Given the density of copper 8.96g/mL, zinc 7.14g/mL, and brass 8.36g/mL. What is the fraction of copper and zinc in brass (expressed as %)? Please show me step by step how to calculate this. Thank you.
To calculate the fraction of copper and zinc in brass, you need to know the densities of copper and zinc, as well as the density of brass. Here is a step-by-step guide:
Step 1: Calculate the density difference between copper and brass:
Density difference = Density of brass - Density of copper
Density difference = 8.36g/mL - 8.96g/mL
Density difference = -0.6g/mL
Step 2: Calculate the density difference between zinc and brass:
Density difference = Density of brass - Density of zinc
Density difference = 8.36g/mL - 7.14g/mL
Density difference = 1.22g/mL
Step 3: Calculate the total density difference between copper and zinc in brass:
Total density difference = Density difference between copper and brass + Density difference between zinc and brass
Total density difference = -0.6g/mL + 1.22g/mL
Total density difference = 0.62g/mL
Step 4: Calculate the fraction of copper in brass:
Fraction of copper = Density difference between copper and brass / Total density difference
Fraction of copper = -0.6g/mL / 0.62g/mL
Fraction of copper = -0.9677
Step 5: Calculate the fraction of zinc in brass:
Fraction of zinc = Density difference between zinc and brass / Total density difference
Fraction of zinc = 1.22g/mL / 0.62g/mL
Fraction of zinc = 1.9677
Step 6: Convert the fractions to percentages:
Percentage of copper = Fraction of copper * 100
Percentage of zinc = Fraction of zinc * 100
Therefore, the fraction of copper in brass is approximately -96.77% and the fraction of zinc in brass is approximately 196.77%. Please note that a negative value for the fraction of copper means that copper is not present in brass, which is unlikely. It is possible that there was an error in the given densities or calculations.
To calculate the fraction of copper and zinc in brass, we need to consider their densities.
Step 1: Determine the total density of the brass.
The density of brass is given as 8.36 g/mL.
Step 2: Calculate the density of copper in brass.
The density of copper is given as 8.96 g/mL.
Density of copper in brass = (density of copper / density of brass) * 100
Density of copper in brass = (8.96 g/mL / 8.36 g/mL) * 100
Density of copper in brass = 1.07 * 100
Density of copper in brass = 107%
Step 3: Calculate the density of zinc in brass.
The density of zinc is given as 7.14 g/mL.
Density of zinc in brass = (density of zinc / density of brass) * 100
Density of zinc in brass = (7.14 g/mL / 8.36 g/mL) * 100
Density of zinc in brass = 0.855 * 100
Density of zinc in brass = 85.5%
Step 4: Calculate the fraction of copper and zinc in brass.
The fraction of copper in brass = Density of copper in brass / Total density of brass * 100
The fraction of copper in brass = 107% / (107% + 85.5%) * 100
The fraction of copper in brass = 107% / 192.5% * 100
The fraction of copper in brass = 55.58%
The fraction of zinc in brass = Density of zinc in brass / Total density of brass * 100
The fraction of zinc in brass = 85.5% / (107% + 85.5%) * 100
The fraction of zinc in brass = 85.5% / 192.5% * 100
The fraction of zinc in brass = 44.42%
Therefore, the fraction of copper in brass is approximately 55.58%, and the fraction of zinc in brass is approximately 44.42%.
Let x = fraction Cu
Then 1-x = fraction Zn
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(x*8.96) + (1-x)*7.14 = 8.36
Solve for x and 1-x and convert fractions to percent.