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?
To determine the number of gallons of solution that contain 2.3 kg of copper, we need to follow these steps:
Step 1: Determine the mass of copper in the 15.7% solution.
First, we'll calculate the mass of copper (I) chloride in the solution. Since the solution is 15.7% by mass copper (I) chloride and 35.8% of copper (I) chloride is copper, we can determine the mass of copper in the solution as follows:
Mass of copper = 15.7% * 2.3 kg = 0.157 * 2.3 kg
Step 2: Determine the mass of copper (I) chloride in the solution.
Since we know that 35.8% of copper (I) chloride is chlorine, we can calculate the mass of copper (I) chloride in the solution as follows:
Mass of copper (I) chloride = Mass of copper / 35.8%
Step 3: Determine the volume of the solution.
To find the volume of the solution, we'll use the density of the solution. Density is defined as mass per unit volume, so we can rearrange the equation to solve for volume:
Volume = Mass / Density
Using the given density of 1.045 g/cm³ and converting the mass from kg to g (1 kg = 1000 g), we can calculate the volume of the solution.
Step 4: Convert the volume from cm³ to gallons.
Finally, we need to convert the volume of the solution from cm³ to gallons. There are approximately 3785.41 cm³ in a gallon, so we need to divide the volume in cm³ by 3785.41 to get the volume in gallons.
By following these steps, we can determine the number of gallons of solution that contain 2.3 kg of copper.