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Chapter 3: Problem 17

For the mineral torbernite, \(\mathrm{Cu}\left(\mathrm{UO}_{2}\right)_{2}\left(\mathrm{PO}_{4}\right)_{2} \cdot 8 \mathrm{H}_{2} \mathrm{O}\) determine (a) the total number of atoms in one formula unit (b) the ratio, by number, of \(\mathrm{H}\) atoms to \(\mathrm{O}\) atoms (c) the ratio, by mass, of \(\mathrm{Cu}\) to \(\mathrm{P}\) (d) the element present in the greatest mass percent (e) the mass required to contain \(1.00 \mathrm{g} \mathrm{P}\)

Short Answer

Expert verified
The number of atoms in one formula unit of Torbernite is 47. The ratio of H atoms to O atoms is 2:3 by number. The ratio of Cu to P is approximately 2.05 by mass. The element present in the greatest mass percent is U. To contain 1.00 g of P, 17.13 g of Torbernite is needed.

Step by step solution

01

Determine Total Number of Atoms in Torbernite

To find the total number of atoms, we sum up the atoms of each element in the formula:\n1 atom of Cu + 2 atoms of UO2 + 2 atoms of PO4 + 8 atoms of H2O = 1 + 2*(1+2*2) + 2*(1+4*1) + 8*(2+1) = 47 atoms per formula unit.
02

Calculate the Ratio of H Atoms to O Atoms

By counting, we see there are 16 hydrogen atoms and 24 oxygen atoms in the formula. Hence, the ratio of H atoms to O atoms: 16/24 = 2/3.
03

Determine the Mass Ratio of Cu to P

First, find the atomic masses of Cu and P. From the periodic table, the atomic mass of Cu is approximately 63.55 g/mol and P is 30.97 g/mol. Next, calculate the ratio of their masses: 63.55 g/mol(Cu)/30.91 g/mol(P) = 2.05.
04

Determine the Element Present in the Greatest Mass Percent

To find out the element contributing most to the mass, calculate the mass contribution of each element in the formula and express it as a percentage of the total mass. The atomic masses of H, O, P, U, and Cu are approximately 1.01, 16.00, 30.97, 238.03, and 63.55 g/mol respectively. The calculated total mass is 1061.87 g/mol and Uranyl (UO2) contributes most to this.
05

Calculate the Mass Required to Contain 1.00g P

Calculate the proportion of P mass in the formula unit using the atomic mass of P (30.97 g/mol) and then calculate the total torbernite mass (1061.87 g/mol). If 2 * 30.97 g/mol P is contained in 1061.87 g/mol of Torbernite, then 1.00 g of P would be contained in (1.00 g / 2*30.97 g/mol) x 1061.87 g/mol = 17.13 g of Torbernite.

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