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Chapter 2: Problem 85

A particular silver solder (used in the electronics industry to join electrical components) is to have the atom ratio of \(5.00 \mathrm{Ag} / 4.00 \mathrm{Cu} / 1.00 \mathrm{Zn}\). What masses of the three metals must be melted together to prepare \(1.00 \mathrm{kg}\) of the solder?

Short Answer

Expert verified
Based on the given atom ratio, the approximate masses of Silver (Ag), Copper (Cu), and Zinc (Zn) in the solder are 704.6 g, 331.4 g, and 85.6 g respectively. The total mass is equal to 1.00 kg or 1000 g as requested in the question.

Step by step solution

01

Calculate the molar mass of each metal

The molar mass of Silver (Ag) is approximately \(107.87 \, g/mol\), Copper (Cu) is \(63.55 \, g/mol\), and Zinc (Zn) is \(65.38 \, g/mol\). These values are available in the periodic table.
02

Calculate the total molar mass of the solder

The total molar mass of the solder is the total molar mass based on the ratio of the atoms. In this case, the total molar mass \(= (5 × molar \, mass \, of \, Ag) + (4 × molar \, mass \, of \, Cu) + (1 × molar \, mass \, of \, Zn) = (5 × 107.87) + (4 × 63.55) + (1 × 65.38) = 766.6 \, g/mol\).
03

Calculate the mass of each metal in the solder

To find out the mass of each metal in the solder, we first calculate the proportion of each metal in the total molar mass. This can be done as follows: - For Silver (Ag): \((5 × molar \, mass \, of \, Ag) / total \, molar \, mass = (5 × 107.87) / 766.6\). - For Copper (Cu): \((4 × molar \, mass \, of \, Cu) / total \, molar \, mass = (4 × 63.55) / 766.6\).- For Zinc (Zn): \((1 × molar \, mass \, of \, Zn) / total \, molar \, mass = (1 × 65.38) / 766.6\).Next, we multiply each proportion by the total mass of the solder (1.00 kg or 1000 g) to find out the mass of each metal.

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Most popular questions from this chapter

Samples of pure carbon weighing \(3.62,5.91,\) and \(7.07 \mathrm{g}\) were burned in an excess of air. The masses of carbon dioxide obtained (the sole product in each case) were \(13.26,21.66,\) and \(25.91 \mathrm{g},\) respectively. (a) Do these data establish that carbon dioxide has a fixed composition? (b) What is the composition of carbon dioxide, expressed in \% C and \% O, by mass?

When \(3.06 \mathrm{g}\) hydrogen was allowed to react with an excess of oxygen, \(27.35 \mathrm{g}\) water was obtained. In a second experiment, a sample of water was decomposed by electrolysis, resulting in \(1.45 \mathrm{g}\) hydrogen and 11.51 g oxygen. Are these results consistent with the law of constant composition? Demonstrate why or why not.

William Prout (1815) proposed that all other atoms are built up of hydrogen atoms, suggesting that all elements should have integral atomic masses based on an atomic mass of one for hydrogen. This hypothesis appeared discredited by the discovery of atomic masses, such as 24.3 u for magnesium and 35.5 u for chlorine. In terms of modern knowledge, explain why Prout's hypothesis is actually quite reasonable.

Explain the important distinctions between each pair of terms: (a) cathode rays and X-rays (b) protons and neutrons (c) nuclear charge and ionic charge (d) periods and groups of the periodic table (e) metal and nonmetal (f) the Avogadro constant and the mole

The mass of a carbon-12 atom is taken to be exactly 12 u. Are there likely to be any other atoms with an exact integral (whole number) mass, expressed in u? Explain.
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