How can the mass of the oxygen that reacted with magnesium be calculated in the following scenario? The mass of the crucible to start with was 9.295g, and the mass of Mg used was 0.426g. After heating magnesium in the crucible, the mass of the crucible with the magnesium is found to be 9.773g.

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The total mass you started with was 9.295 g for the crucible plus 0.426 g of magnesium for a total of 9.721 g.  After heating your total mass was 9.773 g.  9.773 g - 9.721g = .052 g of oxygen.

However, since you started with 0.426 g of magnesium (.0175...

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The total mass you started with was 9.295 g for the crucible plus 0.426 g of magnesium for a total of 9.721 g.  After heating your total mass was 9.773 g.  9.773 g - 9.721g = .052 g of oxygen.

However, since you started with 0.426 g of magnesium (.0175 moles), this should combine with 0.2804 g of oxygen (.0175 moles x 16 g/mole for oxygen).  Since you only found 0.052 g, it would seem that either some material was lost during the reaction, or the weighing is incorrect, or the magnesium only partially reacted when heated.

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The mass of the empty crucible you started with was 9.295 g. And the mass of the magnesium you used was 0.426 g.

After heating the magnesium in the crucible you weighed it again and found its mass to be 9.733g

The final mass measured included the mass of the crucible, the mass of the magnesium you used and the mass of the oxygen that reacted with the magnesium. This was equal to 9.733g.

The sum of the mass of the crucible and the magnesium is 9.295 + 0.426 = 9.721 g

But the final mass you got was 9.733, so the extra mass was due to the oxygen that reacted with the magnesium.

This is equal to 9.733 - 9.721 = 0.012 g.

The mass of the oxygen that reacted with magnesium was 0.012g.

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