

Substituting values

h = 5.7/(3.14 x 0.05²)

h = 5.7 / 0.0025

h = 7159.2 cm ≈ 7160 cm

eduard [2.7K]3 months ago
7 0

Answer:

The wire's length is 1477 cm

Explanation:

Step 1: Provided Data

Diameter = 1.00 mm

Gold moles = 1.00 mol

Gold density = 17.0 g/cm³

Molar mass of gold = 196.97 g/mol

Step 2: Determining volume

Volume = mass / density

Volume = 196.97 grams / 17.0 g/cm³

Volume = 11.6 cm³

Step 3: Finding length

Volume = π*r²*length

11.6 = π *(0.05)² *length

length = 1477 cm

<pThus, the wire's length is 1477 cm
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