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?

Trying to help my son study.

Thank you.

masscopper=.157*(1-.358)*masscopperI chloride.

solve for mass of copper(I) chloride from that.

Now, consider density.

density=mass/volume=(masswater+massCopperchloride)/volume

density=masswater/volume + masscopperchloride/volume

density=densitywater+(masscopperchloride/volume)
from that you know everything except volume. Solve for volume, in cm^3

now, convert cm^3 to gallons. Watch units carefully here, giving the copper content is kg, density in g... Work it in g/cm^3 until the last conversion to gallons.

To solve this problem, we need to follow a few steps:

Step 1: Calculate the mass of copper (I) chloride in the solution.
We know that the solution is 15.7% by mass copper (I) chloride, and we have 2.3 kg of copper. So we can use the percentage to calculate the mass of copper (I) chloride in the solution.
Mass of copper (I) chloride = (15.7/100) * 2.3 kg

Step 2: Calculate the mass of chlorine in the copper (I) chloride.
We know that copper (I) is 35.8% by mass chlorine. To find the mass of chlorine, we can multiply the mass of copper (I) chloride by the percentage of chlorine.
Mass of chlorine = (35.8/100) * Mass of copper (I) chloride

Step 3: Calculate the volume of the solution.
We are given the density of the solution, which is 1.045 g/cm³. To convert the mass of the solution into volume, we can use the formula:
Volume = Mass / Density

Step 4: Convert the volume of the solution to gallons.
Since we're asked for the volume in gallons, we need to convert the volume from cm³ to gallons. There are 3785.41 cm³ in one gallon. So we can divide the volume in cm³ by this value to get the volume in gallons.

Let's plug in the values and calculate step by step.

Step 1: Mass of copper (I) chloride = (15.7/100) * 2.3 kg
= 0.3611 kg

Step 2: Mass of chlorine = (35.8/100) * Mass of copper (I) chloride
= (35.8/100) * 0.3611 kg
= 0.1293 kg

Step 3: Volume = Mass / Density
= (2.3 kg + 0.3611 kg + 0.1293 kg) / 1.045 g/cm³
= 2.7904 kg / 1.045 g/cm³
≈ 2.6684 cm³

Step 4: Volume in gallons = 2.6684 cm³ / 3785.41 cm³/gallon
≈ 0.0007 gallons

Therefore, approximately 0.0007 gallons of solution contain 2.3 kg of copper.