High School

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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 find out how many moles are in 151 grams of sulfur dioxide ([tex]\( SO_2 \)[/tex]), we need to follow several steps:

1. Determine the Molar Mass of [tex]\( SO_2 \)[/tex]:
- Sulfur ([tex]\( S \)[/tex]) has an atomic mass of approximately 32.06 grams/mole.
- Oxygen ([tex]\( O \)[/tex]) has an atomic mass of approximately 16.00 grams/mole.
- Since [tex]\( SO_2 \)[/tex] consists of one sulfur atom and two oxygen atoms, the molar mass of [tex]\( SO_2 \)[/tex] can be calculated as follows:

[tex]\[
\text{Molar mass of } SO_2 = 32.06 + (16.00 \times 2) = 32.06 + 32.00 = 64.06 \text{ grams/mole}
\][/tex]

2. Use the Molar Mass to Convert Grams to Moles:
- We are given 151 grams of [tex]\( SO_2 \)[/tex].
- To find the number of moles, we divide the mass of the substance by its molar mass:

[tex]\[
\text{Number of moles of } SO_2 = \frac{151 \text{ grams}}{64.06 \text{ grams/mole}}
\][/tex]

3. Calculate and Round to Three Significant Figures:
- Performing the division:

[tex]\[
\frac{151}{64.06} \approx 2.357
\][/tex]

- When rounded to three significant figures, the number of moles is [tex]\( 2.36 \)[/tex].

Therefore, 151 grams of [tex]\( SO_2 \)[/tex] is equal to approximately 2.36 moles.

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