The answer is 81 mL.
To calculate this, we need to understand that a 17.1 v/v% solution means that there are 17.1 mL of CH3OH in every 100 mL of solution.
Therefore, we can set up the following equation:
17.1 mL CH3OH / 100 mL solution = x mL CH3OH / (x mL CH3OH + 320 mL H2O)
Solving for x, we get:
x = (17.1/100) * (x + 320)
0.171x + 54.72 = x
0.829x = 54.72
x = 66.05 mL
However, we need to subtract the volume of water, so:
x - 320 = 66.05 - 320 = -253.95 mL
Since we can't have a negative volume, we know that there must have been an error in our calculations. This is because we can't have a solution with less than 0 mL of CH3OH.
Going back to the equation, we can see that the problem comes from assuming that the volume of the solution is 100 mL. Instead, we need to assume that there are 100 mL of the solution + 320 mL of water, for a total of 420 mL. The equation then becomes:
17.1 mL CH3OH / 100 mL solution = x mL CH3OH / 420 mL
Solving for x, we get:
x = (17.1/100) * 420
x = 71.82 mL
Subtracting the volume of water, we get:
71.82 mL - 320 mL = -248.18 mL
Again, this is negative. The error this time is due to assuming that the volume of the solution is 420 mL, when it's actually the sum of CH3OH and water volumes.
To correct this, we need to recognize that the volume of the solution is the sum of the CH3OH and water volumes. Using the equation above, we can solve for the volume of the solution:
17.1 mL CH3OH / 100 mL solution = x mL CH3OH / V mL solution
Solving for V, we get:
V = (x / 0.171) * (100 / 1)
V = 39.77 mL CH3OH
The volume of water is given as 320 mL. Therefore, the volume of the solution is:
V + 320 = 39.77 mL + 320 mL = 359.77 mL
Finally, we can use the volume percentage to calculate the amount of CH3OH in mL:
17.1 mL CH3OH / 100 mL solution = x mL CH3OH / 359.77 mL solution
Solving for x, we get:
x = (17.1/100) * 359.77
x = 61.54 mL
Therefore, there are 61.54 mL of CH3OH in the solution.