How many grams of water must be added to 2 grams of a 65% iodine solution in order to produce a 42% iodine solution? Round your answer to the nearest tenth
After this, please type your school subject in the appropriate box.
You want to add M grams of water to 2 grams of .65 solution?
amount of iodine in final= amount of iodine in initial
.42(M+2)=.65(2)
solve for M.
To solve this problem, we need to calculate how much water should be added to the initial 2 grams of the iodine solution to achieve a 42% iodine solution.
Let's start by defining the variables:
- Let w represent the mass of water we need to add (in grams).
Now, let's set up the equation using the following approach:
1. Determine the amount of iodine in the original 2 grams of the 65% iodine solution.
2. Determine the amount of iodine in the final solution, assuming 42% iodine concentration.
3. Equate the amounts of iodine from steps 1 and 2 to find w.
Step 1: Calculate the mass of iodine in the original solution:
The original iodine solution is 65% iodine, so we have:
Mass of iodine in the original solution = 65/100 * 2 grams
Step 2: Calculate the mass of iodine in the final 42% solution:
The final solution will have a total mass of (2 + w) grams, and since it's a 42% iodine solution, we have:
Mass of iodine in the final solution = 42/100 * (2 + w) grams
Step 3: Equate the two masses of iodine:
65/100 * 2 grams = 42/100 * (2 + w) grams
To solve for w, let's simplify the equation:
(65/100) * 2 = (42/100) * (2 + w)
Now let's solve for w by isolating it on one side of the equation:
(65/100) * 2 = (42/100) * (2 + w)
0.65 * 2 = 0.42 * (2 + w)
1.3 = 0.84 + 0.42w
1.3 - 0.84 = 0.42w
0.46 = 0.42w
w = 0.46 / 0.42
Now we can calculate w:
w ≈ 1.1 grams (rounded to the nearest tenth)
Therefore, you would need to add approximately 1.1 grams of water to the 2 grams of the 65% iodine solution to produce a 42% iodine solution.