Question

Carboplatin \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{N}_{2} \mathrm{O}_{4} \mathrm{Pt}\right)\) is a platinum-containing compound that is used to treat certain forms of cancer. This compound contains 52.5\(\%\) platinum. If the price for platinum is \(\$ 1047 / \mathrm{troy}\) ounce, what is the cost of the platinum in 2.00 \(\mathrm{g}\) of this compound? A troy ounce is equal to 480 grains, and one grain is equal to 64.8 \(\mathrm{mg}\) .

Short answer

The mass of platinum in 2.00 g of Carboplatin is \(0.525 * 2.00 g = 1.05 g\). We can convert this to milligrams: \(1.05 g * 1000 = 1050 mg\). Then, we convert to grains: \(\frac{1050 mg}{64.8} = 16.2 \text{ grains}\). Next, we convert to troy ounces: \(\frac{16.2 \text{ grains}}{480} = 0.03375 \text{ troy ounces}\). Finally, we calculate the cost of platinum: \(0.03375 \text{ troy ounces} * $1047 = $35.34\). Therefore, the cost of the platinum in 2.00 g of Carboplatin is $35.34.

Step-by-step solution

Calculate the mass of platinum in Carboplatin

First, we need to find how much platinum is present in 2.00 g of Carboplatin. Since Carboplatin is 52.5% platinum by mass, we can calculate the mass of platinum as: Mass of platinum = 0.525 * Mass of Carboplatin Plug the mass of Carboplatin: Mass of platinum = 0.525 * 2.00 g

Convert mass of platinum from grams to milligrams

To continue with the conversion to troy ounces, we first need to convert the mass of platinum from grams to milligrams: 1 g = 1000 mg Mass of platinum = (Mass in grams) * 1000

Convert mass of platinum from milligrams to grains

Now that we have the mass of platinum in milligrams, we can convert it to grains using the given conversion: 1 grain = 64.8 mg Mass of platinum (in grains) = (Mass in milligrams) / 64.8

Convert mass of platinum from grains to troy ounces

Now that we have the mass of platinum in grains, we can convert it to troy ounces using the given conversion: 1 troy ounce = 480 grains Mass of platinum (in troy ounces) = (Mass in grains) / 480

Calculate the cost of platinum in Carboplatin

Finally, with the mass of platinum in troy ounces, we can calculate the cost of platinum in 2.00g Carboplatin using the provided price: Cost of platinum = (Mass in troy ounces) * (Price per troy ounce) After calculating each step, we will find the total cost of platinum in the 2.00 g of Carboplatin.

Key concepts

Molar Mass Calculations

Understanding molar mass is crucial to mastering stoichiometry in chemistry. It refers to the mass of one mole of a given substance and is measured in grams per mole (g/mol). To calculate molar mass, you sum the weighted average masses of each element in a compound, multiplied by the number of atoms of that element present in the formula.

For example, in the compound Carboplatin \(\mathrm{C}_{6}\mathrm{H}_{12}\mathrm{N}_{2}\mathrm{O}_{4}\mathrm{Pt}\), each element contributes to the total molar mass. By adding the mass of carbon (C) times six, hydrogen (H) times 12, and so on, we can determine the molar mass of the entire compound. This step is instrumental when determining the amount of a single element, like platinum, within the compound.

Unit Conversion

Chemistry calculations often require converting units to align with the question's needs. As seen in the step-by-step solution for calculating the cost of platinum in 2.00g of Carboplatin, there is a transition from grams to milligrams, followed by conversion to grains, and ultimately to troy ounces.

Each unit conversion requires knowledge of the conversion factor, like knowing that 1 gram is equivalent to 1000 milligrams. Unit conversion is a fundamental skill to ensure accurate results in chemical calculations and is widely applicable in real-world situations beyond the classroom.

Percent Composition

The percent composition of an element in a compound represents the percentage of the compound's total mass contributed by that element. This concept is key in stoichiometry because it allows chemists to understand the composition of substances and predict reactions' outcomes. In the given exercise, Carboplatin consists of 52.5% platinum by mass. To find the actual mass of the platinum in a given sample, this percentage is applied to the total mass of the sample. Percent composition plays a vital role in pharmaceuticals, where the precise formulation of compounds can mean the difference between a successful medication and a harmful one.

Chemistry in Real-Life Applications

The principles of chemistry, such as those discussed in stoichiometry, have numerous real-life applications. For instance, understanding the cost of raw materials in pharmaceuticals by quantifying the amount of a precious metal like platinum in a drug is an illustration of practical stoichiometry. This approach is used in cost-benefit analysis, product development, and economic forecasting within the chemical industry.

In environmental science, we apply stoichiometry to predict pollutant dispersal or nutrient cycles. In engineering, it supports materials science in developing stronger alloys. Clearly, these foundational concepts of chemistry extend well beyond the classroom, influencing various aspects of science and industry.