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To convert grams per decimeter cubed (g dm^-3) to moles per decimeter cubed (mol dm^-3), you need to divide the mass in grams by the molar mass of the substance in grams per mole to find the number of moles. Then, you can convert the mass concentration into molar concentration by dividing the number of moles by the volume in decimeters cubed.
The convention is that when you just write "mol" or "mole" you are referring to gmol so the conversion is to just replace gmol with mol.
In chemical engineering where the quantities of material being processed may be on the scale of tons, other "mole" related units are defined such as kg-mol and ton-mol.
As examples:
Since the molecular weight of a diatomic molecule of oxygen is 31.9988,
31.9988 g of oxygen gas = 1 g-mol
31.9988 lb of oxygen gas = 1 lb-mole
31.9988 kg of oxygen gas = 1 kg-mole
31.9988 tons of oxygen gas = 1 ton-mole.
These units make stoiciometric calculations convenient for designing industrial processes.
First, you need to know the Molar Mass of the substance, then you divide the g dm-3 (i.e. concentration) by the Molar Mass.
Explaination:
The concentration is in the units of g / dm3
The Molar Mass of the substance is in the units of g / mol
When you divide the concentration by the Molar Mass you get:
(g / dm3) / (g / mol )
The "g"s cancels out and we are left with mol dm-3
i.e. g dm-3 * g-1 mol = mol dm-3
6.17 x 10-3 mol dm-3
To convert mm^3 to dm^3, you need to divide by 1,000,000 (since 1 mm^3 is equal to 1/1,000,000 dm^3). Therefore, to convert 16.74 mm^3 to dm^3, you would divide by 1,000,000 to get 0.00001674 dm^3.
10000 cm^3 is equivalent to 10 dm^3. To convert from cm^3 to dm^3, you need to divide by 1000 since 1 dm^3 is equal to 1000 cm^3.
To calculate the pH of a 0.001 mol/dm³ HCl solution, you use the formula pH = -log[H+]. For HCl, since it is a strong acid, it dissociates completely into H⁺ ions. Thus, the concentration of H⁺ ions in a 0.001 mol/dm³ HCl solution is also 0.001 mol/dm³. Taking the negative logarithm of 0.001 gives a pH of 3.
To convert from decimeters (dm) to kilometers (km), divide by 10,000. Therefore, 24 dm is equal to 0.0024 km.