Question

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

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

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.

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.

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.

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.

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.

Key concepts

Chemical Formula Analysis

To properly understand the chemistry of the mineral torbernite, analyzing its chemical formula is crucial. Torbernite is denoted as \( \mathrm{Cu}\left(\mathrm{UO}_{2}\right)_{2}\left(\mathrm{PO}_{4}\right)_{2} \cdot 8 \mathrm{H}_{2} \mathrm{O} \), which tells us about its composition at a molecular level. This formula shows us the elements present and their respective quantities.
Here’s a breakdown:

• Copper (Cu): One atom per formula unit.
• Uranium Dioxide (UO₂): Unlike individual atoms, UO₂ is a group treated as one unit; there are two of these units in each formula, contributing to a total of 4 oxygen atoms and 2 uranium atoms.
• Phosphate (PO₄): Also a grouped entity, with 2 PO₄ in the formula unit, contributing 2 phosphorus and 8 oxygen atoms.
• Water (H₂O): This is a hydrated compound, having 8 water molecules, providing 16 hydrogen atoms and 8 additional oxygen atoms.

By understanding these groups and their multiplicities, we can calculate the total number of atoms: 47 in total for one formula unit of torbernite. Recognizing how chemical formulas provide such detailed information can help in a variety of further analyses.

Atomic Mass Calculation

Calculating atomic mass involves summing the mass contributions of each element in a compound according to the periodic table. For torbernite, we calculated its molecular mass by adding up the mass of all its constituent atoms.
Here’s a step-by-step on how this is accomplished:

• Each hydrogen atom weighs approximately 1.01 g/mol and since there are 16 hydrogen atoms (from H₂O), they contribute 16.16 g/mol to the total mass.
• Each oxygen atom has a mass of about 16.00 g/mol. With 24 oxygen atoms present, oxygen contributes a substantial 384 g/mol.
• Copper, with a single atom in the formula, adds 63.55 g/mol.
• Each of the two phosphorus atoms weighs roughly 30.97 g/mol, contributing 61.94 g/mol in total.
• Uranium, considerably heavy, contributes significantly as each atom weighs about 238.03 g/mol, resulting in 476.06 g/mol for both U atoms.

Summing these contributions gives us a total mass of approximately 1061.87 g/mol for torbernite. Understanding these calculations aids in knowing how much of a particular element is present, by mass, in any compound or mineral.

Elemental Mass Percent

Determining the elemental mass percent involves calculating how much of a given element contributes to the total mass of the compound. To find the mass percent of elements in torbernite, we looked at the contribution of each element or group of elements towards the overall mass.
Here's the breakdown for torbernite's components:

• Uranium (U): Given its large atomic mass of 238.03 g/mol and its significant number in the formula, uranium has the greatest mass contribution.
• Oxygen (O): Given its presence in multiple structural groups (UO₂, PO₄, H₂O), oxygen forms a considerable part of the total mass.
• Phosphorus (P), Hydrogen (H), and Copper (Cu): These contribute less in terms of total percentage due to their relatively lower atomic masses and quantities.

The total mass of torbernite is dominated by oxygen and uranium, with uranium leading in mass percentage. This analysis helps in understanding the distribution of different elements by their mass, which is critical in determining a mineral's properties and its practical applications.