Problem 42 - Chemistry and Chemical Reactivity

Question

The solder once used by plumbers to fasten copper pipes together consists of \(67 \%\) lead and \(33 \%\) tin. What is the mass of lead in a \(250-\mathrm{g}\) block of solder?

Step-by-Step Solution

Answer

There are 167.5 grams of lead in the solder block.

Step 1: Understand the Problem

We are given a block of solder that weighs 250 grams, and we know it consists of 67% lead and 33% tin. The task is to find out how many grams of lead are present in this block.

Step 2: Convert the Percentage to a Decimal

Convert the percentage of lead into a decimal for calculation. Since 67% is the same as 67 per 100, we express this as a decimal by dividing by 100, i.e., \(67\% = 0.67\).

Step 3: Calculate the Mass of Lead

Multiply the total mass of the solder block by the decimal equivalent of the lead percentage to find the mass of lead. This calculation is as follows: \(250 \, \text{g} \times 0.67 = 167.5 \, \text{g}\).

Step 4: Answer Verification

Ensure the calculation is accurate by checking the multiplication: \(250 \, \text{g} \times 0.67 = 167.5 \, \text{g}\). This confirms our solution as correct.

Key Concepts

Mass Percentage

Mass percentage is a critical concept in chemistry, especially in stoichiometry. This concept simplifies how we discuss the composition of mixtures and alloys, like the combination of different metals.
For instance, when we examine an alloy, the mass percentage tells us how much of each substance is present in terms of mass.

• A percentage is simply a part of the whole, expressed per hundred, making it easy to understand and communicate fractions of a mixture.
• To calculate mass percentage, we use the formula: \( \text{mass percentage} = \left( \frac{\text{mass of component}}{\text{total mass of mixture}} \right) \times 100 \% \).

This formula helps to find out what portion of the total mass comes from a specific component. For example, if you have a solder made from lead and tin with 67% being lead, it implies that 67% of the alloy's mass consists of lead atoms.
Understanding mass percentage is vital not only for solving chemical computation exercises but also for real-world applications in manufacturing and quality control of products.

Lead-Tin Alloy

A lead-tin alloy is a common mixture used in applications like soldering, where high melting points and ease of use are essential. Alloying metals mix properties and create materials with characteristics not available in pure metals alone.
This specific alloy consists of two metals: lead and tin.

• Lead contributes to the alloy's mass and balance, providing durability.
• Tin facilitates the easy melting and manipulation of the alloy, making it practical for joining metal parts.

Plumbers and other technicians have historically used this alloy for joining metal pipes. A standard composition might involve 67% lead and 33% tin, just like in the problem at hand.
The ratio helps in determining the alloy's strength, flexibility, and melting point, making it much more useful than the individual metals alone. Knowing the exact percentages of each metal helps in engineering the material for the specific application needs.

Mass Calculation

When tasked with calculating mass in a mixed element such as an alloy, understanding how to apply composition percentages is key. This integrates mathematics with chemistry to derive precise component masses from a total mass.
To determine the mass of a specific element within a mixture:

• First, convert the given percentage into a decimal. For example, 67% becomes 0.67.
• Next, multiply the total mass of the mixture by this decimal.

For our solder block problem:The formula used is \( \text{mass of lead} = \text{total mass} \times \text{percentage as a decimal} \).
Plugging in the numbers, we find that:\( 250 \, \text{g} \times 0.67 = 167.5 \, \text{g} \)..
In this way, we determine the mass of lead in our block as 167.5 grams. This method ensures accuracy regardless of the total mass or percentage of components involved.