3) Some ionic compounds contain a mixture of different charged cations. For example, some titanium oxides contain a mixture of and ions. Consider a certain oxide of titanium that is 28.31% oxygen by mass and contains a mixture of and ions. Determine the formula of the compound and the relative numbers of and ions.
To determine the formula of the compound and the relative numbers of ions, we need to use some principles of stoichiometry.
1. Start by assuming that there are x moles of oxygen in the compound. Since the compound is 28.31% oxygen by mass, we can convert this percentage to grams and then to moles. The molar mass of oxygen is 16.00 g/mol.
Mass of the compound = Mass of oxygen = 28.31% × mass of compound
Mass of compound = (28.31/100) × mass of compound
Mass of compound = 0.2831 × mass of compound
Now, we can calculate the moles of oxygen:
Moles of oxygen = Mass of oxygen / Molar mass of oxygen
Moles of oxygen = 0.2831 × mass of compound / 16.00 g/mol
Moles of oxygen = 0.01769 × mass of compound
Therefore, we have x = 0.01769 × mass of compound moles of oxygen in the compound.
2. Next, let's consider the mixture of cations in the compound. The compound contains both and ions. We need to determine the relative number of each ion.
Let's assume there are y moles of ions and z moles of ions in the compound.
3. To form an electrically neutral compound, the total positive charges from cations must balance the total negative charges from anions. In this case, we have two cations () per formula unit. Since the formula unit is neutral, the total positive charge must be equal to the total negative charge.
From the information given, we know that 1 mole of compound contains y moles of ions, and each ion has a charge of +2.
So, the total positive charge from cations in 1 mole of compound is equal to 2 × y.
From the information given, we also know that 1 mole of compound contains z moles of oxygen ions (ions), and each ion has a charge of -2.
So, the total negative charge from anions in 1 mole of compound is equal to 2 × z × (-2) = -4z.
In an electrically neutral compound, the total positive charge from cations must balance the total negative charge from anions. Therefore:
2 × y = -4z
4. Now, let's consider the mole ratios of the elements in the compound. We know that the mole ratio of oxygen to titanium in the compound is 1:?
From the balanced formula for the compound, we can see that the ratio of moles of oxygen to moles of titanium is 2z:1.
From our previous calculation, we know that there are 0.01769 × mass of compound moles of oxygen in the compound. That means the moles of titanium are half that value:
Moles of titanium = (0.01769/2) × mass of compound
Now, we can set up an equation based on the mole ratio to find the value of z:
(0.01769/2) × mass of compound / y = 1/2z
Simplifying further:
y = (2z/0.01769) × (mass of compound)
5. Now we have two equations based on charge balance and the mole ratios:
Equation 1: 2y = -4z
Equation 2: y = (2z/0.01769) × (mass of compound)
We can solve these equations simultaneously to find the values of y and z.
Once we have the values of y and z, we can determine the formula of the compound based on the ratio of ions.
Please note that without the actual mass of the compound, we cannot determine the actual values of y and z or provide a specific formula for the compound.