I think I have these figured out correctly but I'm not sure if I might have converted in the wrong direction;

The rate of the enzyme activity of a certain reaction is
a. 0.0027 μmol/min/mL.
Express it as __ μmol/min/L
My answer: 2.7 μmol/min/L

b. 15,000 μmol/min/L.
Express it as __ μmol/min/mL
My answer: 15 μmol/min/mL

c. 0.0018 μmol/min/mL.
Express it as __ IU
My answer: 1.8 IU

d. producing 2 mg phenol/60min/100 mL (m.w. phenol = 94).
Express this value in IU.
My math:
2 mg phenol/60min/100 mL
2/94 0.0213 mmol/60min/100mL
0.0213 x 1000 21.3 umol/60min/100mL
21.3/60 0.355 umol/min/100mL
3.55 umol/min/L or 3.55 IU

all correct.

To convert between different units, you need to use conversion factors. Here's how you can solve each of the conversions:

a. To express 0.0027 μmol/min/mL as μmol/min/L:
You can start by noticing that 1 mL is equal to 0.001 L (since there are 1000 mL in 1 L). So, you can multiply the given value by the conversion factor:
0.0027 μmol/min/mL * (1 mL / 0.001 L) = 2.7 μmol/min/L

b. To express 15,000 μmol/min/L as μmol/min/mL:
Similarly, you can divide the given value by the conversion factor:
15,000 μmol/min/L * (0.001 L / 1 mL) = 15 μmol/min/mL

c. To express 0.0018 μmol/min/mL as IU:
To convert between μmol/min/mL and IU, you need to know the specific conversion factor for the enzyme you are working with. Without this information, it is not possible to provide an accurate conversion.

d. To express producing 2 mg phenol/60 min/100 mL as IU:
First, convert the mass of phenol to micromoles (μmol):
2 mg phenol * (1 mmol / 1000 mg) * (1 μmol / 1 mmol) = 0.002 μmol phenol

Next, convert the time to minutes per liter:
60 min/100 mL * (1000 mL / 1 L) = 60 min/L

Finally, divide the micromoles by the time to get the enzyme activity in micromoles per minute per liter (μmol/min/L):
0.002 μmol phenol / 60 min/L = 0.000033 μmol/min/L

Since IU is a unit specific to each enzyme, you need to refer to the specific activity conversion for the enzyme you are working with to convert the activity to IU.