Question

how much water should be added to 89 liters of a 45% saccharine solution to get a 40% saccharine solution?

Answer 1

11.125 liters

Explanation:

`\[ C_1V_1 + C_2V_2 = C_fV_f \]`

Where:

-
`\( C_1 \) and \( V_1 \)` are the concentration and volume of the first solution,

-
`\( C_2 \) and \( V_2 \)` are the concentration and volume of the second solution,

-
`\( C_f \)` is the final concentration,

-
`\( V_f \)` is the final volume.

In this case:

-
`\( C_1 = 45\% \)` (0.45 in decimal form),

-
`\( V_1 = 89 \)` liters,

-
`\( C_2 = 0\% \)` (since water has no saccharine),

-
`\( V_2 \)` is what we're trying to find,

-
`\( C_f = 40\% \) (0.40 in decimal form)`,

-
`\( V_f = 89 + V_2 \)`.

Now plug these values into the equation:

`\[ (0.45)(89) + (0)(V_2) = (0.40)(89 + V_2) \]`

Simplify the equation:

`\[ 40.05 = 35.6 + 0.40V_2 \]`

Subtract 35.6 from both sides:

`\[ 4.45 = 0.40V_2 \]`

Now, solve for
`\(V_2\)`:

`\[ V_2 = (4.45)/(0.40) \]`

`\[ V_2 = 11.125 \]`

So, you would need to add 11.125 liters of water to 89 liters of a 45% saccharine solution to get a 40% saccharine solution.