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Answer :
Sure, let's solve this step-by-step to determine how many moles are in 151 grams of [tex]\( \text{SO}_2 \)[/tex].
### Step 1: Determine the Molar Mass of [tex]\( \text{SO}_2 \)[/tex]
First, we need to find the molar mass (molecular weight) of [tex]\( \text{SO}_2 \)[/tex]. Here's how you calculate it:
- The atomic mass of sulfur ([tex]\( S \)[/tex]) is approximately 32.06 grams per mole.
- The atomic mass of oxygen ([tex]\( O \)[/tex]) is approximately 16.00 grams per mole.
Since [tex]\( \text{SO}_2 \)[/tex] has one sulfur atom and two oxygen atoms, its molar mass is:
[tex]\[ 32.06 + (2 \times 16.00) = 32.06 + 32.00 = 64.066 \text{ grams per mole} \][/tex]
### Step 2: Calculate the Number of Moles
Now, we use the molar mass to convert grams to moles. The formula to convert grams to moles is:
[tex]\[ \text{Number of moles} = \frac{\text{Mass (in grams)}}{\text{Molar Mass (in grams per mole)}} \][/tex]
Plugging in the given values:
[tex]\[ \text{Number of moles} = \frac{151 \text{ grams}}{64.066 \text{ grams per mole}} \][/tex]
When you perform this division, you get:
[tex]\[ \text{Number of moles} \approx 2.3569444010863796 \][/tex]
### Step 3: Round to Three Significant Figures
Finally, we need to express our answer to three significant figures:
[tex]\[ \text{Number of moles} \approx 2.357 \][/tex]
### Final Answer
151 grams of [tex]\( \text{SO}_2 \)[/tex] is equal to 2.357 moles.
### Step 1: Determine the Molar Mass of [tex]\( \text{SO}_2 \)[/tex]
First, we need to find the molar mass (molecular weight) of [tex]\( \text{SO}_2 \)[/tex]. Here's how you calculate it:
- The atomic mass of sulfur ([tex]\( S \)[/tex]) is approximately 32.06 grams per mole.
- The atomic mass of oxygen ([tex]\( O \)[/tex]) is approximately 16.00 grams per mole.
Since [tex]\( \text{SO}_2 \)[/tex] has one sulfur atom and two oxygen atoms, its molar mass is:
[tex]\[ 32.06 + (2 \times 16.00) = 32.06 + 32.00 = 64.066 \text{ grams per mole} \][/tex]
### Step 2: Calculate the Number of Moles
Now, we use the molar mass to convert grams to moles. The formula to convert grams to moles is:
[tex]\[ \text{Number of moles} = \frac{\text{Mass (in grams)}}{\text{Molar Mass (in grams per mole)}} \][/tex]
Plugging in the given values:
[tex]\[ \text{Number of moles} = \frac{151 \text{ grams}}{64.066 \text{ grams per mole}} \][/tex]
When you perform this division, you get:
[tex]\[ \text{Number of moles} \approx 2.3569444010863796 \][/tex]
### Step 3: Round to Three Significant Figures
Finally, we need to express our answer to three significant figures:
[tex]\[ \text{Number of moles} \approx 2.357 \][/tex]
### Final Answer
151 grams of [tex]\( \text{SO}_2 \)[/tex] is equal to 2.357 moles.
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