How much water must be added to 24.0 grams of salt ot make a solution that is 12.0% by mass?
176
.12(24+W)=24
That reads 12 percent of total mass is 24 g
solve for W.
To solve this problem, you need to use the concept of mass percent. Mass percent is defined as the mass of the solute divided by the mass of the solution, multiplied by 100%. Using this information, we can set up a proportion to find the mass of the solution.
Let x be the mass of water added to the 24.0 grams of salt.
The total mass of the solution is the sum of the mass of the salt and the mass of the water, which is 24.0 grams + x grams.
The mass percent of the salt is 12.0%, which can be written as 12.0/100.
Now we can set up the proportion:
12.0/100 = 24.0/(24.0 + x)
To solve for x, cross-multiply:
12.0 * (24.0 + x) = 100 * 24.0
Expand and simplify the equation:
288.0 + 12.0x = 2400.0
Subtract 288.0 from both sides:
12.0x = 2400.0 - 288.0
Combine like terms:
12.0x = 2112.0
Divide both sides by 12.0 to solve for x:
x = 2112.0 / 12.0
The mass of water, x, that must be added to 24.0 grams of salt to make a solution that is 12.0% by mass is approximately 176 grams.