Problem 80 - Chemistry The Molecular Science

Question

The cancer drug cisplatin contains \(65.0 \%\) platinum. You have a \(1.53-\mathrm{g}\) sample of the compound; calculate the mass of platinum it contains.

Step-by-Step Solution

Answer

The sample contains approximately 0.995 grams of platinum.

Step 1: Understand the Problem

We have a sample of the cancer drug cisplatin, which is composed of 65.0% platinum by mass. We need to find out how much of this 65% is in a 1.53-gram sample of cisplatin.

Step 2: Convert Percentage to Decimal

Convert the percentage of platinum into a decimal by dividing by 100. This can be expressed as\[\text{Decimal form} = \frac{65.0}{100} = 0.65\]

Step 3: Calculate the Mass of Platinum

To find the mass of platinum, multiply the decimal form of the percentage by the total mass of the sample:\[\text{Mass of platinum} = 0.65 \times 1.53 \]Performing this calculation gives:\[\text{Mass of platinum} = 0.9945 \, \text{grams}\]

Step 4: Rounding the Answer

Since it is often appropriate to show the result to the correct number of significant figures based on the input data, round the result to three significant figures (which matches the number in the initial mass provided):\[\text{Mass of platinum} \approx 0.995 \, \text{grams}\]

Key Concepts

Cisplatin Chemistry

Cisplatin is a powerful chemotherapy drug used to treat various types of cancer. Its effectiveness stems from its ability to bind to DNA within cancer cells, preventing them from replicating and growing. The chemical formula of cisplatin is Pt(NH₃)₂Cl₂, indicating that it consists of a platinum atom at its core, surrounded by two ammonia molecules and two chloride ions. This structure allows it to form cross-links in DNA, disrupting the cell's normal function. When dealing with cisplatin in chemical calculations, knowing its composition is essential, especially its platinum content, which is a significant percentage of the whole compound. Understanding the exact composition and behavior of cisplatin in biological systems helps chemists and biologists alike in optimizing its use and improving therapeutic strategies.

Significant Figures in Calculations

Significant figures are crucial in scientific calculations because they communicate the precision of measurements. When performing calculations, the number of significant figures indicates the reliability of the data. For instance, in this exercise, the starting mass of cisplatin is given with three significant figures (1.53 grams), meaning any result should reflect that same level of precision. To determine the number of significant figures:

• All non-zero digits are significant.
• Any zeros between significant digits are also significant.
• Leading zeros are not significant, but trailing zeros in a decimal fraction are.

In our earlier calculation, the mass of platinum is initially calculated to be 0.9945 grams, then rounded to 0.995 grams, ensuring three significant figures, consistent with the starting measurement.

Mass Calculation

The process of calculating mass in compositions like cisplatin involves a straightforward method using percentages. In our exercise, cisplatin contains 65.0% platinum by mass. To find out how much platinum is in a given mass of cisplatin, you must first convert the percentage to a decimal format by dividing by 100, which gives 0.65. Next, this decimal is multiplied by the mass of the entire sample (1.53 grams in this case) to find the mass of platinum:\[\text{Mass of platinum} = 0.65 \times 1.53 = 0.9945 \text{ grams}\]The final step is rounding the product to the correct number of significant figures, which matched the initial data at three, resulting in 0.995 grams. This simple calculation process allows one to determine the constituent mass within a mixture or compound based on percentage mass composition.