Final answer:
To determine the percent composition of titanium in titanium(IV) permanganate, calculate the molar mass of the compound and then find the ratio of the mass of titanium to the total mass. The calculated percentage does not match any of the provided options, indicating a potential error in the question or options.
Step-by-step explanation:
To calculate the percent composition by mass of titanium(IV) permanganate, we need to first determine the formula for titanium(IV) permanganate, which is Ti(MnO4)4. Next, we calculate the molar mass of the entire compound by summing the atomic masses of all the atoms present in the formula. The atomic masses are approximately Ti = 47.867 g/mol, Mn = 54.938 g/mol, and O = 15.999 g/mol.
Using these atomic masses, the molar mass of titanium(IV) permanganate is calculated as follows:
Ti(MnO4)4 = 1(Ti) + 4(Mn) + 16(O) = 1(47.867 g/mol) + 4(54.938 g/mol) + 16(15.999 g/mol) = 47.867 g/mol + 219.752 g/mol + 255.984 g/mol = 523.603 g/mol.
Now, we find the mass percent composition of titanium in the compound:
(% Ti) = (mass of Ti / molar mass of compound) * 100 = (47.867 g/mol / 523.603 g/mol) * 100 ≈ 9.14%
However, none of the options given (a. 23.5%, b. 45.2%, c. 31.8%, d. 15.7%) match the calculated percentage. It appears there may have been an error in either the question or the options provided. As the calculated percent composition by mass of titanium in titanium(IV) permanganate does not match any given options, we cannot accurately select one of the given answers.