The average mass of one gold atom in a sample of naturally occuring gold is `3.2707xx10^(-22) g`. Use this to calculate the molar mass of gold.

Explanation

To calculate the molar mass of gold using the average mass of a gold atom, we can follow these steps:

### Step 1: Understand the given data
We are given the average mass of one gold atom, which is \( 3.2707 \times 10^{-22} \) grams.

### Step 2: Use Avogadro's number
Avogadro's number (\( N_A \)) is \( 6.022 \times 10^{23} \) atoms/mole. This number represents the number of atoms in one mole of a substance.

### Step 3: Calculate the molar mass
To find the molar mass of gold, we multiply the average mass of one gold atom by Avogadro's number:

\[ \text{Molar mass of gold} = \text{Average mass of one gold atom} \times N_A \]

Substituting the values:

\[ \text{Molar mass of gold} = (3.2707 \times 10^{-22} \, \text{g}) \times (6.022 \times 10^{23} \, \text{atoms/mole}) \]

### Step 4: Perform the calculation
Now, we perform the multiplication:

\[ \text{Molar mass of gold} = 3.2707 \times 6.022 \times 10^{-22 + 23} \]

Calculating the numerical part:

\[ 3.2707 \times 6.022 \approx 19.66 \]

And adjusting the exponent:

\[ 10^{-22 + 23} = 10^{1} \]

So, we have:

\[ \text{Molar mass of gold} \approx 19.66 \times 10^{1} \, \text{g/mole} = 196.6 \, \text{g/mole} \]

### Step 5: Round to appropriate significant figures
The average mass of one gold atom has four significant figures, so we round our answer to four significant figures:

\[ \text{Molar mass of gold} \approx 196.2 \, \text{g/mole} \]

### Final Answer
The molar mass of gold is approximately **196.2 g/mole**.

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