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A solution of acid having 62% by mass o...

A solution of acid having 62% by mass of acid has specific gravity of 1.8 g. If the solution is to be diluted to attain a specific gravity of 1.2 then what volume of water should be added to 100 ml of this solution?

A

200 ml

B

1000 ml

C

500 ml

D

300 ml

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we will follow these calculations: ### Step 1: Determine the mass of the acid solution. Given that the specific gravity of the acid solution is 1.8, we can find the density of the solution: - Density of solution = Specific gravity × Density of water - Density of water = 1 g/mL - Density of solution = 1.8 g/mL Now, we can calculate the mass of the solution in 100 mL: - Mass of solution = Density × Volume - Mass of solution = 1.8 g/mL × 100 mL = 180 g ### Step 2: Calculate the mass of the acid in the solution. The solution is 62% acid by mass: - Mass of acid = 62% of mass of solution - Mass of acid = (62/100) × 180 g = 111.6 g ### Step 3: Determine the mass of the water added. Let \( x \) be the mass of water added (in grams). The new mass of the solution after adding water will be: - Mass of new solution = Mass of original solution + Mass of water added - Mass of new solution = 180 g + \( x \) ### Step 4: Calculate the new volume of the solution. Since the density of water is 1 g/mL, the volume of water added will also be \( x \) mL. Therefore, the new volume of the solution will be: - Volume of new solution = Original volume + Volume of water added - Volume of new solution = 100 mL + \( x \) mL ### Step 5: Set up the equation for the new specific gravity. We want the new specific gravity to be 1.2: - Density of new solution = Specific gravity × Density of water - Density of new solution = 1.2 g/mL Using the formula for density (mass/volume): - Density = (Mass of new solution) / (Volume of new solution) - 1.2 = (180 + \( x \)) / (100 + \( x \)) ### Step 6: Solve the equation. Cross-multiplying gives: - 1.2(100 + \( x \)) = 180 + \( x \) - 120 + 1.2\( x \) = 180 + \( x \) Rearranging the equation: - 1.2\( x \) - \( x \) = 180 - 120 - 0.2\( x \) = 60 - \( x \) = 60 / 0.2 - \( x \) = 300 ### Conclusion: The volume of water that should be added to 100 mL of the acid solution is **300 mL**. ---
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