Ch.1 - Chemical Tools: Experimentation & Measurement

McMurry8th EditionChemistryISBN: 9781292336145Not the one you use?Change textbook

McMurry 8th Edition

Ch.1 - Chemical Tools: Experimentation & Measurement

Problem 117

Chapter 1, Problem 117

Brass is a copper–zinc alloy. What is the mass in grams of a brass cylinder having a length of 1.62 in. and a diameter of 0.514 in. if the composition of the brass is 67.0% copper and 33.0% zinc by mass? The density of copper is 8.92 g/cm3, and the density of zinc is 7.14 g/cm3. Assume that the den-sity of the brass varies linearly with composition.

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Convert the dimensions of the brass cylinder from inches to centimeters using the conversion factor 1 inch = 2.54 cm.

Calculate the volume of the cylinder using the formula for the volume of a cylinder: \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height.

Determine the density of the brass using the linear relationship between the densities of copper and zinc: \( \text{Density of brass} = (0.67 \times \text{Density of copper}) + (0.33 \times \text{Density of zinc}) \).

Calculate the mass of the brass cylinder using the formula: \( \text{Mass} = \text{Density} \times \text{Volume} \).

Ensure all units are consistent and check calculations for accuracy.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Density and Composition

Density is defined as mass per unit volume and varies with the composition of a material. In the case of brass, which is an alloy of copper and zinc, the density can be calculated based on the mass percentages of each metal. The linear variation of density with composition means that the overall density of brass can be determined by a weighted average of the densities of copper and zinc, reflecting their respective proportions in the alloy.

Volume of a Cylinder

The volume of a cylinder can be calculated using the formula V = πr²h, where r is the radius and h is the height (or length) of the cylinder. In this problem, the diameter is given, so the radius can be found by dividing the diameter by two. This volume will be essential for determining the mass of the brass cylinder when combined with its density.

Mass Calculation

Mass can be calculated using the formula m = ρV, where m is mass, ρ is density, and V is volume. Once the volume of the brass cylinder is determined, the density of the brass, derived from the composition of copper and zinc, can be used to find the mass. This relationship is crucial for solving the problem and understanding how the properties of the materials affect the overall mass of the alloy.

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Ocean currents are measured in Sverdrups (sv) where 1 sv = 109 m3/s. The Gulf Stream off the tip of Florida, for instance, has a flow of 35 sv. (c) How much time is required for 1 petaliter (PL; 1 PL = 10¹⁵ L) of seawater to flow past a given point?

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At a certain point, the Celsius and Fahrenheit scales 'cross,' giving the same numerical value on both. At what tempera-ture does this crossover occur?

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