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The density of titanium is 4.50 g/cm3 . What is the edge length (in cm ) of a titanium cube that contains 2.23×1024 titanium atoms? Express your answer to three significant figures.

User BuraCULa
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Answer:

3.37 cm

Step-by-step:

The edge length of the titanium cube can be calculated using the formula:

Edge length = (Volume of cube)^(1/3)

And the volume of the cube can be calculated as follows:

1. Calculate the mass of the titanium atoms in the cube.

The mass of one titanium atom can be calculated by dividing the molar mass of titanium by Avogadro's number:

Mass of one titanium atom = Molar mass of titanium / Avogadro's number

= 47.867 g/mol / (6.022 × 10^23 atoms/mol)

= 7.943 × 10^-23 g/atom

The total mass of the titanium atoms in the cube is then:

Total mass of titanium atoms = (2.23 × 10^24 atoms) × (7.943 × 10^-23 g/atom)

= 1.773 × 10^2 g

2. Calculate the volume of the titanium cube.

The volume of the cube can be calculated by dividing the total mass of the titanium atoms by the density of titanium:

Volume of cube = Total mass of titanium atoms / Density of titanium

= 1.773 × 10^2 g / 4.50 g/cm^3

= 39.4 cm^3

3. Calculate the edge length of the titanium cube.

Finally, the edge length of the cube can be calculated as:

Edge length = (Volume of cube)^(1/3)

= (39.4 cm^3)^(1/3)

= 3.37 cm

So the edge length of the titanium cube is 3.37 cm, rounded to three significant figures.

Hope this helps!

User Origamic
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