Question

Iron pyrite, often called "fool's gold," has the formula FeS\(_{2} .\) If you could convert \(15.8 \mathrm{kg}\) of iron pyrite to iron metal, what mass of the metal would your obtain?

Short answer

You would obtain 7.35 kg of iron.

Step-by-step solution

Determine Molar Mass of Components

Calculate the molar mass of Fe and S. For Fe (Iron), it is approximately 55.85 g/mol, and for S (Sulfur), it is approximately 32.07 g/mol.

Calculate Molar Mass of FeS2

The formula for iron pyrite is \(\text{FeS}_2\). The molar mass of FeS\(_2\) is given by the sum of molar masses of Fe and two S atoms: \(55.85 + 2(32.07) = 119.99\) g/mol.

Convert Kilograms to Grams

Convert the given mass of iron pyrite into grams: \(15.8 \text{kg} = 15800 \text{g}\).

Calculate Moles of FeS2

Using the molar mass of FeS\(_2\), convert the mass of FeS\(_2\) into moles: \(\frac{15800 \text{g}}{119.99 \text{g/mol}} = 131.68 \text{ moles of FeS}_2\).

Determine Moles of Iron from FeS2

Since each molecule of FeS\(_2\) contains one atom of Fe, the moles of Fe will be the same as the moles of FeS\(_2\): 131.68 moles of Fe.

Calculate Mass of Iron

Convert the moles of Fe back to grams using the molar mass of iron. Multiply the moles of Fe by the molar mass of Fe: \(131.68 \text{ moles} \times 55.85 \text{ g/mol} = 7354.76 \text{ g}\).

Convert Grams to Kilograms

Convert 7354.76 g of Fe to kilograms: \(\frac{7354.76 \text{g}}{1000} = 7.35 \text{kg}\).

Key concepts

Molar Mass Calculation

Calculating the molar mass is an essential technique in chemistry that assists in converting between mass and moles. The molar mass is the mass, in grams, of one mole of a substance. To find the molar mass of a compound, sum up the molar masses of all the elements that make up that compound.

Take, for example, iron pyrite, which has the chemical formula FeS\(_2\). To calculate the molar mass of iron pyrite, first determine the molar masses of its elements. For iron (Fe), the molar mass is approximately 55.85 g/mol, whereas for sulfur (S), it is approximately 32.07 g/mol. Since the formula for iron pyrite involves one iron atom and two sulfur atoms, the total molar mass of iron pyrite is calculated as follows:

\( 55.85 + 2 \times 32.07 = 119.99 \text{ g/mol} \).

Understanding how to perform these calculations makes it easier to approach more complex chemical problems.

Chemical Conversion

In chemistry, converting between different substances is an important aspect of problem-solving, often referred to as stoichiometry. This process involves using balanced chemical equations to calculate the masses, moles, or volumes of reactants and products.

Looking at the conversion of iron pyrite to iron, this involves determining how much iron can be obtained from a given mass of iron pyrite. This means reconciling the moles of the reactants (iron pyrite) to the moles of the product (iron). The number of moles can be directly related if the chemical reaction is known or if there's a one-to-one correspondence in the chemical formula.

This skill is vital in many chemical applications, including industry and research, as it allows chemists to predict and measure the outcomes of chemical processes.

Iron Pyrite

Iron pyrite, with the formula FeS\(_2\), is commonly known as "fool's gold" due to its metallic luster and pale brass-yellow hue, which gives it a superficial resemblance to gold. It is a naturally occurring mineral found in many geological formations.

Despite its misleading appearance, iron pyrite is rarely confused for real gold, but rather is valued for its sulfur content in the production of sulfuric acid. Chemically, it consists of iron and sulfur where the iron is in a +2 oxidation state, making it a valuable subject for various chemical processes including the extraction of iron.

Understanding the properties and composition of iron pyrite is crucial in fields like mineralogy, geology, and industrial chemistry.

Moles and Mass Conversion

Converting between moles and mass is a fundamental concept in chemistry. This conversion is often necessary for quantitative chemical analysis and synthesis. The link between these two is provided by the molar mass – the mass of one mole of a substance.

To perform a moles and mass conversion, you typically start with a known mass, convert it to moles using the molar mass, and then, if necessary, convert those moles back into another mass. For instance, in the conversion of iron pyrite to pure iron, knowing the mass of FeS\(_2\) allows us to determine the moles of iron we can obtain and subsequently calculate the mass of that iron.

This conversion process is key when working with chemical equations, as it helps calculate theoretical yields and compare them to actual yields in reaction efficiency studies.