What is the maximum amount of silver in grams that can be plated out of 3.8L of an AgNO3 solution containing 3.3% Ag by mass?
(Assume that the density of the solution is 1.02g/mL .)
3.3% by mass means 3.3g Ag/100 g solution. The density of the solution is 1.02 g/mL so 3.8L (3,800 mL) has a mass of 1.02 g/mL x 3800 mL = 3876 g.
(x g Ag/3876)*100 = 3.3
x g Ag = approx 128 g. That's an estimate.
To find the maximum amount of silver that can be plated out, we need to calculate the mass of silver from the given information.
Step 1: Calculate the mass of the AgNO3 solution.
Given:
Volume of AgNO3 solution = 3.8L
Density of solution = 1.02g/mL
We can calculate the mass of the solution using the formula:
Mass = Volume × Density
Mass of AgNO3 solution = 3.8L × 1.02g/mL
Step 2: Calculate the mass of AgNO3 in the solution.
Given:
Percentage of Ag in AgNO3 solution = 3.3% by mass
Mass of the AgNO3 solution = calculated in Step 1
We can calculate the mass of AgNO3 in the solution using the formula:
Mass = Percentage × Mass of the solution
Mass of AgNO3 = 3.3/100 × Mass of the AgNO3 solution
Step 3: Calculate the mass of silver (Ag) in AgNO3.
Given:
One mole of AgNO3 contains one mole of Ag (molar mass of Ag = 107.87 g/mol)
We can calculate the mass of silver in AgNO3 using the formula:
Mass of Ag = Mass of AgNO3 × (1 mole of AgNO3 / molar mass of AgNO3) × (molar mass of Ag / 1 mole of AgNO3)
Now, let's calculate the maximum amount of silver that can be plated out:
Mass of AgNO3 solution = 3.8L × 1.02g/mL = 3.876g
Mass of AgNO3 = 3.3/100 × 3.876g = 0.1277988g
Mass of Ag = 0.1277988g × (1 mole / 169.87g) × (107.87g / 1 mole) = 0.080470613g
Therefore, the maximum amount of silver that can be plated out from 3.8L of an AgNO3 solution containing 3.3% Ag by mass is approximately 0.0805 grams.
To find the maximum amount of silver that can be plated out of the given solution, we can follow these steps:
Step 1: Calculate the mass of the solution.
To find the mass of the solution, we need to multiply its volume by its density.
Mass of solution = volume of solution × density of solution
Mass of solution = 3.8 L × 1.02 g/mL
Step 2: Calculate the mass of silver in the solution.
To calculate the mass of silver in the solution, we need to use the mass percent of silver.
Mass of silver = mass of solution × mass percent of silver
Mass of silver = mass of solution × (3.3 / 100)
Step 3: Convert the mass of silver to grams.
The mass of silver is currently in percentage form, so we need to convert it to grams.
Mass of silver in grams = Mass of silver × 1000 g/kg
Given that 1 kg = 1000 g, we can rearrange the equation as:
Mass of silver in grams = (mass of silver × 1000) / 1 kg
Now, let's substitute the values and calculate the maximum amount of silver in grams that can be plated.
Mass of solution = 3.8 L × 1.02 g/mL = 3.876 g
Mass of silver = 3.876 g × (3.3 / 100) = 0.127708 g
Mass of silver in grams = (0.127708 g × 1000) / 1 kg = 127.708 g
Therefore, the maximum amount of silver that can be plated out of 3.8L of the AgNO3 solution is approximately 127.708 grams.