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Answer :
To find the molarity of the sulfuric acid solution, we need to follow these steps:
1. Understand the problem: We have a 65.0% by mass sulfuric acid solution, which means 65 grams of sulfuric acid in every 100 grams of solution. The density of the solution is 1.55 g/mL, and the molar mass of sulfuric acid ([tex]\( H_2SO_4 \)[/tex]) is 98.0 g/mol.
2. Calculate the mass of the solution per liter:
- Since density is given as 1.55 g/mL, the mass of 1 liter (1000 mL) of the solution is:
[tex]\[
\text{Mass of solution per liter} = 1.55 \, \text{g/mL} \times 1000 \, \text{mL} = 1550 \, \text{g}
\][/tex]
3. Calculate the mass of [tex]\( H_2SO_4 \)[/tex] in grams per liter:
- 65% by mass means 65% of the mass of the solution is [tex]\( H_2SO_4 \)[/tex].
- Therefore, the mass of [tex]\( H_2SO_4 \)[/tex] per liter is:
[tex]\[
\text{Mass of } H_2SO_4 \text{ per liter} = 0.65 \times 1550 \, \text{g} = 1007.5 \, \text{g}
\][/tex]
4. Calculate the molarity of the solution:
- Molarity is defined as the number of moles of solute (in this case, [tex]\( H_2SO_4 \)[/tex]) per liter of solution.
- First, calculate the number of moles of [tex]\( H_2SO_4 \)[/tex]:
[tex]\[
\text{Moles of } H_2SO_4 = \frac{1007.5 \, \text{g}}{98.0 \, \text{g/mol}} \approx 10.28 \, \text{mol}
\][/tex]
- Since these moles are in 1 liter of solution, the molarity of the solution is:
[tex]\[
\text{Molarity} = 10.28 \, \text{M}
\][/tex]
Thus, the molarity of the sulfuric acid solution is approximately 10.3 M.
1. Understand the problem: We have a 65.0% by mass sulfuric acid solution, which means 65 grams of sulfuric acid in every 100 grams of solution. The density of the solution is 1.55 g/mL, and the molar mass of sulfuric acid ([tex]\( H_2SO_4 \)[/tex]) is 98.0 g/mol.
2. Calculate the mass of the solution per liter:
- Since density is given as 1.55 g/mL, the mass of 1 liter (1000 mL) of the solution is:
[tex]\[
\text{Mass of solution per liter} = 1.55 \, \text{g/mL} \times 1000 \, \text{mL} = 1550 \, \text{g}
\][/tex]
3. Calculate the mass of [tex]\( H_2SO_4 \)[/tex] in grams per liter:
- 65% by mass means 65% of the mass of the solution is [tex]\( H_2SO_4 \)[/tex].
- Therefore, the mass of [tex]\( H_2SO_4 \)[/tex] per liter is:
[tex]\[
\text{Mass of } H_2SO_4 \text{ per liter} = 0.65 \times 1550 \, \text{g} = 1007.5 \, \text{g}
\][/tex]
4. Calculate the molarity of the solution:
- Molarity is defined as the number of moles of solute (in this case, [tex]\( H_2SO_4 \)[/tex]) per liter of solution.
- First, calculate the number of moles of [tex]\( H_2SO_4 \)[/tex]:
[tex]\[
\text{Moles of } H_2SO_4 = \frac{1007.5 \, \text{g}}{98.0 \, \text{g/mol}} \approx 10.28 \, \text{mol}
\][/tex]
- Since these moles are in 1 liter of solution, the molarity of the solution is:
[tex]\[
\text{Molarity} = 10.28 \, \text{M}
\][/tex]
Thus, the molarity of the sulfuric acid solution is approximately 10.3 M.
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