A water sample contains 5 mg SO42- per liter. What is the concentration in micromoles/L?

Answer 1

Hey Sydney,

Great question! This question is testing the fundamentals of unit conversions using the chemistry concept of moles. When doing conversions, I always find it helpful to write down the pathway/map of all the steps needed to perform the conversion. Most often you will be given a multi-step conversion question, meaning that you cannot go straight from the given unit to the ending unit with only one conversion factor. This is the case in your question. Therefore, let's start with our pathway and break down the question from there with the following steps:

1. The question starts with milligrams/Liter (mg/L) and asks for the answer in micromoles/Liter (umoles/L). For the sake of simplicity, since the Liters stay the same and only the top unit changes, we can focus on converting mg --> umol and don't need to worry about the Liters in our calculation. The general steps to get from mg to umol is this:
2. milligrams (mg) --> grams (g) --> moles (mol) --> micromoles (umol)
3. Now that we know the pathway, we just need to find the corresponding conversion factors specifically from the question.
4. Start with 5mg of SO₄^2-
5. There are 1,000mg in 1g
6. Molar mass of SO₄^2- (from the periodic table):
7. Sulfur = 32.06 g/mol x 1 = 32.06g/mol
8. Oxygen = 16 g/mol x 4 = 64g/mol
9. total = 32.06 + 64 = 96.06g/mol
10. There are 1,000,000umol in 1mol
11. Next, plug-in the conversion factors in the correct place and multiply/divide to get the final answer.
12. (5mg SO₄^2-/1) x (1g/1000mg) x (1mol SO₄^2-/96.06g SO₄^2-) x (1,000,000umol/1mol) = 52.05micromol SO₄^2-/L
13. Specifically, the question only gives you 1 significant digit in the original amount (5mg/L), therefore your answer is limited to also only 1 significant digit. So, your answer should be rounded to 50umol SO₄^2-/L.
14. Helpful hint: When plugging in conversion factors, it is important to make sure that they are in the correct place (i.e. numerator vs. denominator). To ensure this, make sure that the units cancel out. For example, in the problem above, mg starts in the numerator and is multiplied by a factor with mg in the denominator. Therefore, the mg will cancel out when multiplied and leave you with the new unit of grams. Next, you multiply to cancel out the grams and are left with moles.

Answer 2

This is a question of conversion between mass (mg) to amount (µmol).

The molar mass of SO₄^2- is calculated as

1 x 32.07 g/mol + 4 x 16.00 g/mol = 96.07 g/mol = 0.09607 mg/µmol (1g = 1000 mg; 1 mol = 1000000 µmol)

The amount (mmol) of SO₄^2- is calculated as

5 mg SO₄^2- x 1 µmol/0.09607 mg = 50 µmol

Therefore the concentration of SO₄^2- is 50 µmol/L.

Hope this helps.