Problem 46 - Chemistry and Chemical Reactivity

Question

Calculate the weight percent of titanium in the mineral ilmenite, FeTiO \(_{3}\). What mass of ilmenite (in grams) is required if you wish to obtain 750 g of titanium?

Step-by-Step Solution

Answer

The weight percent of titanium in ilmenite is 31.56%. Approximately 2377.57 g of ilmenite is required to obtain 750 g of titanium.

Step 1: Molar Mass Calculation

First, we need to calculate the molar mass of ilmenite, FeTiO_3. The molar mass is the sum of the atomic masses of all the atoms in the formula. Ilmenite consists of iron (Fe), titanium (Ti), and oxygen (O)._ - Iron, Fe: 55.85 g/mol- Titanium, Ti: 47.87 g/mol- Oxygen, O: 16.00 g/mol (since there are three oxygens, it's 16.00*3 = 48.00 g/mol) Therefore, the molar mass of FeTiO_3 is:\[ 55.85 + 47.87 + 48.00 = 151.72 \, \text{g/mol} \]

Step 2: Calculate Weight Percent of Titanium

Now we calculate the weight percent of titanium in ilmenite. The weight percent is determined by the ratio of the mass of titanium to the total molar mass of ilmenite, then multiplied by 100.\[ \text{Weight Percent of Ti} = \left(\frac{47.87}{151.72}\right) \times 100 = 31.56\,\% \]

Step 3: Determine Mass of Ilmenite for 750 g Titanium

We need to find out how much ilmenite is needed to obtain 750 g of titanium. Using the weight percent of titanium calculated previously, we set up the equation:\[ \text{Mass of Ilmenite} = \frac{\text{Mass of Ti}}{\text{Weight Percent of Ti}} \]Substitute 750 g for the mass of titanium:\[ \text{Mass of Ilmenite} = \frac{750 \, \text{g}}{31.56\%} = \frac{750}{0.3156} = 2377.57 \, \text{g} \]

Key Concepts

Molar Mass

Understanding molar mass is fundamental in chemistry. It represents the mass of one mole of a compound. In general, you can find the molar mass by adding up the atomic masses of all the atoms in the chemical formula.
For instance, in the mineral ilmenite, with the chemical formula \( \text{FeTiO}_3 \), there are three types of atoms: iron (Fe), titanium (Ti), and oxygen (O).

• Iron has an atomic mass of 55.85 g/mol.
• Titanium has an atomic mass of 47.87 g/mol.
• Oxygen has an atomic mass of 16.00 g/mol, but there are three oxygen atoms, contributing \( 16.00\times3 = 48.00 \) g/mol to the molar mass.

When you add these values together: 55.85 + 47.87 + 48.00, you find that ilmenite's molar mass is 151.72 g/mol.
This calculation is crucial as it allows us to understand the proportion of each element within a compound.

Chemical Composition

Chemical composition refers to the types and amounts of elements present in a compound. It's a vital concept for determining how much of each element is in an object or substance, such as a mineral. To calculate the weight percent of an element, like titanium in ilmenite, use the formula:\[ \text{Weight Percent} = \left( \frac{\text{mass of element}}{\text{total molar mass of compound}} \right) \times 100 \]For ilmenite, you're focusing on titanium. With the known molar mass of titanium being 47.87 g/mol and the total molar mass of ilmenite at 151.72 g/mol, the weight percent calculation becomes:\[ \text{Weight Percent of Ti} = \left( \frac{47.87}{151.72} \right) \times 100 = 31.56\% \]
Understanding the chemical composition helps us predict how much ilmenite is necessary to extract a desired amount of titanium.

Ilmenite Mineral

Ilmenite is a naturally occurring mineral composed of iron, titanium, and oxygen. Its chemical formula is \( \text{FeTiO}_3 \). This mineral is significant in industries as a major source of titanium, often used for making pigments or as a structural material in alloys.
When tasked with extracting a specific amount of titanium from ilmenite, it's essential to know its composition and perform accurate calculations. Using its weight percent, you can determine how much of the mineral is required to obtain the desired titanium. For example, to get 750 g of titanium using the previously calculated weight percent:

1. Convert the percentage into a decimal by dividing it by 100, which gives 0.3156.
2. Set up your equation: \( \text{Mass of Ilmenite} = \frac{\text{Mass of Ti}}{\text{Weight Percent of Ti}} \).
3. Substitute the values and solve: \( \frac{750 \text{ g}}{0.3156} = 2377.57 \text{ g} \).

This calculation tells you the mass of ilmenite needed to yield the specific mass of titanium.