A 62% by mass of aqueous solution. of acid has specific gravity 1.8 . This solution is diluted such that. the specific gravity of solution become 1.2 fine find Percent by weight. of acid in this solution.
To solve this problem, we first need to determine the mass of the acid in the original aqueous solution.
Let's assume we have a 100g sample of the original aqueous solution.
Given that the specific gravity of the solution is 1.8, we know that 1 liter of the solution weighs 1.8 kg or 1800g.
Since 62% of the solution is acid by mass, the mass of acid in the solution is 0.62 * 100g = 62g.
Now, let's determine the volume of the original solution. To do this, we'll use the specific gravity and the known mass of 100g.
The volume of 100g of the original solution is 100g / (1.8g/mL) = 55.56 mL.
Now, let's dilute this solution in such a way that the specific gravity becomes 1.2.
Given the specific gravity of 1.2 and the volume of the original solution (55.56 mL), we can determine the new mass of the diluted solution.
Let's assume the new mass of the diluted solution is x g.
The mass of the acid in the diluted solution will still be 62g.
So, the new volume of the diluted solution can be calculated using the specific gravity and the new mass:
x g / (1.2g/mL) = 55.56 mL
x = 55.56 mL * 1.2g/mL = 66.67 g
Therefore, the percent by weight of the acid in the diluted solution is:
(62g / 66.67g) * 100% = 93%
To find the percent by weight of acid in the diluted solution, we can use the concept of specific gravity and the given information.
Let's denote the initial solution (62% by mass of aqueous solution) as Solution A and the diluted solution as Solution B.
Step 1: Calculate the mass of acid in Solution A:
Since Solution A is 62% by mass of aqueous solution, it means that 62% of Solution A is acid, and the remaining 38% is water.
Given the specific gravity of Solution A is 1.8, it means that 1 liter of Solution A weighs 1.8 kg.
Let's assume we have 100 grams of Solution A, which means that 62 grams of it is acid and 38 grams is water.
Step 2: Calculate the volume of Solution A:
To find the volume of Solution A, we can use the formula:
Volume = Mass / Density
Density is calculated by dividing the mass by the specific gravity.
Density = Mass / Specific Gravity
For Solution A:
Density (A) = 100 grams / 1.8 kg = 55.56 g/L (grams per liter) or 555.6 kg/m³ (kilograms per cubic meter)
Step 3: Calculate the dilution ratio:
Since the specific gravity of the diluted solution (Solution B) is given as 1.2, and assuming the volume of Solution B is also 1 liter, the mass of Solution B can be calculated using the formula:
Mass = Volume x Density
For Solution B:
Mass (B) = 1 liter x 1.2 kg/L = 1.2 kg
Step 4: Calculating the mass of acid in Solution B:
To find the mass of acid in Solution B, we need to know the mass of the water in Solution B. Since the volume of Solution B is 1 liter, and the mass is 1.2 kg, the difference in mass between Solution B and water will give us the mass of the acid.
Mass of water in Solution B = Mass (B) - Mass of acid in Solution B
Mass of water in Solution B = 1.2 kg - 62 grams = 1.2 kg - 0.062 kg = 1.138 kg
Step 5: Calculate the percent by weight of acid in Solution B:
Using the mass of acid (62 grams) and the mass of Solution B (1.2 kg), we can calculate the percent by weight of acid in Solution B using the formula:
Percent by weight = (Mass of acid / Mass of Solution B) x 100%
Percent by weight = (62 grams / 1,200 grams) x 100% = 5.17%
Therefore, the percent by weight of acid in the diluted solution (Solution B) is approximately 5.17%.