What volume of distilled water should be added to 500ml of a solution of sulphuric acid to 90% by weight, density 1.81 g.mL-1, to obtain a 10 Molar solution?
snow, Taylor, Shania
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First determine the M of the initial H2SO4. That's
1.81 g/mL x 1000 mL x 0.90 x 1/98 = ?M which I will call y.
Then mL1 x M1 = mL2 x M2
500 mL x yM = mL2 x 10
Solve for mL2 which is approx 850. Subtract 500 from that to see what volume should be added. The answer is approx 350.
To find out how much distilled water should be added to the sulfuric acid solution, we need to start by determining the initial amount of sulfuric acid in the 500 mL solution.
Step 1: Calculate the mass of the sulfuric acid
The density of the solution is given as 1.81 g/mL, and the volume is 500 mL. So, the total mass of the solution can be calculated as follows:
Mass of solution = Density × Volume = 1.81 g/mL × 500 mL = 905 g
The solution is stated to be 90% sulfuric acid by weight, so we can calculate the mass of sulfuric acid in the solution:
Mass of sulfuric acid = 0.9 × Mass of solution = 0.9 × 905 g = 814.5 g
Step 2: Calculate the number of moles of sulfuric acid
To calculate the number of moles of sulfuric acid, we need to know the molar mass of sulfuric acid. The molar mass of H2SO4 is 98.09 g/mol.
Number of moles of sulfuric acid = Mass of sulfuric acid / Molar mass of sulfuric acid
= 814.5 g / 98.09 g/mol
≈ 8.30 mol
Step 3: Calculate the volume of the final solution
To prepare a 10 Molar solution, we can use the formula:
Number of moles = Concentration (Molarity) × Volume (in liters)
We want to find the volume of the final solution, so we rearrange the formula:
Volume (in liters) = Number of moles / Concentration (Molarity)
Volume (in liters) = 8.30 mol / 10 M = 0.83 L
Step 4: Convert the volume to mL
The volume of the final solution is 0.83 L, which is equivalent to 830 mL.
Step 5: Calculate the volume of distilled water to be added
To find the volume of distilled water to be added, we subtract the volume of the initial solution from the volume of the final solution:
Volume of distilled water = Volume of final solution - Volume of initial solution
= 830 mL - 500 mL
= 330 mL
Therefore, 330 mL of distilled water should be added to 500 mL of the 90% sulfuric acid solution to obtain a 10 Molar solution.