Sugar cubes are added to a solution of water and lemon juice to make lemonade. The solubility of sugar is 200 g/100 g #H_2O# at the temperature of the solution. What can be done to increase the rate of dissolution without affecting the solubility?
Of course, heating is out, because a hot solvent will hold more solute than a cold one. What you could try is a sonicator, i.e. putting your flask in an ultrasonic bath. (These are very good for cleaning too!)
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To increase the rate of dissolution without affecting the solubility, you can:
- Increase the surface area of the sugar cubes by crushing them into smaller pieces or using powdered sugar.
- Stir or agitate the solution to enhance the mixing of sugar molecules with water molecules.
- Increase the temperature of the solution, as higher temperatures generally increase the rate of dissolution for solid solutes like sugar, while keeping the solubility constant.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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