Problem: Lead metal can be extracted from a mineral called galena, which contains 86.6% lead by mass. A particular ore contains 68.5% galena by mass.If the lead can be extracted with 92.5% efficiency, what mass of ore is required to make a lead sphere with a 6.00 cm radius?

FREE Expert Solution

We are asked to calculate for the mass of ore required to make a lead (Pb) sphere with a 6.00 cm radius.

To solve this problem, we shall follow these steps:

Step 1: Determine the volume of the sphere.

Step 2: Using density, determine the mass of the ore required to make the lead sphere.

Step 1: The equation for the volume of a sphere is given as:

$\overline{){\mathbf{V}}{\mathbf{o}}{\mathbf{l}}{\mathbf{u}}{\mathbf{m}}{{\mathbf{e}}}_{\mathbf{s}\mathbf{p}\mathbf{h}\mathbf{e}\mathbf{r}\mathbf{e}}{\mathbf{=}}\left(\frac{\mathbf{4}}{\mathbf{3}}\right)\left(\mathbf{\pi }\right){{\mathbf{r}}}^{{\mathbf{3}}}}$

Where π = 3.1416 (constant)

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Problem Details

Lead metal can be extracted from a mineral called galena, which contains 86.6% lead by mass. A particular ore contains 68.5% galena by mass.

If the lead can be extracted with 92.5% efficiency, what mass of ore is required to make a lead sphere with a 6.00 cm radius?