An aqueous solution of copper (I) chloride is 15.7% by mass copper (I) chloride. Copper (I) is 35.8% by mass chlorine. If the solution has a density of 1.045 g/cm³, how many gallons of solution contain 2.3 kg of copper?
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To find the number of gallons of solution that contain 2.3 kg of copper, we need to follow a step-by-step approach:
Step 1: Convert the given mass of copper (2.3 kg) to the mass of copper (I) chloride.
Copper (I) chloride is 15.7% by mass in the solution. Therefore, we can calculate the mass of copper (I) chloride using the given mass of copper as follows:
Mass of copper (I) chloride = (Mass of copper) / (Percentage of copper (I) chloride)
Mass of copper (I) chloride = 2.3 kg / 0.157 = 14.65 kg
Step 2: Determine the mass of chlorine in the copper (I) chloride.
Copper (I) chloride consists of 35.8% chlorine by mass. Therefore, we can calculate the mass of chlorine using the mass of copper (I) chloride as follows:
Mass of chlorine = (Percentage of chlorine) x (Mass of copper (I) chloride)
Mass of chlorine = 0.358 x 14.65 kg = 5.2467 kg
Step 3: Calculate the total mass of the aqueous solution.
The total mass of the solution can be found by adding the mass of copper (I) chloride and the mass of chlorine:
Total mass of the solution = Mass of copper (I) chloride + Mass of chlorine
Total mass of the solution = 14.65 kg + 5.2467 kg = 19.8967 kg
Step 4: Convert the mass of solution to the volume of solution in gallons.
Density = Mass / Volume
Volume = Mass / Density
Volume = 19.8967 kg / 1.045 g/cm³ = 19029.9 cm³
1 gallon = 3785.41 cm³ (approximately)
Volume of solution in gallons = 19029.9 cm³ / 3785.41 cm³ = 5.032 gallons (approximately)
Therefore, 2.3 kg of copper would be contained in approximately 5.032 gallons of the aqueous solution.