Answer:
1476.43 cm
Explanation:
From the question given above, the following data were obtained:
Diameter = 1 mm
Number of mole of Au = 1 mole
Density of Au = 17.0 g/cm³
Length of wire =?
Next, we shall determine the mass of 1 mole of Au. This can be obtained as follow:
Number of mole of Au = 1 mole
Molar mass of Au = 197 g/mol
Mass of Au =?
Mole = mass / Molar mass
1 = mass of Au / 197
Mass of Au = 1 × 197
Mass of Au = 197 g
Next, we shall determine the volume of the Au. This can be obtained as follow:
Density of Au = 17.0 g/cm³
Mass of Au = 197 g
Volume of Au =
Density = mass /volume
17 = 197 / Volume of Au
Cross multiply
17 × volume of Au = 197
Divide both side by 17
Volume of Au = 197 / 17
Volume of Au = 11.59 cm³
Next, we shall determine the radius of the gold wire. This can be obtained as follow:
Diameter = 1 mm
Radius =?
Radius = Diameter /2
Radius = 1/2
Radius = 0.5 mm
Converting 0.5 mm to cm, we have:
10 mm = 1 cm
Therefore,
0.5 mm = 0.5 mm × 1 cm / 10 mm
0.5 mm = 0.05 cm
Thus, the radius of the gold wire is 0.05 cm
Finally, we shall determine the length of the wire. This can be obtained as follow:
Volume of Au (V) = 11.59 cm³
Radius (r) = 0.05 cm
Pi (π) = 3.14
Length (L) =?
V = πr²L
11.59 = 3.14 × 0.05² × L
11.59 = 3.14 × 0.0025 × L
11.59 = 0.00785 × L
Divide both side by 0.00785
L = 11.59 / 0.00785
L = 1476.43 cm
Thus, the length of the gold wire is 1476.43 cm
