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stiks02 [169]
4 years ago
6

The rock in a lead ore deposit contains 89 % PbS by mass. How many kilograms of the rock must be processed to obtain 1.5 kg of P

b?
Chemistry
1 answer:
Zolol [24]4 years ago
5 0

Answer:

Approximately 1.9 kilograms of this rock.

Explanation:

Relative atomic mass data from a modern periodic table:

  • Pb: 207.2;
  • S: 32.06.

To answer this question, start by finding the mass of Pb in each kilogram of this rock.

89% of the rock is \rm PbS. There will be 890 grams of \rm PbS in one kilogram of this rock.

Formula mass of \rm PbS:

M(\mathrm{PbS}) = 207.2 + 32.06 = 239.26\; g\cdot mol^{-1}.

How many moles of \rm PbS formula units in that 890 grams of \rm PbS?

\displaystyle n = \frac{m}{M} = \rm \frac{890}{239.26} = 3.71980\; mol.

There's one mole of \rm Pb in each mole of \rm PbS. There are thus \rm 3.71980\; mol of \rm Pb in one kilogram of this rock.

What will be the mass of that \rm 3.71980\; mol of \rm Pb?

m(\mathrm{Pb}) = n(\mathrm{Pb}) \cdot M(\mathrm{Pb}) = \rm 3.71980 \times 207.2 = 770.743\; g = 0.770743\; kg.

In other words, the \rm PbS in 1 kilogram of this rock contains \rm 0.770743\; kg of lead \rm Pb.

How many kilograms of the rock will contain enough \rm PbS to provide 1.5 kilogram of \rm Pb?

\displaystyle \frac{1.5}{0.770743} \approx \rm 1.9\; kg.

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3 years ago
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