College

Sarah measures out 151 grams of [tex]$SO_2$[/tex]. How many moles is this? Express your answer to three significant figures.

151 grams of [tex]$SO_2$[/tex] is equal to [tex]\square[/tex] moles.

Answer :

To determine the number of moles in 151 grams of [tex]\( \text{SO}_2 \)[/tex], we need to follow these steps:

1. Find the Molar Mass of [tex]\( \text{SO}_2 \)[/tex]:
- The molar mass of sulfur (S) is approximately [tex]\( 32.07 \, \text{g/mol} \)[/tex].
- The molar mass of oxygen (O) is approximately [tex]\( 16.00 \, \text{g/mol} \)[/tex].
- Since [tex]\( \text{SO}_2 \)[/tex] contains one sulfur atom and two oxygen atoms, the molar mass is calculated as:
[tex]\[
32.07 \, \text{g/mol} + 2 \times 16.00 \, \text{g/mol} = 64.07 \, \text{g/mol}
\][/tex]

2. Calculate the Number of Moles:
- To convert the mass of [tex]\( \text{SO}_2 \)[/tex] to moles, use the formula:
[tex]\[
\text{moles of } \text{SO}_2 = \frac{\text{mass of } \text{SO}_2}{\text{molar mass of } \text{SO}_2}
\][/tex]
- Plug in the values:
[tex]\[
\text{moles of } \text{SO}_2 = \frac{151 \, \text{g}}{64.07 \, \text{g/mol}} \approx 2.356797 \, \text{moles}
\][/tex]

3. Round to Three Significant Figures:
- The final step is to round the result to three significant figures:
[tex]\[
2.357 \, \text{moles}
\][/tex]

So, 151 grams of [tex]\( \text{SO}_2 \)[/tex] is equal to approximately 2.357 moles.

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