ethanol mixture\ngallons ethanol concentration total\nx% ethanol 20 x\n12% ethanol 60 0.12 7.2\nmixture 80…

ethanol mixture\ngallons ethanol concentration total\nx% ethanol 20 x\n12% ethanol 60 0.12 7.2\nmixture 80 0.10\nwhat is the value of x, the concentration of the unknown ethanol solution?\n0.02\n0.04\n0.05\n0.08

ethanol mixture\ngallons ethanol concentration total\nx% ethanol 20 x\n12% ethanol 60 0.12 7.2\nmixture 80 0.10\nwhat is the value of x, the concentration of the unknown ethanol solution?\n0.02\n0.04\n0.05\n0.08

Answer

Explanation:

Step1: Set up equation based on ethanol - amount conservation

The amount of ethanol in the first solution plus the amount of ethanol in the second solution equals the amount of ethanol in the mixture. The amount of ethanol in a solution is the product of the volume of the solution and its concentration. So, (20x+60\times0.12 = 80\times0.10).

Step2: Simplify the right - hand side of the equation

First, calculate (60\times0.12 = 7.2) and (80\times0.10 = 8). The equation becomes (20x+7.2 = 8).

Step3: Isolate the term with (x)

Subtract 7.2 from both sides of the equation: (20x=8 - 7.2), so (20x = 0.8).

Step4: Solve for (x)

Divide both sides of the equation by 20: (x=\frac{0.8}{20}=0.04).

Answer:

0.04