Suppose you designed an experiment in which you burned a known quantity of magnesium in air. You used the product to determine how many moles of oxygen would react with the known number of moles of magnesium. Why would burning magnesium in air cause a source of error for this calculation?

2Mg + O2 ==> 2MgO

BUT air also contains N2 and at the elevated temperature of burning Mg it also combines with N2 as
3Mg + N2 ==> Mg3N2.
So when you weigh the MgO you actually are weighing mostly MgO but with some Mg3N2. Since O2 and N2 don't weigh the same and since O and N don't combine in the same ratio with Mg you have an error.

I actually have a question

I have a question how many miles of oxygen would it take to react with 1.0 moles of magnesium

Burning magnesium in air can introduce a source of error when calculating the number of moles of oxygen that react with the known number of moles of magnesium due to contaminants present in the air.

To explain how burning magnesium in air as a source of error, we first need to understand the reaction that occurs during the burning of magnesium. When magnesium reacts with oxygen, it forms magnesium oxide according to the following chemical equation:

2Mg + O2 → 2MgO

From this equation, we can determine that for every two moles of magnesium that react, one mole of oxygen is consumed.

However, air is not pure oxygen but rather a combination of different gases. It contains approximately 78% nitrogen, 21% oxygen, and trace amounts of other gases such as argon, carbon dioxide, and water vapor. When magnesium burns in air, it reacts not only with the oxygen present but also with nitrogen and other impurities.

The presence of nitrogen and impurities affects the accuracy of determining the number of moles of oxygen that reacted with magnesium because these substances can interfere with the reaction or contribute to the overall mass of the product. As a result, the actual measurement of the products will include the mass of the impurities, leading to an overestimation of the moles of oxygen consumed.

To minimize this source of error, it is essential to use pure oxygen gas instead of air while conducting the experiment. By using pure oxygen, you can eliminate the potential interference from other gases and accurately determine the number of moles of oxygen that react with the known number of moles of magnesium.