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Which clue suggest that a cake is not a mixture?

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Baking a cake is a chemical reaction, meaning that it cannot be described as a mixture.

Here's some clues:

If it were a mixture, the volume would remain the same before and after. A cake rises as it bakes, hinting that a gas is released in the reaction process which causes this.

Your products have been used up. The egg is gone, and it's not coming back. You began with multiple reactants (Sugar, flour, eggs, vanilla, water etc.) and now you have a single product: cake.

You cannot separate a cake to retrieve initial ingredients.
I could mix salt and water, but I could separate them by evaporating the water I could mix silly putty and Playdoh, and while it would be tough, I could pick them apart again. But I cannot remove the egg from the cake.

I'm a bored university student studying Chemical Engineering.
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In Cakes

Is cake a mixture?

Yes. Regardless of the type of cake you're fabricating -- edible,cement, mud or other -- each is a mixture of ingredients balancedto produce the type of cake desired.