Using density to find the % composition of an alloy

[Kushal]

Homework Statement

The densities (at 25*C) of tin and lead are 7.3 g/cm3 and 11.3 g/cm3 respectively. Plumber's solder is an alloy of tin and lead and has a density of 9.7 g/cm3.

Estimate the composition by mass, of the two metals in this solder.

Homework Equations

The Attempt at a Solution

i assumed the % composition of lead to be X%. so % composition of tin is (100 - X)%.
using [(X*11.3)/100] + [((100-X)*7.3)/100] = 9.7

i got % lead as 60% and % tin as 40%.

but the answers from the book are 30.1% for tin and 69.9% for lead.

any help!

 

[Mapes]

Amount fractions can be measured in weight percent (wt%) or atomic percent (at%), so just writing "%" is ambiguous. Perhaps this explains the difference.

 

[Blueshift5]

Your approach is correct, but there may have been a mistake in your calculation. Here is the correct calculation:

Let X = % composition of lead, then (100-X)% is the % composition of tin.

To find the density of the alloy, we can use the formula:

Density = (Mass of lead * Density of lead) + (Mass of tin * Density of tin)

Substituting the values given in the problem, we get:

9.7 g/cm3 = (X * 11.3) + ((100-X) * 7.3)

Solving for X, we get:

X = (9.7 - 7.3) / (11.3 - 7.3) = 2.4 / 4 = 0.6 = 60%

Therefore, the % composition of lead is 60% and the % composition of tin is (100-60) = 40%. The book's answer of 30.1% for tin and 69.9% for lead is incorrect. It is possible that there was a mistake in the book or in the given data.