Three students were asked to find the identity of the metal in a particular sulfate salt. They dissolved a 0.1472-g sample of the salt in water and treated it with excess barium chloride, resulting in the precipitation of barium sulfate. After the precipitate had been filtered and dried, it weighed 0.2327 g. Each student analyzed the data independently and came to different conclusions. Pat decided that the metal was titanium. Chris thought it was sodium. Randy reported that it was gallium. What formula did each student assign to the sulfate salt? Look for information on the sulfates of gallium, sodium, and titanium in this text and reference books such as the CRC Handbook of Chemistry and Physics. What further tests would you suggest to determine which student is most likely correct?

First, we can determine the moles of sulfate ions (SO4) in the sample. To do this, we need the mass of barium sulfate (BaSO4) formed (0.2327 g) and the molar mass of BaSO4. The molar mass of BaSO4 can be calculated as: Ba: 137.33 g/mol S: 32.07 g/mol O: 4 * 16.00 g/mol = 64.00 g/mol Molar mass of BaSO4 = 137.33 + 32.07 + 64.00 = 233.4 g/mol Now, we can find the moles of sulfate ions: moles of BaSO4 = mass of BaSO4 / molar mass of BaSO4 moles of BaSO4 = 0.2327 g / 233.4 g/mol ≈ 0.001 mol Since barium sulfate has one sulfate ion per formula unit, there are 0.001 moles of sulfate ions in the sample.

Next, we need to calculate the moles of each metal in the sample. We can do this using the moles of sulfate ions and the stoichiometry of the possible sulfate salts that students assigned: A) Pat's molecular formula (titanium sulfate): Ti(SO4)2 B) Chris's molecular formula (sodium sulfate): Na2SO4 C) Randy's molecular formula (gallium sulfate): Ga2(SO4)3 Calculate moles of metal for each student: A) Pat (Ti): moles of Ti = 0.5 * moles of SO4 = 0.5 * 0.001 mol = 0.0005 mol B) Chris (Na): moles of Na = 2 * moles of SO4 = 2 * 0.001 mol = 0.002 mol C) Randy (Ga): moles of Ga = (2/3) * moles of SO4 = (2/3) * 0.001 mol ≈ 0.00067 mol

Now that we have the moles of each metal, we can get the formula each student assigned by calculating the mass of the metal in the sample and using initial the mass (0.1472 g). We must consider that the sample has the mass of the metal and the sulfate ions. We can now calculate the molecular weight of each compound. Molar mass of SO4 = 32.07 + 4 * 16.00 = 96.07 g/mol A) Pat's formula (Ti(SO4)2): Molar mass of Ti(SO4)2 = (1 * 47.87) + (2 * 96.07) = 47.87 + 192.14 = 240.01 g/mol B) Chris's formula (Na2SO4): Molar mass of Na2SO4 = (2 * 22.99) + (1 * 96.07) = 45.98 + 96.07 = 142.05 g/mol C) Randy's formula (Ga2(SO4)3): Molar mass of Ga2(SO4)3 = (2 * 69.72) + (3 * 96.07) = 139.44 + 288.21 = 427.65 g/mol Finally, we can check which of these salts' molecular weight matches the initial mass presented (0.1472 g) and the results of step 1 (0.001 mol of sulfate ions).

We can suggest further tests to determine which student is most likely correct: 1) Perform a flame test on the original sulfate salt sample. Sodium and gallium salts have distinct flame colors (yellow and violet, respectively), while titanium salts do not produce any color. 2) Use X-ray diffraction on the original sulfate salt sample to identify the crystal structure of the compound, which may help in identifying the metal in the salt. 3) Perform complexometric titrations to determine the concentration of the metal ions in solution. This method would help differentiate between the salts based on their metal concentration. Overall, these tests will provide additional information to determine which student is correct and confirm the identity of the metal in the sulfate salt.