Quick question about Concentration Cells

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If there is a concentration cell with the same electrode (made of Zinc) and 2 half cells with different Molarities...(Cell 1 = 0.1M) & (Cell 2 = 0.3M).

My book says that the Cell 1 will be the anode and Cell 2 will be the cathode. This means that electrons will flow from Cell 1 to Cell 2.

Should it be the other way around? Shouldn't it flow from Cell 2 to Cell 1 because Cell 2 is of high molarity/concentration?

I know I am wrong, but why.
 
If there is a concentration cell with the same electrode (made of Zinc) and 2 half cells with different Molarities...(Cell 1 = 0.1M) & (Cell 2 = 0.3M).

My book says that the Cell 1 will be the anode and Cell 2 will be the cathode. This means that electrons will flow from Cell 1 to Cell 2.

Should it be the other way around? Shouldn't it flow from Cell 2 to Cell 1 because Cell 2 is of high molarity/concentration?

I know I am wrong, but why.

Cathode is a site of reduction. Current flow OUT of cathode, electrons flow in.

Anode is a site of oxidation. Current flows into anode, electrons flow out.

Zn2+ is a positively charged species. There is a high concentration of zinc in cell 2. Since there is more positive charge in cell 2, (+++++++++++++) you would expect that to be reduced, right? (+++++ ------)

This would make cell 2 the cathode (site of reduction), which would mean current flows OUT of cell 2 to cell 1 but electrons flow IN.

Cell 1 has less positive charge (+++--------------) and will need to be oxidized to reach equilbrium (+++++ ------). Making it the anode.
 
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If there is a concentration cell with the same electrode (made of Zinc) and 2 half cells with different Molarities...(Cell 1 = 0.1M) & (Cell 2 = 0.3M).

My book says that the Cell 1 will be the anode and Cell 2 will be the cathode. This means that electrons will flow from Cell 1 to Cell 2.

Should it be the other way around? Shouldn't it flow from Cell 2 to Cell 1 because Cell 2 is of high molarity/concentration?

I know I am wrong, but why.

The cell will try to equilibrate. If cell 1 is the anode, the electrode is oxidized, and releases Zn2+ ions into solution. If cell 2 is the cathode, the ions in solution are reduced, depositing on the electrode and reducing the concentration of Zn2+ ions.
 
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