Test to distinguish between NaHCO3 and Na2CO3

There are many methods, some of them may be performed in home:
1. Solubility of both compounds are quite different,
2. NaHCO₃ does not form hydrates,
3. Na2CO₃ change color of phenolphtalein, hydrogen carbonate usually change color to pale pink since small content od carbonate,
4. Titration.
And many others.

Sodium hydrogen carbonate start decomposing at ~60 C - solid, or ~40 C - in water solution. This is an equilibrium reaction and carbon dioxide is removed to atmosphere. After many hours of warming at these temperatures you can obtain almost pure sodium carbonate. But air contains some amount of carbon dioxide, and in this way you will never get absolutely pure  sodium carbonate, even at higher temperatures. The only simple and quantitative way to determine contents of you sample is titration.
May first three suggestions can be used qualitatively. Just one of these  is sufficient, and it depends on you home lab possibility, you invention, and your knowledge.
In the same way past great chemists worked. But the did not wait for precise procedure from others that solve their problems.

Thank you for your replies.

I did notice some colour change, but didn't consider that t be enough of a uniform indicator of the change.

Not being a chemist I'm not sure how to try your fourth suggestion "Titration" and would like to know, with home appliances, what would be the simplest method to uniformly confirm the change please?

Thanks again, in advance.

Quote from:

There are many methods, some of them may be performed in home:
1. Solubility of both compounds are quite different,
2. NaHCO₃ does not form hydrates,
3. Na2CO₃ change color of phenolphtalein, hydrogen carbonate usually change color to pale pink since small content od carbonate,
4. Titration.
And many others.

Agreed.

I think elemental analysis also works very well

I ain't no chemist mate. I'm just trying to make laundry powder.

From GOOGLE

Arm & Hammer Super Washing Soda Detergent Booster & Household Cleaner, 55 oz $6.65
6.65 / 55 = 0.120909

ARM & HAMMER Pure Baking Soda 16 oz $0.75
0.75 / 16 = 0.046875

By the way
 can we assume you have read
https://en.wikipedia.org/wiki/Sodium_bicarbonate
and
https://en.wikipedia.org/wiki/Sodium_carbonate

From WIKI
Quote

Thermal decomposition

Above 50 °C, sodium bicarbonate gradually decomposes into sodium carbonate, water and carbon dioxide. The conversion is fast at 200 °C:[12]

    2 NaHCO₃  Na₂CO₃ + H₂O + CO₂

Most bicarbonates undergo this dehydration reaction. Further heating converts the carbonate into the oxide (at over 850 °C):[12]

    Na₂CO₃  Na₂O + CO₂

Titration seems to be the easiest approach here, seeing how much of your solid is required to neutralize given amount of a strong acid.

See www.titrations.info for a general description of the titration itself, you need a variant of what is described in the acid-base section.