Problem 102 - Chemistry The Molecular Science

Question

The cancer drug cisplatin contains \(65.0 \%\) platinum. If you have \(1.53 \mathrm{~g}\) of the compound, calculate how many grams of platinum the sample contains.

Step-by-Step Solution

Answer

The sample contains 0.9945 grams of platinum.

Step 1: Understanding the Problem

We need to determine how many grams of platinum are present in a 1.53 g sample of a compound that contains 65% platinum.

Step 2: Convert Percentage to Decimal Form

Since the percentage of platinum in the compound is given as 65%, we convert this percentage to decimal form by dividing by 100. So, in decimal form, it is \(0.65\).

Step 3: Calculate the Mass of Platinum

To find the mass of platinum in the sample, we multiply the total mass of the compound by the decimal form of the percentage of platinum. \[ \text{Mass of platinum} = 0.65 \times 1.53 \] Perform the multiplication to find the result.

Step 4: Compute the Result

Performing the multiplication from Step 3 gives: \[ 0.65 \times 1.53 = 0.9945 \] Therefore, the mass of platinum in the sample is \(0.9945\) grams.

Key Concepts

Understanding Percentage Composition

Percentage composition is a crucial concept in chemistry, especially when analyzing compounds. It tells us what fraction of a compound is made up of a specific element by mass. For example, in the exercise, cisplatin is stated to be 65% platinum by mass. This means that in every 100 grams of cisplatin, 65 grams are pure platinum.
Understanding this helps us perform various calculations related to chemical quantities. To express percentage composition mathematically, we divide the mass of the element by the total mass of the compound and multiply by 100 to get a percentage. To use it in calculations like our exercise, it’s often necessary to convert this percentage to a decimal by dividing it by 100, so it integrates easily into mathematical operations.

Performing Mass Calculation

Mass calculation involves using known quantities and relationships to determine unknown masses within a compound. In the exercise, we know the total mass of the compound (1.53 g) and the percentage composition of platinum (65%). Our goal is to find the mass of platinum within that sample.
To do this, we first convert our percentage of platinum to a decimal which is 0.65. Next, we use this decimal to find the mass of platinum by multiplying it by the total mass of the compound. Essentially, the formula looks like this:

• \( \text{Mass of platinum} = \text{Decimal form of percentage} \times \text{Total mass of compound} \)

By plugging in the values from the problem, the calculation becomes:

• \( \text{Mass of platinum} = 0.65 \times 1.53 \)

Executing this multiplication gives us the grams of platinum in the sample.

Solving Chemistry Problems

Chemistry problem-solving often involves multiple steps that closely follow logical sequences just like mathematical puzzles. Here's how to efficiently tackle problems like these:

• First, ensure you understand the problem by identifying known and unknown quantities. In the exercise, the knowns are the total mass of cisplatin and its percentage composition of platinum.
• Next, use simpler operations for conversion and calculation, such as turning percentages into decimals.
• Then, utilize fundamental formulas for computation. In this case, multiplying the total mass by the decimal value of the percentage gives the mass of the specific element.

Each step should be thought through clearly before moving to the next, to avoid errors in calculating. By practicing meticulousness in each part of problem-solving, students can confidently tackle increasingly complex chemistry problems.