Question

1. how many moles is 3.14×10²⁴ atoms of gold?\

\\(\frac{196.966}{3.14}=62.737\\)\
answer: 62.737×10²⁴\

1. how many molecules is 0.15 moles of nitrogen?\

answer: 2.105×10²³

Explanation:

Question 3: How many moles is \( 3.14 \times 10^{24} \) atoms of gold?

Step 1: Recall Avogadro's number

Avogadro's number is \( 6.022 \times 10^{23} \) atoms/mol, which is the number of atoms in one mole of a substance.

Step 2: Use the formula to find moles

The formula to calculate moles from the number of atoms is:
\( \text{Moles} = \frac{\text{Number of atoms}}{\text{Avogadro's number}} \)

Substitute the given values:
\( \text{Moles} = \frac{3.14 \times 10^{24}}{6.022 \times 10^{23}} \)

Simplify the expression:
First, divide the coefficients: \( \frac{3.14}{6.022} \approx 0.521 \)
Then, divide the powers of 10: \( \frac{10^{24}}{10^{23}} = 10^{1} = 10 \)
Multiply the results: \( 0.521 \times 10 = 5.21 \) (approximate value, or using more precise calculation: \( \frac{3.14 \times 10^{24}}{6.022 \times 10^{23}}=\frac{3.14}{6.022}\times10^{24 - 23}\approx0.521\times10 = 5.21 \) moles. Note: The handwritten answer in the image seems incorrect; the correct approach uses Avogadro's number.)

Step 1: Recall Avogadro's number for molecules

Avogadro's number is \( 6.022 \times 10^{23} \) molecules/mol (for molecular substances, this relates moles to number of molecules).

Step 2: Use the formula to find molecules

The formula to calculate number of molecules from moles is:
\( \text{Number of molecules} = \text{Moles} \times \text{Avogadro's number} \)

Substitute the given values:
\( \text{Number of molecules} = 0.15 \times 6.022 \times 10^{23} \)

Calculate the product:
\( 0.15 \times 6.022 = 0.9033 \)
So, \( 0.9033 \times 10^{23} = 9.033 \times 10^{22} \) (or \( 9.03 \times 10^{22} \) for simplicity; the handwritten answer in the image is \( 2.10105 \times 10^{23} \), which is incorrect. The correct approach uses Avogadro's number for molecules.)

Answer:

Approximately \( 5.21 \) moles (or more precisely, using \( 6.022 \times 10^{23} \): \( \frac{3.14 \times 10^{24}}{6.022 \times 10^{23}} \approx 5.21 \) moles)

Question 4: How many molecules is \( 0.15 \) moles of nitrogen?