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How many moles are there in 45.0 grams of sulfuric acid, [tex]H_2SO_4[/tex]?

Your answer should be rounded to three significant figures.

A. 98.1 moles
B. 2.18 moles
C. 0.459 moles

Answer :

Sure! Let's determine the number of moles in 45.0 grams of sulfuric acid ([tex]\( \text{H}_2\text{SO}_4 \)[/tex]) step-by-step.

1. Find the molar mass of sulfuric acid ([tex]\( \text{H}_2\text{SO}_4 \)[/tex]):
- Hydrogen (H): [tex]\( 2 \times 1.01 \, \text{g/mol} = 2.02 \, \text{g/mol} \)[/tex]
- Sulfur (S): [tex]\( 1 \times 32.07 \, \text{g/mol} = 32.07 \, \text{g/mol} \)[/tex]
- Oxygen (O): [tex]\( 4 \times 16.00 \, \text{g/mol} = 64.00 \, \text{g/mol} \)[/tex]

Adding these values together:
[tex]\[
2.02 \, \text{g/mol} + 32.07 \, \text{g/mol} + 64.00 \, \text{g/mol} = 98.09 \, \text{g/mol}
\][/tex]

2. Use the molar mass to find the number of moles:
The formula to convert grams to moles is:
[tex]\[
\text{moles} = \frac{\text{mass in grams}}{\text{molar mass in g/mol}}
\][/tex]

For sulfuric acid:
[tex]\[
\text{moles} = \frac{45.0 \, \text{grams}}{98.09 \, \text{g/mol}}
\][/tex]

3. Calculate the moles:
[tex]\[
\text{moles} = \frac{45.0}{98.09} \approx 0.459
\][/tex]

4. Round the result to three significant figures:
The result is already in three significant figures.

Therefore, there are 0.459 moles of sulfuric acid in 45.0 grams of sulfuric acid.

So, the correct answer is [tex]\( \boxed{0.459 \, \text{moles}} \)[/tex].

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