Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Problem 109

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 \(=\frac{\text { mass of copper }}{\text { total mass }} \times 100\)

Short Answer

Expert verified
The mass percent of copper in the sterling silver necklace is approximately \(25.369\%.\)

Step by step solution

01

Find the densities of silver and copper from the given table

Refer to Table 1.5 and look for the densities of silver and copper: Density of silver (Ag) = 10.5 g/mL Density of copper (Cu) = 8.92 g/mL
02

Calculate the mass of silver using its volume and density

Let x be the volume of silver in mL and (10.12 - x) be the volume of copper. Using the total volume equation provided in the problem: x + (10.12 - x) = 10.12 mL Thus, x is the volume of silver and 10.12 - x is the volume of copper. Now, we'll use the density formula to calculate the mass of silver: mass of silver = volume of silver × density of silver mass of silver = x × 10.5 g/mL
03

Calculate the mass of copper using its volume and density

Now, calculate the mass of copper: mass of copper = volume of copper × density of copper mass of copper = (10.12-x) × 8.92 g/mL
04

Calculate the total mass of the necklace piece

The total mass of the necklace piece is given in the problem as 105.0 g.
05

Write the equation for the total mass of the necklace piece

We have the total mass of the necklace piece equal to the sum of the masses of silver and copper: 105.0 g = mass of silver + mass of copper
06

Solve the equation for x

Substitute the expressions of mass of silver and mass of copper from step 2 and 3 in the equation obtained in step 5: 105.0 g = x × 10.5 g/mL + (10.12 - x) × 8.92 g/mL Now, solve this equation for x. x ≈ 7.134 mL
07

Calculate the mass of copper present in the necklace piece

Now that we have the value of x, calculate the mass of copper using the expression from step 3: mass of copper ≈ (10.12 - 7.134) × 8.92 g/mL mass of copper ≈ 26.637 g
08

Calculate the mass percent of copper

Using the mass percent formula provided in the problem, we can find the mass percent of copper: mass percent of copper = (mass of copper / total mass) × 100 mass percent of copper ≈ (26.637 g / 105.0 g) × 100 mass percent of copper ≈ 25.369% The mass percent of copper in the sterling silver necklace is approximately 25.369%.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

You are in Paris, and you want to buy some peaches for lunch. The sign in the fruit stand indicates that peaches cost \(2.45\) euros per kilogram. Given that 1 euro is equivalent to approximately \(\$ 1.46\), calculate what a pound of peaches will cost in dollars.

Many times errors are expressed in terms of percentage. The percent error is the absolute value of the difference of the true value and the experimental value, divided by the true value, and multiplied by 100 . Percent error \(=\frac{\mid \text { true value }-\text { experimental value } \mid}{\text { true value }} \times 100\) Calculate the percent error for the following measurements. a. The density of an aluminum block determined in an experiment was \(2.64 \mathrm{~g} / \mathrm{cm}^{3}\). (True value \(2.70 \mathrm{~g} / \mathrm{cm}^{3}\).) b. The experimental determination of iron in iron ore was \(16.48 \%\). (True value \(16.12 \% .)\) c. A balance measured the mass of a \(1.000-\mathrm{g}\) standard as \(0.9981 \mathrm{~g}\)

A measurement is a quantitative observation involving both a number and a unit. What is a qualitative observation? What are the SI units for mass, length, and volume? What is the assumed uncertainty in a number (unless stated otherwise)? The uncertainty of a measurement depends on the precision of the measuring device. Explain.

Perform the following mathematical operations, and express each result to the correct number of significant figures. a. \(\frac{0.102 \times 0.0821 \times 273}{1.01}\) b. \(0.14 \times 6.022 \times 10^{23}\) c. \(4.0 \times 10^{4} \times 5.021 \times 10^{-3} \times 7.34993 \times 10^{2}\) d. \(\frac{2.00 \times 10^{6}}{3.00 \times 10^{-7}}\)

The U.S. trade deficit at the beginning of 2005 was \(\$ 475,000,000\). If the wealthiest \(1.00\) percent of the U.S. population \((297,000,000)\) contributed an equal amount of money to bring the trade deficit to \(\$ 0\), how many dollars would each person contribute? If one of these people were to pay his or her share in nickels only, how many nickels are needed? Another person living abroad at the time decides to pay in pounds sterling (f). How many pounds sterling does this person contribute (assume a conversion rate of \(1 \mathrm{f}=\$ 1.869) ?\)
See all solutions

Recommended explanations on Chemistry Textbooks

Chemical Analysis

Read Explanation

Kinetics

Read Explanation

Chemistry Branches

Read Explanation

Ionic and Molecular Compounds

Read Explanation

The Earths Atmosphere

Read Explanation

Organic Chemistry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free