Question

Brass is an alloy of copper and zinc. Varying the mass percentages of the two metals produces brasses with different properties. A brass called yellow zinc has high ductility and strength and is \(34-37 \%\) zinc by mass. (a) Find the mass range (in g) of copper in \(185 \mathrm{~g}\) of yellow zinc. (b) What is the mass range (in \(\mathrm{g}\) ) of zinc in a sample of yellow zinc that contains \(46.5 \mathrm{~g}\) of copper?

Short answer

Copper: 116.6 g to 122.1 g; Zinc: 23.95 g to 27.31 g

Step-by-step solution

Determine Zinc Percentage

Yellow zinc contains between 34% and 37% zinc by mass. Therefore, the percentage of copper in yellow zinc is given by 100% - zinc percentage.

Calculate Mass Range of Copper in 185 g of Yellow Zinc

If yellow zinc weighs 185 g and contains 34% zinc, then the percentage of copper is 66%. Similarly, if yellow zinc contains 37% zinc, then the percentage of copper is 63%. Therefore, calculate the mass range of copper as follows: Lower bound: percentage of copper = 66% mass of copper = 66/100 * 185 g mass of copper ≈ 122.1 gUpper bound: percentage of copper = 63% mass of copper = 63/100 * 185 g mass of copper ≈ 116.6 gHence, the mass range of copper is approximately 116.6 g to 122.1 g.

Calculate Mass Range of Zinc with 46.5 g Copper

Given 46.5 g of copper in the yellow zinc, and recalling that yellow zinc contains 34 - 37% zinc: Lower bound (34%): mass of zinc = total mass - mass of copper let total mass be X, 0.66X = 46.5 g (since 66% is copper) solve for X: X ≈ 70.45 g mass of zinc = 70.45 g - 46.5 g ≈ 23.95 gUpper bound (37%): mass of zinc = total mass - mass of copper let total mass be Y, 0.63Y = 46.5 g (since 63% is copper) solve for Y: Y ≈ 73.81 g mass of zinc = 73.81 g - 46.5 g ≈ 27.31 gTherefore, the mass range of zinc is approximately 23.95 g to 27.31 g.

Key concepts

Alloy Composition

An alloy is a mixture of two or more elements, where at least one is a metal. Alloys are designed to have specific properties by mixing different ratios of elements. When it comes to brass, which is an alloy of copper and zinc, the properties can be changed by varying the amounts of these two metals. In our example, 'yellow zinc' brass can have a zinc content between 34% and 37%, giving it high ductility and strength. This specific composition allows it to be used for various applications that require both flexibility and resilience. By understanding the composition, one can predict the properties and suitable uses of the alloy.

Mass Percentage Calculations

Mass percentage calculations are essential to determine the relative amounts of each element in an alloy. The mass percentage is simply the mass of one component divided by the total mass of the mixture, multiplied by 100.
For example, if we have 185 g of yellow zinc containing 34% zinc, we can calculate the amount of copper as follows:
1. Determine the percentage of copper: 100% - 34% = 66% copper.
2. Calculate the mass: (66/100) * 185 g ≈ 122.1 g of copper.
Similar steps are followed if the zinc content is 37%, leading to 63% copper, which results in: (63/100) * 185 g ≈ 116.6 g.
These calculations help in understanding the variation in alloy composition and adjusting it according to specific needs.

Metal Properties

The properties of metals in an alloy like brass depend on their composition. With higher zinc content (closer to 37%), yellow zinc brass has increased strength and ductility. This makes it suitable for applications like forming into shapes and resisting wear. On the other hand, with a lower zinc content (around 34%), there might be slight variations in these mechanical properties.
The ability to tweak these properties by adjusting the metal composition is one of the significant advantages of alloys. This customization allows engineers and scientists to develop materials tailor-made for specific tasks. Understanding these principles is key to material science and engineering.