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Chapter 2: Problem 86

A low-melting Sn-Pb-Cd alloy called eutectic alloy is analyzed. The mole ratio of tin to lead is 2.73: 1.00 and the mass ratio of lead to cadmium is 1.78: 1.00 . What is the mass percent composition of this alloy?

Short Answer

Expert verified
The mass percent composition of the eutectic alloy is approximately: 50.04% Sn, 31.95% Pb, and 17.96% Cd.

Step by step solution

01

Convert the Mole Ratio to Mass Ratio

Firstly, it is necessary to convert the mole ratios into mass ratios. To accomplish this, the atomic masses of tin (Sn, 118.71 g/mol) and lead (Pb, 207.2 g/mol) are used. The mass of tin for the given mole ratio is \(2.73 \times 118.71 \, g/mol = 324.3773 \, g/mol\). For lead, the mass is \(1.00 \times 207.2 \, g/mol = 207.2 \, g/mol\). This gives a mass ratio of Sn to Pb of 324.3773 : 207.2.
02

Derive the Mass Ratio of Sn to Cd

The mass ratio of Lead to Cadmium is given as 1.78 : 1, which means for 1.78 g of Pb, there is 1 g of Cd. From step 1, we know that there are 207.2g of Pb, so the mass of Cd is calculated using cross multiplication as \( \frac{207.2 \, g}{1.78} = 116.4045 \, g\). Thus, the mass ratio of tin is to cadmium is 324.3773 : 116.4045.
03

Calculate the Mass Percent Composition

The last step is to calculate the percent composition by mass for each element. First add up all the masses to find the total mass of the alloy., which is \( 324.3773 \, g + 207.2 \, g + 116.4045 \, g = 647.9818 \, g\). Then the mass percent of each element is calculated as follows: for Sn \(\frac{324.3773}{647.9818} \times 100\%\), for Pb \(\frac{207.2}{647.9818} \times 100\%\), and for Cd \(\frac{116.4045}{647.9818} \times 100\%\).

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