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Chapter 14: Problem 10

Suppose you have 50 grams of copper and 50 grams of gold. Which sample has more atoms? Explain your thinking.

Short Answer

Expert verified
Copper has more atoms than gold.

Step by step solution

01

Determine Molar Mass

First, find the molar masses of copper and gold. Copper (Cu) has a molar mass of approximately 63.55 g/mol, and Gold (Au) has a molar mass of approximately 197.0 g/mol.
02

Calculate Moles of Each Element

Use the formula: \[ \text{Moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]. For Copper: \( \frac{50}{63.55} \approx 0.787 \) moles. For Gold: \( \frac{50}{197.0} \approx 0.254 \) moles.
03

Determine Number of Atoms Using Avogadro's Number

Avogadro's Number is \( 6.022 \times 10^{23} \) atoms/mol. Multiply the moles of each element by Avogadro鈥檚 Number to get the number of atoms. For Copper: \( 0.787 \times 6.022 \times 10^{23} \approx 4.74 \times 10^{23} \) atoms. For Gold: \( 0.254 \times 6.022 \times 10^{23} \approx 1.53 \times 10^{23} \) atoms.
04

Compare Number of Atoms

Compare the number of atoms in each sample: Copper has approximately \( 4.74 \times 10^{23} \) atoms, while Gold has approximately \( 1.53 \times 10^{23} \) atoms. Clearly, Copper has more atoms than Gold based on these calculations.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Avogadro's Number
Avogadro's number is a crucial concept in chemistry that helps us relate microscopic atomic measurements to the macroscopic world we observe. Named after the Italian scientist Amedeo Avogadro, this number is defined as the number of atoms, molecules, or particles in one mole of a substance. It is approximately \(6.022 \times 10^{23}\). This large number helps chemists convey the idea of grouping atoms in a quantity that can be easily weighed and manipulated in a laboratory setting. When discussing substances like copper and gold in large enough masses, Avogadro's number provides a bridge between their molar mass and the number of atoms they contain.
Performing Moles Calculations
The concept of a mole is central to chemistry, as it allows for counting entities like atoms, ions, or molecules on a large scale. The mole relates mass to the number of atoms or molecules through the substance's molar mass.To calculate the number of moles in a substance, use the formula:
  • \(\text{Moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}\)
In the provided exercise, to find how many moles are in 50 grams of copper, you divide the mass by its molar mass (63.55 g/mol), resulting in approximately 0.787 moles. Similarly, for gold, the calculation yields around 0.254 moles. These calculations show how crucial knowing the molar mass is, acting as a stepping stone to further determine the quantity of atoms.
Essence of Atoms Comparison
Comparing atoms between elements starts with understanding that different substances have different molar masses. The molar mass impacts how many atoms exist in a given sample mass. Using the exercise, although both copper and gold have the same mass of 50 grams, due to their differing molar masses, they contain different numbers of moles and subsequently different numbers of atoms upon application of Avogadro鈥檚 number. Copper (with a lower molar mass) yields more atoms (approximately \(4.74 \times 10^{23}\)) than gold (around \(1.53 \times 10^{23}\)), emphasizing the inverse relationship between molar mass and the quantity of atoms in equal masses.
Elementary Chemistry Concepts
In chemistry, understanding the interaction between molar mass, moles, and Avogadro's number is foundational. These concepts allow chemists to translate between a macro perception of mass and the micro scale of individual atoms. Key concepts include:
  • Molar Mass: Reflects the mass of one mole of a substance and is unique to each element, influencing the calculations of moles.
  • Moles: Act like a bridge between the mass you measure and the number of atoms you seek, using formulas to calculate understanding.
  • Avogadro's Number: Essential for converting between moles and actual count of particles, embodying large-scale practicality of molecular calculations.
Together, these fundamental chemistry tools facilitate detailed analysis and understanding of reactions and materials in scientific studies and practical applications.

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Most popular questions from this chapter

Find at least i ve products at home with labels that warn of toxicity. Give the name of each product, and answer these questions: a. How does each label advise you to avoid harmful exposure to the product? b. What does each label tell you to do if a dangerous exposure does occur? c. Using all of this information, what can you hypothesize about the chemical properties of each product? d. Look at the recommended treatment for dangerous exposure to each product. What chemical and physical processes do you think might be involved in the treatment?

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Copper is the third most used metal after iron and aluminum. Copper usage is rapidly expanding as more products are duys conper compounds and then components. Suppose you run a company that buys comper compounds and then recycles the copper for resale. Your company wants to get the most pure copper for the lowest cost. Three different suppliers want to sell you 1 mol \(\mathrm{CuO}(s), 1\) mol \(\mathrm{CuCO}_{3}(s),\) and 1 \(\mathrm{mol} \mathrm{Cu}_{2} \mathrm{O}(s)\) for the same price. a. Which compound has the greatest total mass? Show your work. b. Which compound has the greatest mass of Cu? Show your work. c. Assuming it costs the same to extract the copper from each compound, which compound represents the best deal for your company? Explain.

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