Sterling silver is a solid solution of silver and copper. If...

Sterling silver is a solid solution of silver and copper. If a piece of a sterling silver necklace has a mass of $105.0 \mathrm{~g}$ and a volume of $10.12 \mathrm{~mL}$, calculate the mass percent of copper in the piece of necklace. Assume that the volume of silver present plus the volume of copper present equals the total volume. Refer to Table $1.5$. Mass percent of copper $=\frac{\text { mass of copper }}{\text { total mass }} \times 100$

Sterling silver is a solid solution of silver and copper. If a piece of a sterling silver necklace has a mass of $105.0 \mathrm{~g}$ and a volume of $10.12 \mathrm{~mL}$, calculate the mass percent of copper in the piece of necklace. Assume that the volume of silver present plus the volume of copper present equals the total volume. Refer to Table $1.5$.
Mass percent of copper $=\frac{\text { mass of copper }}{\text { total mass }} \times 100$

Key Concepts

Solid Solution

A solid solution is a homogeneous crystalline phase that consists of two or more elements incorporated into one crystal structure. In metallurgy, this term is often used to describe alloys where one metal consistently replaces or is dispersed within another, leading to improved properties compared to the individual metals.

Mass Percent

Mass percent is a way to express the concentration of a particular component in a mixture or alloy. It is calculated by taking the mass of a single component, dividing it by the total mass of the mixture, and multiplying by 100 to convert it to a percentage. This metric is fundamental in compositional analysis of materials.

Density

Density is the measure of mass per unit volume of a substance. In the context of alloys, differences in density between the constituent metals are important for determining the individual contributions of each metal to the overall properties of the alloy, often influencing calculations involving proportions of each component.

Volume Additivity

Volume additivity is the assumption that the total volume of a mixture or alloy is equal to the sum of the volumes of its individual components. This assumption simplifies calculations in cases where precise measurement of individual volumes is difficult, and it is especially useful in problems involving mixtures and alloys.

Transcript

00:01 So in this question, starling silver is a mixture of civil and copper.

00:05 And from a table 1.5 in the textbook, we can look up.

00:08 Density of silver is tampering for graham pally leader, immensity of copper.

00:14 He's 8.96 grand for me, leader.

00:17 The mass off, um, the think that we have this 105 grand.

00:23 The volume is 10.12 mil leader.

00:26 And so what is the mass percent off cover? so, uh, we have and the question also say that we could make assumption that the walter bohlin off the thing it caused to the volume off copper plus the volume of silver so we can have the equation.

00:50 Iss mass off copper last mass observer equal one or five bring zero cram and ah, volume off copper plus volume of silver equals 10.

01:07 I went to me, leader.

01:10 And so this one can give us the relationship that mass observer equals 10540 minus mass off copper and using the relationship that volume ecos nous sorry.

01:27 Mass over density mass over density.

01:35 We can rewrite this equation as my scupper minus density off cop divided by density of copper plus mass silver divided my density observer equal 10 pointer.

01:53 That's called this a question one and equation, too.

01:57 All right, so let's rewrite a question.

01:59 One over here are super equal.

02:03 One of 5.0 minus minus copper and mass copper over.

02:10 Density of copper.

02:12 Less mar sewer over.

02:15 Density observer.

02:17 Equal toe 10 point throw.

02:20 Uh um, 10.12.

02:25 All right, so, uh, let's step to do.

02:30 And this one, we can rewrite it as the super mass copper plus the copper maciver equal 10.12...