Question

1. a teacher has given a student a white powder sample and asks her to confirm that it contains $3.25 \times 10^{23}$ formula units of calcium chloride ($\ce{cacl_{2}}$). using the balance in the laboratory, what mass of $\ce{cacl_{2}}$ would the student need to measure to verify the teacher’s claim?

1. a chemistry instructor provides a student with a clear crystalline solid and states that it contains $9.60 \times 10^{22}$ formula units of potassium nitrate ($\ce{kno_{3}}$). using laboratory equipment, what mass of $\ce{kno_{3}}$ should the student find to confirm this amount?

1. a silver coin contains 18.2 grams of silver. how many silver atoms are present in the coin?

1. a copper wire sample has a mass of 12.4 grams. how many copper atoms are present in this sample?

1. a piece of solid iron has a mass of 22.0 grams. how many iron atoms are contained in this piece?

Explanation:

Problem 1

Step 1: Find moles of \( \text{CaCl}_2 \)

Use Avogadro's number (\( 6.022 \times 10^{23} \) formula units/mol).
Moles (\( n \)) = \( \frac{\text{Formula Units}}{N_A} = \frac{3.25 \times 10^{23}}{6.022 \times 10^{23}} \approx 0.5397 \, \text{mol} \)

Step 2: Calculate molar mass of \( \text{CaCl}_2 \)

Molar mass (\( M \)) = \( 40.08 + 2(35.45) = 40.08 + 70.90 = 110.98 \, \text{g/mol} \)

Step 3: Find mass using \( m = n \times M \)

\( m = 0.5397 \, \text{mol} \times 110.98 \, \text{g/mol} \approx 60.0 \, \text{g} \)

Step 1: Find moles of \( \text{KNO}_3 \)

Moles (\( n \)) = \( \frac{9.60 \times 10^{22}}{6.022 \times 10^{23}} \approx 0.1594 \, \text{mol} \)

Step 2: Calculate molar mass of \( \text{KNO}_3 \)

Molar mass (\( M \)) = \( 39.10 + 14.01 + 3(16.00) = 39.10 + 14.01 + 48.00 = 101.11 \, \text{g/mol} \)

Step 3: Find mass using \( m = n \times M \)

\( m = 0.1594 \, \text{mol} \times 101.11 \, \text{g/mol} \approx 16.1 \, \text{g} \)

Step 1: Find moles of Ag

Molar mass of Ag = \( 107.87 \, \text{g/mol} \).
Moles (\( n \)) = \( \frac{18.2 \, \text{g}}{107.87 \, \text{g/mol}} \approx 0.1687 \, \text{mol} \)

Step 2: Find atoms using \( \text{Atoms} = n \times N_A \)

\( \text{Atoms} = 0.1687 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol} \approx 1.016 \times 10^{23} \, \text{atoms} \)

Answer:

\( \approx 60.0 \, \text{g} \)

Problem 2