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A good balance is an important piece of equipment for chemistry. For home chemistry, the price of the balance is unfortunately limiting ..

How should one go about picking a balance (for home chemistry; general guidelines are welcome too)? Specifically, I'm thinking whether to buy a model with 0.01g precision (up to 200g), or a one with 0.001g precision (up to 20g) (the latter is a so called "diamond balance" but probably does the job). Which one would serve me better?

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Home chemistry can be difficult sometimes due to the expense of the essential working materials and instruments required. As a mathematician all I need is a sharp pen (which is sometimes still quite difficult to obtain!) and blank paper. I can give you the following general (personal) advice regarding purchasing chemistry lab equipment:

  • Determine your budget and the needs for the experiments you want to perform. Do you really need a scale that has to weight with an accuracy of 0.001g or is 0.01g sufficient (or even 0.1g)? Ask yourself what you REALLY need for an experiment BEFORE searching for instruments. If you do it in the converse order you often buy something way more fancier (and pricier) than what you actually needed in the first place.
  • Look at specialized chemistry equipment supply websites to orientate on what is available and in what price range certain products are (think of scales, chemicals, glassware, etc.)
  • A lot of stuff can be bought incredibly cheap on websites where you not expect (at least I did not) people to sell lab supplies/instruments. Think of ebay.com and amazon.com as examples. They sometimes list items at a fifth of the usual price that would have to be paid at a specialized store.
  • Take a look at local non-specialized stores like the construction market (you know, the place where they sell all kinds of construction material). They sometimes hide hidden (cheap) gems! As an example I was able to obtain a vacuum source (membrane pump) for < 100\$, which would have cost me easily > 400\$ at a chemical supply website.

About your particular question: I really recommend a 0.01g precision 200g (or 600g) scale. It brings the benefit of having relatively accurate weighting for even small samples, while still being able to weight bulk mass. Furthermore, they are most common in the lab/home environment and hence relatively cheap in comparison with professional analytical scales. If you plan to do a lot of microscale experiments (yielding a product < 200 mg) the analytical scale (precision of 0.001g) may suit your needs better.

I wish you much success, think and buy wisely!

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Let me first say that @Jori's answer is excellent. I would only add two things.

1) A range of equipment is usually desirable if it is also affordable. So measures across all 3 accuracies (0.1, 0.01, and 0.001) is what you want ideally, particularly given that precision tends to decrease with absolute mass.

2) There is a trend towards green chemistry, which emphasizes minimal reactants, products, and waste whenever possible. Thus, there will be a trend towards microchemistry where small amounts of reactants are the norm, and this will necessitate higher precision balances (i.e 0.001g precision).

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